Deleuze's Difference and Repetition PDF
Deleuze's Difference and Repetition PDF
Deleuze's Difference and Repetition PDF
Deleuze's Difference
mM . . . . . . . . .
epetition
An Edinburgh Philosophical Guide
Henry Som.ers-Hall
EDINBURGH
University Press
BM0637619
978
978
978
97B
97B
0
0
0
0
0
7486
74B6
HB6
74B6
HB6
4G78 4 (hardback)
4677 7 (paperhack)
69G7 7 (webready PDF)
69G8 4 (epub)
6969 1 (Amazon ebook)
Contents
VI
VII
Vlll
Introduction
1. A Guide to the Text
Introduction: Repetition and Difference
Chapter 1. Difference in Itself
Chapter 2. Repetition for Itself
Chapter 3. The Irnage ofThought
Chapter 4. Ideas and the Synthesis of Difference
Chapter 5. The Asymmetric Synthesis of the Sensible
The Two Prefaces
7
7
21
55
96
128
166
188
2.
191
191
194
199
Study Aids
Glossary
Further Reading
Tips for Writing about Deleuze
Bibliography
Index
200
206
To us, the principle of this series of books is clear and simple: what
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We have designed each volume in the series to correspond to the way
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This will enable you to make your own judgements on the texts, and on
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Douglas Burnham
Acknowledgetnents
Abbreviations
Abbreviations
IX
Introduction
Gilles Deleuze is one of the most influential post-war French philosophers. While his influence in the Anglo-American world began with
the translation of his collaborations with Flix Guattari, Diffrence and
RelJetition has a good daim to be his philosophical masterpiece. It's difficult to situate Dijference and RejJetition within the philosophical tradition.
Deleuze characterises his project as a 'transcendental empiricism', which
suggests affinities with eighteenth and nineteenth-century German
idealist thought. Nonetheless, Deleuze presents an account critical of
both the transcendental idealist characterisation of experience and its
account of knowledge. Similarly, we find strands of the early twentiethcentury phenomenological project both affirmed and critiqued throughout Diffrence and Repetition. We can also see an ambivalent relationship to
the structuralist tradition charted throughout the text, and a substantial
engagement with the philosophies of science and mathematics. In this
book, 1 have tried to present as many of these engagements as possible,
but the emphasis is on Deleuze's own characterisation of himself as a
'pure metaphysician'. That is, 1 take Deleuze to be giving us an account
of the nature of the world, broadly construed. What rnakes his project
appear almost unrecogl1isable when compared with traditional metaphysical approaches is that he is attempting to provide a metaphysics
of difference. As we shall see, his daim is that when we take identity as
prior to difference, exemplified in the belief in judgement as the basis for
philosophical enquiry, we are constrained to make a number of daims
about the nature of the world and the nature of knowledge. These
daims together form the traditional image of metaphysics. In Dijference
and Repetition, Deleuze renounces the priority of identity, which leads to
a very different kind of metaphysical inquiry.
Introduction
Introduction
new urgency to projects in literature and the arts that attempt to explore
the genesis of what in a different philosophical register has been caUed
the 'thingliness' of things. Furthermore, Diffrence and Repetition contains a
re-reading of the history of philosophy, developing an alternative tradition of thinkers of intensity, drawing in Lucretius, Duns Scotus, Spinoza,
Feuerbach and Nietzsche, among others. Alongside this tradition runs a
series of critiques of canonical thinkers from Plato to Heidegger. While
we will not be able to explore aU of these aspects of Deleuze's philosophy, we will touch on as many of these themes as possible.
10
As it stands, this criticism is quite obscure, but the first point is straightfmward enough. The moral must be conceived of as separate from the
natural. The natural realm is governed by causality, making free action
impossible, therefore the moral must be seen as separate from it. VVhy
must it then be seen according to the model of natural law? Deleuze
explains in Kant)s Oritical Plzilosop/~)! that this is an implication of the
difference between the two realms:
It is thus in two very different senses that the sensible and the suprasensible each
form a nature. Between the
1:\<\'0
Il
While we may posit the existence of the free moral realm, we lack any
way of conceiving of it, since it differs in kind from the world we find
around us. Thus, if we are to represent it to ourselves, we have to rely on
an analogy with the world we find around us. We therefore project the
model of empirical law onto the rational realm in order to understand
the concept of morallaw:
lVloreover, the idea of a pure world of understanding as a whole of all intelligences, to which we ourselves belong as rational beings (though on the other
side we are also mernbers of the world of sense), remains always a useful and
permitted idea for the sake of a rational belief~ even if all knowledge stops at
its boundary useful and permitted for producing in us a lively interest in the
morallaw by means of the noble ideal of a univers al kingdom of ends in themselves (rational beings) to which we can belong as members only when we carefully conduct ourselves in accordance with maxims of freedom as if they were
laws of nature. (Kant 1998: 66)
In this case, Deleuze argues that Kant's central concept of duty is modelled on habit (or rather, the habit of contracting habits). He argues
that our understanding of habit repeats the errors of natural laws.
Thus, while habit relies on repetition of the similar, it doesn't provide
a criterion by which we can select the relevant similarities ('everything
resembles everything else'). It is only once we have done this that habits
are eXplained, but only on the basis of ig110ring the differences between
events (equalisation).
12
13
cal repetition (the Bible tells usJob gets back twice what he lost, putting
the repetition outside of the sphere of quantitative identity). Rather than
being based on universality, as it is for Kant, for Kierkegaard (and for
Deleuze) it is based on singularity.
Summarising the philosophies of Kierkegaard, Nietzsche and Peguy,
Deleuze provides four criteria for a phi10sophy of repetition. The final
three of these parallel, but are incornmensurate with, the three modes of
naturallaw, morallaw and habit:
1. lVIake something new of repetition itself: connect it with a test, with a selection or selective test; make it the supreme object of the will and of freedom.
(DR 6/6)
In the case of Kierkegaard, this is once again clear. Repetition for hil11.
fans outside of comprehensibility, and hence outside of the field of any
possible scentific enquiry. In this sense, it at least offers the possibility of
eXplaining the kind of repetition that is presupposed by, but falls outside
of, the scientific endeavour.
3. Oppose repetition to morallaw, to the point where it becomes the suspension
of ethics, a thought beyond good and evil. (DR 6/7)
Once again, to the extent that Abraham's actions are incomprehensible from the point of view of ethics, his willingness to sacrifice Isaac
represents a suspension of ethical principles in tvour of God's commandment. God's 'temptation' therefore presents a direct alternative to
Kant's test, the categorical imperative.
4. Oppose repetition not only to the generalities ofhabit but also to the particu
larities ofmemory. (DR 7/8)
Concept cfAnxiety:
14
15
comprehension of the idea triangle includes extension, figure, three lines, three
angles, and the equality of these three angles to two rigid Angles, &c.
I cail the EXTENSION of an idea those subjects to which that idea applies,
which are also cailed the inferiors of a general term, which, in relation to them,
is cailed superior, as the idea of triangle in general extends to ail the different
sorts of triangles. (Arnauld 1850: 49)
16
17
different atoms. In this case, each atom is a repetition of the one before
precisely because they differ, but still faIl under the same concept. While
we might question whether atoms reaIly are identical with one another,
Deleuze daims that the case is mu ch more decisive in the case of words,
where we can repeat tlze same word. This is because each particular
instance of the word is conceptually indistinguishable from each other.
In this situation, we cannot specify each instance conceptuaIly, and so
the 'vulgarized Leibnizianism' of complete conceptual determination
breaks down. Leaving aside the second case, Freud's account of repetition, l want to focus on the final case, as the distinction between concepts and intuitions that it implies will be central to Deleuze's argument
throughout the rest of Diffrence and Repetition.
18
vVe will return to Leibniz in the next chapter, but for now we just need
to note that for him space is a distorted view of what are really con ceptuaI determinations of objects. Space in this sense is therefore secondary
to the 'order of things', and exists only in so far as it allows us to see the
relations which obtain between these entities. Space emerges because
the intellectual nature of the universe is only perceived confusedly by
the finite subject. On this view, therefore, conceptual determinations
precede space, which is in no way a real feature of the world, rendering Ne,vton's absolute theory of space false. A corollary of this is that
monads, the basic elements of reality for Leibniz, do not have any spatial
properties. This does not mean that spatial properties are entirely arbitrary, however. They are what Leibniz calls, 'well-founded phenomena'.
That is, they are analogous with what are in reality conceptual properties. The main point to take from Leibniz, in relation to Deleuze, is that
for Leibniz, aIl of the properties which we encounter in space can be
understood purely in conceptual terms. If that is the case, then because
each object will be conceptually distinct for every other, repetition is
impossible.
19
20
21
22
The first of these represents a space that has not been differenciated.
Without difference, we cannot have anything other than pure abstract
identity. Difference as a concept is what allows us to draw distinctions
within this identity ('this differs from that'). The second quotation brings
out the second role of difference: difference is a relation, and therefore
allows things to be related to one another. Clearly, therefore, we need
a concept of difference. Deleuze here outlines two ways in which we
might understand difference. The first is that diflrence is imposed on
the world, the second is that difference emerges of its own accord, or
immanently from the world. Traditionally, difference has been conceived as operating in the first of these ways. The first of these is tied to
representation andjudgement, the second to immanence and univocity.
Deleuze associates representation with the question, 'what is it?', and
this question implies an answer of the form, 'it is x'. This structure is the
basic structure of judgement: the attribution of a predicate to a subject.
The proper functioning of representation therefore requires two parts
to it. First there is the subject (the 'it'), which defines the 'what' that is
being asked about. Second there is the predicate, or property (the 'is
x'), which is attributed to the subject. So in order to make a judgement
about something, we need both a subject and a predicate. The undifferenciated abyss presents a situation whereby one of the se conditions
has not been met. There are no properties present in the subject, and
so there is no possibility of making a judgement. In fact, we could take
this further and say that as there are no limits to the abyss, there is no
such thing as a subject present, either. The properties lacking a subject
represent the second type of indiflrence. There are properties but no
subjects to attribute them to. The process of representation therefore
collapses again, and thinking is suspended.
The first of these possibilities, the abyss, brings us to the central
problem of representation. While representation is able to qualify fonns
and subjects ('this square is red'), it is unable to account for the genesis
of form itself. Form simply has to be imposed on something fundamentally non-representational; something that simply cannot be captured
within the formaI structures of judgement. Such an abyss is in a literaI
23
sense unthinkable. This is the dialectic of representation which operates in the opening of Chapter 1. If form, and with it the structure of
the world of subjects and properties, emerge From an abyss, and if this
emergence cannot be eXplained in terms of representation, how can it
be eXplained? The difference between the formless abyss and form must
be something that Falls outside of representation. Difference is therefore
Deleuze's name for this process of the emergence of form, which cannot
be captured within the structure of the already formed. The fact that
representation cannot think its own ground presents a serious problem,
and in order to escape From this dilemma, it attempts to think difference
From within the structure of representation itself. It attempts to mediate
this concept of difference through the structures of identity, analogy,
opposition and resemblance ('to "save" difference by representing it'
[DR 29/38J). Deleuze's aim in this chapter is to show the failure of
this project. In the process, he will make the daim that underlying representation is a structure that is different in kind From it. Underneath
the represented world of subjects and properties is a differential field of
intensity.
The structure of Deleuze's argument is therefore as follows. First, he
is going to give an account of Aristotle's theory of species and genera,
a paradig111 case of representation. Second, he will make explicit the
problem with this conception. Third, he will provide an alternative
to Aristotle's equivocal conception of being by tracing an alternative lineage moving From Duns Scotus through Spinoza to Nietzsche.
Fourth, he will try to show how Leibniz and Hegel's attempts to save
representation fail. Finally, Deleuze will condude with a discussion of
Plato as the thinker who founds representation, but in the process shows
the possibility of an alternative ontology. With a few minor deviations,
we will be following this trajectory in this chapter.
24
what he terms a univocal conception of being, and with it a conception of intensive difference. His aim is going to be to show that how
we understand being and difference are fundamentally interrelated.
Following on from the introduction, Deleuze's daim will be that if we
see difference as spatial, then we have to see being as fragmented (analogical). Alternatively, ifwe see difference in terms ofintensity, then our
understanding of being will instead be univocal. In this section, l want
to go through some of the key terms of Aristotle's ontology, namely
genus, species, difference and accident, relying on the account that the
early commentator, Porphyry, gives ofthem, before moving on to why
Deleuze thinks Aristotle's approach leads him into difficulties.
Porphyry defines the genus as 'what is predicated in answer to "What
is it?", of several items which differ in species, for example, animal'
(Porphyry 2003: 4). This fo11ows from Aristotle's own definition: 'what
is predicated in the category of essence of a number of things exhibiting
differences in kind' (Aristotle 1984d: 102a). vVhat does it mean to be
predicated of items that differ in kind? If we take the case of Socrates,
it should be dear that 'animal' can be predicated of him, to the extent
that Socrates is a man (a rational animal). For Porphyry and Aristotle,
however, there is no difference in kind betvveen different men, but rather
a difference in number. While it is the case that a given genus, such
as animal, is predicated of an individual, such as Socrates, the genus
cannot simply be directly used to define the individu al. If it were used
in this way, the genus would be the only function which was essential to
each individu al. This would mean that in essence each individu al wou Id
be different only in number, whereas the definition of genus requires
that it is predicated of what also differs in kind. We therefore need the
intermediary category, which Aristotle and Porphyry caH the species.
Porphyry first defines the species as 'that which is predicated, in answer
to "What is it?", of many things which differ in number' (Porphyry 2003:
5). This case would be the one reached so far, where we have one genus,
one group of individuals, and one level of species (a genus cannot simply
have one species since in this case we could not meet the definition of a
genus as applying to a number of things difIering in kind). We can see
that a given germs can be predicated of a species, and both the species
and the genus can be predicated of an individu al. We can therefore say
that Socrates is both animal (according to his genus) and man (according
to his species). In fact, we might want to make a more fine-grained definition by adding in more terms. Porphyry writes that 'the intermediate
25
items wiU be species of the items before them and genera of the items
after them. Renee these stand in two relations, one to the items before
them (in virtue of which they are said to be their species), and one to
the items after them (in virtue of which they are said to be their genera)'
(Porphyry 2003: 6). A consequence of this is that we now need to define
the species in terms of something other than the individu al, since only
the lowest species relates directly to things which differ only in number.
Instead, we now define the species in terms of its genus. Thus we have a
hierarchy, reaching from the highest genera to the individual, through
which the individu al is specified by a process of division from the genus
through the various species, gaining determinations as it goes, since each
genus will determine the essence of that below it. The last category we
need to consider are accidents, which do not define a species. These
can either be separable (as in the case of Socrates, who can be sitting or
not sitting), or not separable (for instance, 'being black is an inseparable
accident for ravens and Ethiopians' [porphyry 2003: 12]), in that an
Ethiopian could lose his skin colour without ceasing to be an Ethiopian,
whereas a man without reason (at least potentially) is no longer a man.
What is the role of difference in this hierarchy? In order for two
things to differ, Aristotle argues that they must also have something in
common. VVe cannot have a difference between, far instance, a horse
and an apple, as these two fonns are too far apart from each other; they
are what Aristotle calls 'other' to each other. Thus, a man and a horse
differ in that a man is a rational animal and a horse is a non-rational
animal. The difference of rational or non-rational makes sense because
of the shared predicate of animal. If differences between things of different genera are too broad, how can we formulate a narrower conception
of difference? Porphyry introduces three farms of difference: 'common
difference', 'proper difference', and 'the most proper difference', but
only the third of these is considered by him to be real difference.
Common difference is the difference betvveen t\'vo accidents, or nonessential predicates, and is not effective in determining a real diflrence
between two entities. Proper differences deal "vith inseparable properties of things, and so do reaUy serve to determine the difference between
two things. The most proper difference, hO\,yever, is specifie difference.
Specifie difference is what allows species to be defined in Porphyry's
tree by dividing the genus. So, if we take the genus, animal, we are
able to determine the species, man, by dividing animaIs into twO kinds:
rational and non-rational animaIs. Difference is the criterion by which
26
Of course, POl1)hyry is not implying that what we have here is a temporal constitution (we don't find in the world beings that are only
determined as animaIs, for instance). Rather, his point is that the series
of genera and species provide an account of the logical order of determinations of a particular object.
27
28
This solution itself is problematic fi'om the point of view of the science
of metaphysics, hm,yever, as for Aristotle, science must relate to a unified
class of things. But as we have just seen, Aristotle argues that there are
several different classes of being. It therefore appears that there cannot
be a coherent formulation of the concept of metaphysics. In order to
resolve this problem, Aristotle argues that while these different senses
of being are not identical, neither is it a case of simple equivocation to
relate these various concepts together. Instead, these different senses are
related to one another paronymously.
Ifwe are to be able to talk meaningfully about the world, it cannot be
the case that species and genera merely define general 'heaps' of things.
Instead, they must group things together according to criteria which
capture something common to their essence. For this reason, Aristotle
opens his Categories with a discussion of three tenns, homonymy, synonymy and paronymy:
\\Then things have only a name in common and the definition of being which
corresponds to that name is different, they are called IzollZonymous. Thus, for
example, both a man and a picture [of an animal] are animaIs.
When things have a name in common and the definition of being which corresponds to the name is called the same, they are called ~ynonynlOus. Thus, for
example, both a man and an ox are animaIs.
When things get their name from something, with a difference in ending, they
are called paronymous. Thus, for example, the grammarian gets his name from
grammar, the brave get theirs from bravery. (Aristotle 1984a: 1a)
vVhat these definitions make clear is that sorne attempts to define species
may not capture what is essential to the species itself. Since words apply
to different objects, it might be the case that if we rely on the fact that
the same tenn is used to designate different entities, we may be forced
into a definition of a species which does not accurately capture what
it is to be that particular thing. Thus, in the case above, the species,
animal, may refer both to the man and the picture of a man, despite
the fact that in these cases the term animal is being used in substantially
difirent ways. Rather, we need to look for synonymous expressions,
since it is these that capture something essential about the thing in question. How do these terms relate to the question of being? Being clearly
cannot be synonymous, as the problem of the highest genus shows that
it is impossible to give it a straightforward definition. Being could be
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30
31
32
this raises a problem, since we want to see God as separate From man.
Deleuze l'aises this point as follows in one of his lectures:
Because l say: being is univoca1, this means: there is no categorica1 difirence
between the assumed senses of the word 'being' and being is said in one and the
same sense of everything which is. In a certain manner this means that the tick is
God; there is no difference of category, there is no difference of substance, there
is no difference ofform. It becomes a mad thought. (L 14/01/74)
This view is dearly heretical, since it appearsto be the case that as being
is somehow prior to finite and infinite beings, being appears to operate
as a genus, with finite and infinite beings as its species. Thus being would
seem to occupy a place higher in the Porphyrian hierarchy than God.
We might also want to ask how Scotus is able to explain the simplicity
of the nature of God, given that God's nature seems to now be a compound of two different attributes: being and infinitude.
Scotus' resolution of these difficulties rests on his understanding of
finitude and infinity. To return to Aquinas for a moment, in the Summa
17zeologica, Aquinas defines infinity as follows:
Something is said to be infinite from the fact that it is not 1imited. Now matter
is in a certain way 1imited through form, and form in a certain way through
matter. lVlatter is in fact 1imited through form inasmuch as before it receives a
form, matter is in potency to many forms, but when it receives one, it is limited
by it. Form hovvever is limited through matter inasmuch as a form considered
in itself is common to many things, but by being received in matter it becomes
the form detelminately ofthis thing. (Aquinas, cited by Tomarchio 2002: 176)
The concepts of fini te and infinite are here relalional concepts. The infinite is defined by not being limite d, whereas the finite is defined through
limitation (by matter). If the finite and infinite are understood in these
terms, it is dear that we are going to end up with being as the highest
genus, or at best an analogical conception of being, as these two terms
are opposed to one another. Rather than finitude being defined by
relation to a limit, Scotus instead therefore introduces the notion of an
'intrinsic degree' ofbeing.
To see how such a concept can be formed, we can follow the account
Richard Cross gives in his discussion of Scotus (Cross 1999: 40). Scotus
firsts asks us to imagine an infinitely large magnitude. He then asks us
to apply this model of extensive infinity to a qualitative perfection, such
as goodness. The central daim is that mu ch as we can determine spatial
33
34
that there is a real distinction between the se two terms means that man
shares something with another animal, su ch as a horse, whilst differing
in another respect (rationality). If this kind of distinction was applied to
finite and infinite being, then being would be the genus of God and man,
as the identity under which they are distinguished. In this case, being
would be higher than God. Scotus' notion of the distinction allows us to
avoid this difficulty. Clearly there is a difference between whitenesses of
different degrees of intensity.
When we look at the concept of the intensity itself, however, it should
be apparent that this notion of intensity cannot be grasped as really
distinct from the whiteness itself. If we take away the concept of whiteness, we simply have the concept of'degree', which is meaningless on its
own 'degree ofwhat?' Nevertheless, the degree clearly does distinguish
different 'whitenesses'. We can note however, that it is possible to fornlUlate a concept of whiteness that does not make reference to its degree of
intensity. Such a concept would, however, be 'an imperfect concept of
a thing' as whiteness always shows itself with a given intensity. lt should
be dear that we can apply this conception to the notion ofbeing. Scotus'
daim would then be that being always presents itself with a given degree
of intensity which is inseparable from it. While we can therefore formulate a concept ofbeing without reference to its intensity, such a conception is only formaI, as actual being is always finite or infinite.
Intensity as it stands is purely a difference in the degree ofsomething's
being, and is also pre-categorial. As such, it does not constitute the kind
of distinction that would allow a proper separation between God and
man. Such a position in fact is the one that Deleuze wants to develop in
his own philosophy. For Scotus on the contrary, the difference in degree
between God and his creation becomes a difference in kind once we
recognise that infinite intensity is simply incommensurate with any form
of finite intensity. The gap between finite and infinite is therefore still a
chasm which allows the separation of God and his creation to be maintained. \l\Thile being can conceptually be said univocally, in practice, we
always encounter being with a given intensity, and so in reality being is
always encountered in different forms:
As said of the ten categories, neither metaphysically nor naturally does the term
'being' signify one concept; and being is not a genus of these, neithe1' natu1'ally
no1' metaphysically. However, logically speaking, being is univocal. (Duns
Scotus, In De an., q. 22, n. 33 taken from Hall 2007: 20)
35
36
37
38
of the highest genus, as the highest genus would seem to require a higher
identity in order to be defined, but the presence of such a higher identity
would imply that the highest genus was not, in fact, the highest genus.
In su ch a case, determination relies on a numerical distinction between
terms. We must be able to separate the rational animaIs from the nonrational animaIs (as separately existing entities) in order to define man as
a rational animal. We define something by saying that it is 'this and not
that'. Spinoza's substance, however, has an essence which is expressed
through the attributes. This essence is not one that can be given in terms
of the categories, however, as Spinoza's substance is not subject to any
form of numerical distinction - it is singular. On this basis, it cannot
be determined through the 'this and not that' structure of representation, even in relation to a possible but non-existent object. Substance
does have a structure and an essence, however, as is shown by the finite
modes which as a whole express substance, and which are distinguished
from one another in terms of their intensity. Substance is determined
by a difTerence, but it is not a difTerence between concepts (everything
is substance), but rather a difference that is internaI to substance. This
is therefore one of the most difficult ideas in Deleuze's metaphysics:
substance expresses its essence by difTering :om itself. This is made possible on the basis of the univocal conception ofbeing, whereby an modes
express the same being. Spinoza's system therefore makes no distinction between difTerent ways in which things exist. Although the world
appears to be made up of difTerent substances, in actual fact, everything
is simply an expression of the same substance.
39
being as the highest term in our hierarchy with difference, whilst retaining the insights given by the intensive understanding of difference; it is
Nietzsche, Deleuze daims, who provides the means to do this. 1 want
to come back to his work in the next chapter, but there are two points
in Nietzsche's writings that Deleuze is basing his argument on at this
point. The first is section 13 of Essay 1 of the Genealogy qf.A;!orality, where
Deleuze sees Nietzsche as opposing the subject-property view ofreality,
and the second is aphorism 341 of the Gqy 5cience, where Nietzsche presents the eternal return. Deleuze sees the eternal return as Nietzsche's
formulation of the univocity principle.
Let us begin by looking at the section from the Genealogy qf .A;!orality.
Here, Nietzsche presents a contrast between h.vo basic attitudes towards
the world, that of the lamb and the bird of prey:
There is nothing strange about the fact that lambs bear a grudge towards large
birds of prey: but that is no reason to blame the large birds of prey for carrying
off the little lambs. And if the lambs say to each other, 'These birds of prey
are evil; and whoever is least like a bird of prey and most lil its opposite, a
lamb, - is good, isn't hd', th en there is no reason to l'aise objections to this
setting-up of an ideal beyond the fact that the birds of prey will view it somewhat derisively, and will perhaps say: 'vVe don't bear any grudge at aIl towards
these good lambs, in fact we love them, nothing is tastier than a tender lamb'
... A quantum of force is just such a quantum of drive, will, action, in fact it is
nothing but this driving, willing and acting, and only the seduction of language
(and the fundamental errors of l'eason petrified within it), which construes and
misconstrues aIl actions as conditional upon an agency, a 'subject', can make it
appear otherwise ... no wonder, then, if the entrenched, secl'etly smou1dering
emotions of revenge and hatred put this belief to their own use and, in fact, do
not defend any belief more passionately than that tlze strong are jiee to be weak,
and the birds of prey are free to be lambs: - in this \vay, they gain the right to
make the birds of prey respollsible for being birds of prey. (Nietzsche 2006a: 13)
40
41
same time, and in this sense Aristotle uses these categories to define the
logical space which something occupies. Each term limits the other, but
also, to the same extent, defines it, so that the properties form reciprocal
pairs. In other words, to determine something, we in effect characterise
it as 'this and not that'. This characterisation can also be related once
again to the lamb. The lamb determines itself as good in opposition to the
bird of prey, which it first de termines to be evil. Difference in this sense
is therefore fundamentally tied to the related notions of spatial rnetaphor
(two objects differ in that we characterise them as occupying different
delimited logical territories) and negation. Finally, it provides 'a hierarchy which measures beings according to their limits, and according to
their proximity or distance from a principle' (DR 36/46); in other words,
according to how dosely a being conforms with its essence or is a degenerate instance ofit. A sedentary distribution therefore is a way of ordering
the world that is hierarchical, and proceeds by the delimitation of the
world according to oppositional determinations. The notion of difference
is grounded in negation and operates according to a spatial metaphor.
The second form of distribution is the nomadic distribution. Deleuze
makes dear that this conception of a distribution relies on 'a space which
is unlimited, or at least without precise limits' (DR 36/46). Rather than
being defined by the 'this and not that' conception of difference that
Deleuze finds in Aristotle, it is defined by the notion of intensive difference which, as Scotus showed, does not require definition in oppositional terms. It is therefore not a spatial conception of organisation.
Deleuze introduces the univocal conception of being in order to explain
those features of the world which escaped something like an Aristotelian
conception of the world. The nomadic distribution is intimately connected to this univocal conception: 'Oedipus' chorus cries: "which
demon has leapt further than the highest leap?" The leap here bears
witness to the unsettling difficulties that nomadic distributions introduce
into the sedentary structures of representation' (DR 37/46). If a se dentary distribution is fundamentally tied to an understanding of the world
in terms of subjects and properties, how are we to understand this notion
of a nomadic distribution? The key point is Deleuze's daim that everything goes to the limit of what it can do. He elaborates on this as follows:
Here limit [peras] no longer refers to what maintains a thing under a law, nor
what delimits or separates it fl:om other things. On the contrary, it refers to that
on the basis of which it is deployed and deploys ail of its power; hubris ceases to
42
be simply condemnable and tlze smallest becames equivalent ta tlze largest once it is not
separated from what it can do. (DR 37/46)
V\Then we separa te the bird of prey from its action, or lightning from its
striking, we institute the two moments of an ontology of judgement: the
subject and the property. This moment of separation of something from
what it can do is what gives us the Aristotelian idea of a world of fixed
things. If something is not separated from what it can do, then instead of
an ontology ofbeing, we have an ontology offorces, or becoming. There
are not static points from which movement originates, but rather just
movement itself. We can tie together a number of results at this stage.
Just as Scotus shows that analogy can only operate within a prior univocal framework, Nietzsche shows that the point of view of the Lamb is
derivative of that of the bird of prey. Deleuze similarly argues that 'negation results from affirmation: this means that negation arises in the wake
of affirmation or beside it, but anD' as the shadow qf the more prqfound genetic
element - of that power or "will" which engenders the affirmation and the
difference in affirmation' (DR 55/67). Difference is therefore primaIy
in this scheme. This leads us to the la st aspect of Deleuze's discussion of
univocity: how are we to conceive of a univocal conception ofbecoming?
This principle has two important aspects for Deleuze at this point in
Dijjrence and Repetition. First, the question we need to ask is, what is it that
eternally returns? Second, the eternal return seems to operate as a test;
what is it a test for? Let us begin with the first question. Deleuze has laid
down two different ways of understanding the world. A sedentary distribution essentially understands the world as a collection of things with
properties. If Deleuze's aim is to give us a conception of difference that
is not subordinated to identity, then understanding the return in terrns
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44
to Aristotle. At this point, he makes a distinction between two different ways in which we can characterise philosophies that are based on
the notion of judgement. The first form, which we have been dealing
with, is finite representation. This is based on the idea that judgements
describe the essential structure of things. In other words, they set out the
essential determinations which make up something. \Vhat makes it finite
is the notion of limit. Aquinas' definition of limit, for instance, showed
that finite things failed to properly express their form because they
were limited by matter. This led to a distinction between the essence of
something and its appearance, in that something expresses its essence to
the degree that its actual finite form embodies its essence ('their degree
of proximity or distance from a principle' [DR 37/ 46J). Deleuze's
daim is that infinite representation replaces the notion of matter with
a broader notion of representation. Rather than finite forms occurring
in matter, everything that is exists as a moment of an infinite concept
which encompasses everything. In effect, this is the daim that the world
is therefore conceptual 'aIl the way down': 'Instead of animating judgements about things, orgiastic representation makes things themselves so
many expressions, or so many propositions: infinite analytic or synthetic
propositions' (DR 43/53). 1 want to spend a bit of time outlining how
these approaches might function. In relation to the discussion of representation so far, the foIlowing comment by Deleuze sums up the difirence between finite and infinite representation:
The signification of the very notion of limit changes completely; it no longer
refers to the limits of finite representation, but on the contrary to the womb
in which finite determil1ation never ceases to be born and to disappear, to be
enveloped and deployed withil1 orgiastic representation. (DR 42-3/53)
45
Finite representation therefore emerges for Hegel from the fact that we
take for granted the nature of the distinction between the finite and the
infinite. We presume that: 'There are two worlds, one infinite and one
finite, and in their relationship the infinite is only the limit of the finite
and is thus only a determinate infinite, an ifinite wlziclz is itseiffinite' (Hegel
1999: 139-40). If we just view the infinite as a 'beyond' of the finite, and
remain with finite thinking, however, we end up with an infinite which
is itself limite d, and hence is finite: 'Owing to the inseparability of the
infinite and the finite - or because this infinite remaining aloof on its
own side is itself limited - there arises a limit; the infinite has vanished,
and its other, the finite, has entered' (Hegel 1999: 141). The heart of
the difficulty is that the infinite is supposed to be that which is beyond
limitation, but the basic structure of determining the infinite is by opposition, in other words by saying what the infinite is not. But by doing so,
we introduce a limit into the notion of the infinite. Possessing a limit,
however, is what defines finite things. For this reason, Hegel defines this
understanding of the infinite as a 'spurious infinite' (Hegel 1999: 142).
46
The true infinite emerges when we step back from attempting to formulate the infinite through the progression, and recognise that the process
of the circulaI' movement of the fini te into the infinite and back again
is itself the infinite. Such a process involves seeing the infinite as essentially a contradictory structure the identity of identity and difference.
The finite is in a perpetuaI process of vanishing or negation, and this
movement itself is seen as the infinite. Everything therefore falls under
conceptual determination. Hegel's daim is thus that it is only by moving
to a different way of understanding concepts, namely speculative reason,
that we are able to truly understand either of the categories of finitude
or infinitude.
What, therefore, is the relationship between the infinite and finite
that Hegel develops? Deleuze's daim is that infinite representation is
no better than finite representation. In distinguishing the two, he writes
that 'it treats identity as a pure infini te principle instead of treating it as
a genus, and extends the rights of the concept to the whole instead of
fixing their limits' (DR 50/61). The finite and the infinite are still understood oppositionally, as each is not the other, but at the same time, they
are united together, in that they are part of one process. Now, if two
terms are opposed to each other, but are both asserted simultaneously,
then we have a contradiction. This is why Deleuze daims (and Hegel
would agree) that speculative reason operates by pushing difference
past opposition to contradiction. In that everything is one element (the
infinite), it appears as ifwe have a univocal theory much like Spinoza's.
In actual fact, however, Hegel's theOl)' preserves the central features of
representation: 'Goethe, and even Hegel in certain respects, have been
considered Spinozists, but they are not really Spinozists, because they
47
never ceased to link the plan [e of infinite representation] to the organization of a Form and to the fOrmation of a Subject' (SPP 128-9).
Deleuze makes three main criticisms of this approach. First, '[Hegel]
crea tes movement, even the movement of the infinite, but because he
creates it with words and representations, nothing follows' (DR 52/63).
Deleuze's daim is that Hegel has misunderstood the cause of the movement of thought by continuing to represent it, rather than seeing it as
escaping representation. The aspect of representation which Deleuze
takes to be critical here is the universal. "'Everyone" recognises the
universal because it is itself the universal, but the profound sensitive
conscience which is nevertheless presumed to bear the cost, the singular,
does not recognise it' (DR 52/63). The singular, or singularity, which is
neither particular Bor universal, is exduded by beginning with a term
which is essentially universal. We can return to the figure of Abraham.
Abraham cannot be understood within the framework of the universal,
which is the precise reason for Kierkegaard's introduction ofhim in Fear
and Trembling.
The second criticism is that this movement is always around a particular point. Deleuze is daiming that Hegel relies on a 'monocentring
of cirdes' (DR 49/60) which Deleuze daims cornes about through
Hegel's adherence to the species-genus model. In the case of the finite
and the infinite, movement 'revolves' around the central moment of
the true infinite. Hegel has not got rid of the idea of a central identity,
therefore.
The third point, which relates the previous two, is that the idea of
opposition, which Hegel uses to unite the particular and univers al, is
too rough to provide an adequate description of the world. 'Oppositions
are roughly cut from a delicate milieu of overlapping perspectives, of
communicating distances, divergences and disparities, of heterogeneous potentials and intensities' (DR 50/61). That is, Deleuze asserts
that simply relying on a reinvigorated understanding of the distinction
between finite and infinite will not provide the kinds of fine-gTained distinctions needeel to describe the worlel aelequately. It's worth noting that
whilst there are a number of structural parallels between Hegel's work
anel that of Aristotle, there are also a number of conceptual innovations.
The fact that these parallels exist is not enough, therefore, to refute
Hegel's philosophical position. Exploring possible Hegelian responses
to these criticisms would take us far beyond the scope of this guide,
however.
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means that 'taller thanJohn' will be a property of Paul, and 'shorter than
Paul' will be a property of John. If causal interactions are going to be
understood pUl'ely as properties of each subject, then each monad will
have to contain aIl of its causal interactions with the rest of the world.
Leibniz therefore writes that:
Thi" interconnection or accommodation of ail created things to each other,
and each to ail others, brings it about that each simple substance has relations
that express ail the others, and consequently, that each simple substance is a
perpetuaI, living min'or of the universe. (Leibniz 1989a: 56)
50
are perspectives of, then we are given the answer that they are perspectives of the universe. The notion of the universe itself has to pre-exist
the different perspectives of it, since it is through this notion that God
determines which of the monads can exist and which cannot. Only those
which are compossible, that is, can simultaneously co-exist within the
same world, can exist. We cannot have a world in which Adam both
sinnecl and did not sin, as this woulcl be a contradiction, nor a world in
which difIerent monads see the world in such radically different ways,
as then the impression of causality would break down. 'There are, as it
were, just as many different universes [as there are monads], which are,
nevertheless, only perspectives on a single one' (Leibniz 1989a: 57).
Leibniz's notion of difference therefore still relies on the convergence of
these clifferent perspectives on a single identity, the universe itself:
Leibniz's only error was to have linked difference to the negative oflimitation,
because he maintained the dominance of the old principle, because he linked
the series to a principle of convergence, without seeing that divergence itself was
an object of affirmation. (DR 51/62)
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perspective on the object changes, when 1 return to my original position, something similar to the original perspective returns. On this basis
of the fact that my own memory appears to preserve some perspectives,
1 posit what Merleau-Ponty calls 'the memory of the world' (lVlerleauPonty 1962: 70), which indudes all possible perspectives on the object.
Now, with an understanding of the object based on an infinite number
of possible perspectives, my own view ceases to be relevant (1 become
'forgetful of the perspectivism of my experience'). 1 now suppose that
rather than the object emerging from the accumulation of perspectives
on it, the perspectives are in fact inessential, and logically posterior to
the object itself.
The final stage is to recognise that now the object is not considered
to be constituted by perception, we need another explanation of how it
is constituted. We thus alight on the idea that it can be deduced 'from
a relationship between objects'. This relationship is, of course, the
relationship of opposition and limit. At this point, therefore, negation
enters our world, as a precondition for limit. This account is therefore
the account of the generation of an illusion, which, as Deleuze puts it,
is nonetheless weIl founded. It shows how negation and limit enter the
world through representa tion ignoring its genetic conditions (perspectivism). How do es this then fit in with Deleuze's account?
Such an account fits with Deleuze's characterisation of infinite
representation as the convergence of an points of view (quotation 1).
Opposition comes into play through the graduaI elimination of perspectives. It also fits with Deleuze's desire that each point ofview instead be
the object, or the object must belong to the point of view (quotation 2).
Such a view is a return to a form of perspectivism su ch as that found
in lVlerleau-Ponty. vVhat about Deleuze's final daim that 'difference
must become the elernent, the ultimate unity'? In the next paragraph,
Deleuze daims that 'the intense world of differences, in which we find
the reason behind the qualities and the being of the sensible, is precisely the object of a superior empiricism' (DR 57/68-9). This suggests
that Deleuze's analysis is going to go beyond the kind of perspectivism
Merleau-Ponty proposes.
For Merleau-Ponty, what makes possible the field of perspectives
is the body, but the notion of a body operates as an identity. Instead,
Deleuze is going to try to explore what makes possible the kind of
account lVlerleau-Ponty gives. Su ch an account will be what Deleuze
caIls elsewhere a 'transcendental empiricism', since it will deal with the
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54
the real difficulty, since it appears that there are a large number of people
who fulfil this description: 'merchants, fal'mers, millers and bakers' for
instance (Plato 1997d: 267e). As Deleuze puts it, for Plato, 'difference is
not between species, betvveen two determinations of a genus, but entirely
on one side, within the chosen line of descent' (DR 60/72).
Plato's question is rather, which candidate is truly the statesman?
\I\Thereas Plato is norrnally understood as using myth to allow nonphilosophical readers to understand the point of the dialogue, Deleuze
gives it a more philosophical role. The Statesman introduces the fable of
two cosmic eras, that of Cronos, and the present age of Zeus. Each of
these gods allows ordered existence to carry on in the world by ensuring that the universe continues to revolve around its circle. These gods'
governance of the universe provides us with a model by which to assess
which of the claimants is the true statesman. VVe can see in the god a
metaphor for Plato's theOl'y of Ideas, the theOl'y that what de termines
the nature of something temporal is its relation to an eternal supersensible entity. So actions are just in so far as they participate in, or
resemble, the Idea of justice. The true statesman is therefore the one
who participates in (or best represents in the temporal world) the eternal
Idea of statesmanship, whereas the false claimant does not. Now, obviously a statesman cannot be a god, but there are two ways in which he
can resemble one, which Plato outlines in the Soplzist:
Visitor: One type of imitation l see is the art oflikeness-making. That's the one
we have whenever someone produces an imitation by keeping ta the proportions of length, breadth, and depth of his model, and ais a by keeping ta the
appropriate colours of its parts.
Theaetetus: But don't ail imitators try ta do that?
Visitor: Not the ones who sculpt or draw very large works. Ifthey reproduced
the true propOliions of their beautiful subjects, you see, the upper parts would
appear smailer than they should, and the lower parts would appear larger,
because we see the upper parts from further away and the lower parts from
doser. (Plata 1997 c: 235d-236a)
The true statesman resembles the Idea of the statesman in the first of
these senses, as the form itself cannot be given in appearance, since it is
not spatio-temporal. The pretender only resembles the appearance of
the Idea, not the Idea itself. They are instead tied to the world of appearance. The problem, therefore, is to distinguish the candidates who bear
a true likeness fi'om those which merely appear to do so.
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56
57
So here we have two very different projects. For Kant, we begin with
the notion of the subject and object, and attempt to explain how the n,yo
can enter into a relationship with one another. In this case, therefore,
the 'methodologicaUy reduced plane' is the field of representation, with
its concomitant positing of judgement. Taking judgement as our model
is, according to Deleuze, destined to lead us to the same kinds of difficulties we encountered with A1'istotle in the last chapter. Hume's approach
instead begins with the 'given' that precedes the subject, and attempts
to show how it is constituted, which in tu1'n allows us to explain how the
subject systematises the given into its own categories. Deleuze's aim in
this chapter will be to provide a 'Humean' deduction of how the world
is constituted that does not rely on a subject. In order to do so, he distinguishes ben,yeen Kant's notion of synthesis, which he caUs active synthesis, and another fo1'm of synthe sis that is actually responsible for bringing
subjects into existence, called passive synthesis. By eXplaining how
subjects come into being, Deleuze also aims to show why it is that philosophers have been misled into believing in something like a Kantian
account of the constitution of the world that presupposes rather th an
explains the existence of subjects. In order to do so, he will show how
each of the three active syntheses Kant takes to explain the possibility of
experiencing a world of objects presupposes a prior synthesis whereby
the subject is constituted. In the next section, therefore, l want to make a
short digression into one of the most important sections ofKant's critical
philosophy, the transcendental deduction of the Critique qfPure Reason, in
order to oudine the three syntheses that Deleuze is dealing with.
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59
60
V\Then we walk around a building, we are given a series of perspectives on it. Now, a condition of seeing these different perspectives as
being perspectives on the same building is that l am able to relate them
together as being rt~y perceptions of the building. Otherwise, we would
simply have a series of fragmentary appearances. 'AT e can go further
than this, and say that without the unity of consciousness we would not
just see appearances of different buildings. VVe wou Id simply see a series
of appearances without any kind of unity - they wouldn't relate to anything. Now, this is a key point. Kant has claimed that in order for experience (that is, a relation to the world that gives us knowledge, rather
than just sensation or appearances) to be possible, we need to be able
to see appearances as belonging to the same subject. In order for this
to be the case, they need to exhibit some land of unity. It is the concept
of the object that gives aIl of these moments of appearance a unity, as
it is by seeing aIl the moments of appearance as referring to the same
underlying object that we are able to unifY them. The concept of the
61
object thus makes the unit y of consciousness possible. We can note that,
while for Kant we need the concepts of a subject and an object to nlake
experience possible, precisely because they make experience possible,
we don't have direct experience of subjects and objects. Rather, they are
necessarily prior to experience (and to synthesis). As such, while we need
to presuppose them, we cannot say anything about them. This point will
be important when we look at Kant's criticisms of Descartes in relation
to Deleuze's third synthesis of time (2.6).
We can now return to our initial question. How does Kant show
that the faculties can be related to one another? Well, for experience to
be possible, the subject needs to synthesise appearances into objective
unities. How is it able to do this? The categories give us the essential
characteristics of what it is for something to be an object (to be a substance, to have properties, etc.), and so it makes sense for the categories
of the understanding to provide the rules by which the synthesis takes
place. Thus we have a situation whereby appearances are synthesised
into experience by relating them to the notion of an object, and in order
to relate appearances to the notion of an object, we need rules governing objects in general, and these are the categories of our conceptual
thought (the understanding in Kant's terms).
Kant's account is important because it shows the interrelations
between several concepts which we saw Deleuze opposing in the previous chapter. Kant essentially shows that the notions of objecthood,
judgement and synthesis are aIl interconnected. Because we see experience as being about a subject relating to an object, we are forced to
invoke the concept of judgemcnt. Now, given that aIl of these concepts
reciprocally imply one another, how can we develop the kind of subrepresentational account that Deleuze is seeking? Deleuze's response, as
we shall see, will centre on the concept of synthesis driving this account.
His daim is that Kant has essentially taken a psychological account of
what it is for the temporal world of objects to emerge for us and reiterated it at a transcendental level. Conscious synthesis for Kant takes
the form of judgement. Wh en l count, or bring together the moments
of a judgement ('the table is red'), it is l who actively relates these representations (the table, redness) to one another. By using this model,
Kant ties synthesis to the subject, and hence any form of synthesis
that is not ultimately governed by judgement is going to be ruled out.
Deleuze's approach is therefore going to be to try to provide an alternative account of the synthesis of time which does not rely on this sharp
62
In doing so, he will try to show how our experience is also the result of
syntheses which OCClU' prior to consciousness, and hence prior to our
imposition of the structure ofjudgement. Providing an account of this
kind is going to be the primary focus of Chapter 2.
1.3.16)
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64
65
even our actions and our needs. But irony in turn is still a contemplation,
nothing but a contemplation. (DR 75/96)
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67
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us to act on the basis of prior experience. This was the basis of Kant's
daim that fOl'ming habits required an affinity of perceptions, in order
that relations of similarity and contiguity could be fonned between the
past and present. Now, as Bergson believes that memory is different in
kind from perception, it cannot be the case that memories are simply
representations like perception itself. Rather, memory 'begets sensation'
(Bergson 1991: 141) when it is brought to bear on a present situation.
So the present is the site of the integration of two movements which are
different in kind. This leads to a number of questions. If the past is unlike
the present, how is it structured? And, if the past is unlike the present,
how is it able to be integrated into the present?
Beginning with the first question, we can note that there appears to be
a process of selection involved in action. vVhat is similar to the present
is brought to bear on present experience. As Bergson notes, children
often have far greater facility of recall than adults, which is inversely
proportional to their ability to select the experiences appropria te to the
present context (Bergson 1991: 154). If the detail of one's recollections
is inversely proportional to action in this way, then 'a human being who
should dream his life instead of living it would no doubt keep before
his eyes at each moment the infinite multitude of the details of his past
history' (Bergson 1991: 155). So memory that functions by recollection
contains a greater and greater part of the past, until we reach a point at
which it is completely detached from action and hence, in the state of
pure memory, contains a complete record of the past. Now, for Bergson,
memory is different in kind from the present, which relates itselfby succession to the future. vVe can now give a dearer account ofits structure.
If we recognise that Kant's model sees memory as disconnected and
successive (Bergson's characterisation of 'self-sufficient atoms'), then the
rejection of this model is going to mean that we no longer see memory
as composed of separate parts. If that is the case, then we will not be
able to separate one particular set of memories from others. This implies
that memory stores the ""hole of the past, rather than just moments of
particular interest to the subject. Now, given that the past cannot be
divided up into elements, it must be the case that the whole of the past
is also present in our practical relations to the world. Selection on the
basis of similarity will not explain how only a small part of the past is
related to the present, as selection implies detachable elements, and as
we saw, similarity is presupposed rather than eXplained by the empiricist
model. Instead of a process of selection, we have a process of expansion
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lVIemory, laden with the whole of the past, responds to the appeal of the present
state by two simultaneous movements, one of translation, by which it moves in
its entirety to me et experience, thus contracting more or less, though without
dividing, with a view to action; and the other of rotation upon itself: by which it
turns towards the situation of the moment, presenting to it the side which may
prove to be the most useful. (Bergson 1991: 168-9)
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We can now see how these two syntheses lead to two concepts of repetition. In fact, there are four repetitions at play in Difforence and Repetition
at this point, as we have two levels, habit and memory, and two modes
of synthesis operating at these levels, active and passive synthesis. We
now need to see how these two levels interact. To return once more
to the question of association, the problem with the representational
account was that it was unable to explain IlOW different moments carne
to be selected as a basis for habit, as every marnent possessed an affinity
of sorne sort with every other moment. Now, Hume appears to solve
this problem by introducing the notion of a contractive faculty of the
imagination, rather than the Kantian account, which operated more
like an inference from previous cases to the present case through shared
properties. We still need to know how the imagination is able to select
what it contracts, or what it fixes on as the basis for its anticipation.
This is where the synthesis of the past cornes into play. As we have just
seen, Bergson represents the past as a cone, each level of which con tains
the entirety of the past, but at different levels of contraction and relaxation. At the widest level of the cone, we have the absolute relaxation of
memory, the pure past. At the point of the cone, the past was contracted
down to a point of practical generality. Between the two the pa st was
layered in different degTees of contraction and relaxation. Each of these
layers of contraction and relaxation can be seen as a field of different
similarities and differences between events, just as in Bergson's example
of hearing a word in a foreign language can evoke either the meaning of
the word, or the first time that l heard it. These two syntheses are therefore related as follows: 'The sign of the present is a passage to the limit, a
maximal contraction which comes to sanction the choice of a particular
level as such, which is in itself contracted or relaxed among an infinity
of possible levels' (DR 83/105). The imagination that Hume talks about
is therefore the point of actualisation of a particular plane of memory
in relation to action. We therefore have two different contractions: the
contraction of the plane itself, and then the contraction that relates the
plane of memory to the actual world. Bergson's account supplements
Hume's by providing a model of time within which the first synthesis
can take place, but also by eXplaining how different contractions of the
same temporal field are possible: 'each chooses his pitch or his tone,
perhaps even his lyrics, but the tune remains the same, and underneath
aH the lyrics the same tra-Ia-la, in an possible tones and an pitches' (DR
83-4/105-6).
72
vVe can therefore say there are two forms ofpassive repetition - the
repetition of habit, which is 'empirical', and is the repetition of instants,
and the repetition of memory, whereby the same past is repeated at
a series of different levels, with different degrees of contraction and
relaxation. Habit synthesises essentiaUy indifferent elements into a field
of temporality, or duration, and in doing so creates what Deleuze caUs
'material' or 'bare repetition. It does repeat, as in the case of the he artbeat, but only on the basis of the 'dothed' repetition which underlies it.
This repetition is based on memory, and is responsible for what Deleuze
calls 'Destiny': the fact that everything is determined by the past, but
a past that still allows for freedom through the selection of the level at
which the past is played out.
73
To get dear on what time out of joint might mean, it's helpful to begin
with the notion of what time in joint would mean. In a lecture from
1978, Deleuze makes the following daim:
Cardirlal comes from cardo; cardo is precisely the hinge, the hinge around
which the sphere of celestial bodies turns, and which makes them pass tune and
again through the so-called cardinal points, alld we note their return: ah, there's
the star agairl, it's time to move my sheep! (L 14/03/78)
74
So how does time come about? Vvell, the first tl1ng to note is that
before the universe is organised according to time, it is still in motion,
although this motion is 'disorderly'. Thus, motion is not dependant on
time, which appears afterwards. In fact, Timaeus believes that time is
grounded in the elements which are most perfect in the universe, the
celestial bodies. In what way do the celestial bodies form the ground of
time? The planets move in an orderly manner, which is what allows time
to be related to measure (the star that represents the time to move the
sheep in Deleuze's example).
In this way and for these reasons night-and-day, the period of a single circling,
the wise st one, came to be. A month has passed when the Moon has completed
its own cycle and overtaken the Sun; a year when the Sun has completed its own
cycle. (Plato 1997e: 39c)
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76
77
78
79
Now when we look at the legal conception of the person, it isn't the
case that the unity of the individu a 1 can be given in terms of theu: acts
themselves. Rather, when someone comes before a judge, what the
judge sees is not a unity governed by persona lity, but rather a series of
acts which are unified by the la st act's relationship to the law. So, as
Rosenberg notes, the acts of a murderer are in large part no di:rent
from the acts of anyone else, and are only made criminal by the fact that
they precede the murder itself: 'entering an automobile, stepping on
the gas, obeying the traffic lights' (Rosenberg 1994: 138). In this sense,
when we look at a criminal act, it is the law that provides a framework
for the analysis of action, and which imposes a structure of artifice that
unifies the conduct of the perpetrator. In the case of the law, Rosenberg
notes that if it is suddenly discovered that the alleged perpetrator did
not commit the crime, his en tire identity before the law disintegrates.
The actions of 'stepping on the gas' and 'obeying the traffic lights'
now take on an entirely innocent aspect. In this sense, the law operates according to an active synthe sis, as it provides the active principle
uniting indifferent detenninations. VVe can therefore see Rosenberg's
conception of dassical drama as being one of tune in joint. Here, the
phenomenal manifestations of characters in dassical drama are merely
manifestations of an underlying law, or an underlying judgement: the
fate of the character. Hence, 'psychology can establish the plausibility of
NIacbeth's or Lear's behaviour, but for the sufficiency ofhis motivation,
we must not refer to a possible l\1acbeth or Lear "in reallife" but to the
laws of the Shakespearean universe' (Rosenberg 1994: 140).
How does this differ with Ham/et? Deleuze notes that Hamlet's daim
that 'time is out of joint' can be read as an essentially philosophical
daim. Here we can see that Ham/et was not a purely arbitrary choice on
the part of Deleuze. In fact, we can see in the structure of the play itself
an intimation of the reversaI of the roles of time and succession/ action/
movement.
The first half of Ham/et sees Hamlet himself not as an identity in the
legal sense. As Rosenberg points out, the drama prior to Hamlet's return
from Englancl concerns his inability to act:
Ida not know
"\i\Thy yet I live ta say 'This thing's ta do;'
Sith 1 have cause and will and strength and means
Ta do't. (Shakespeare 2003: IV.iv.43-6)
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81
82
83
synthesis with an active subject, time is simply a mate rial which can be
taken up by the understanding. This means that he cannot fully develop
the implications of this move, and is instead forced to posit the transcendental unity of apperception as responsible for the synthesis of time.
Once we recognise the possibility of syntheses that are not active, we can
understand time as auto-synthetic. Time orders itself according to the
modalities of habit and memory. We can get clearer on what the pure
form of time is by noting that 'the eternal return is neither qualitative
nor extensive, but intensive, purely intensive. In other words, it is said
of difference' (DR 243/303). What returns cannot therefore be actual
states of affairs. To read it as such would be to read it in terms of time
in joint, a mistake that Deleuze accuses Vico ofmaking (DR 92-3/116).
That is, the future, the pure form of time, is the same field of intensive
difference that we encountered in the previous chapter. We can now see
that repetition occurs not because the same forms repeat, but because
the same field of intensive difference engenders these different forms.
\l\1hat returns, therefore, is the pure form of time in the form of intensive
diflrence, in different actual expressions.
This final form of the eternal return therefore unites the first two
chapters of Diffrence and RejJetition. While the f-irst chapter begins from an
analysis of our metaphysical concept of difference, and arrives at a field
of intensive difference, Chapter 2 begins with our experience of habit,
and shows that what makes habit possible is memory, and that in turn,
the relation between habit and memory is made possible by the field of
intensive difference that is the future. Thus, the metaphysical account
of Chapter 1 is reinforced by the transcendental account of Chapter
2. We therefore have two eternal returns in Difference and RejJetition, the
genealogical doctrine of the second chapter and the ontological doctrine
of the first.
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85
86
87
88
89
90
91
As well as the extension of active synthesis, we also have an extension of a passive synthesis. This revolves around the somewhat obscure
notion of a virtual object:
The child constructs for itself another. object, a quite different kind of object
which is a viriual object or centre and which governs and compensates for the
progresses and failures of its real activity: it puts several fingers in its mouth, and
92
appraises the whole situation fi'om the point ofview ofthis virtual mother. (DR
99/123)
93
\f\Then we looked at the syntheses of time, the problem with understanding association as operating purely in terms of actual memory was that
everything was like everything else in some way. That meant that it
was impossible to explain why a particular experience conjured up t/zis
memory. For Deleuze, what ties together two series of events is that the
same virtual object is at play (incorporated) in both series. This explains
why a past event can still influence the present, not because of the actual
events themselves, but because of the virtual object incorporated into
them. This also explains why it is the case that we can see, for instance,
in someone's character, a repetition of the same relationships, or the
same actions, in different situations. The subject does not reason by
94
analogy on the basis of their past responses, but is reacting to the same
event incorporated into a different state of affairs.
In this sense, we can say that what is repeated is something that has
never actually been present, but rather that the 'same' virtual object is
present in disguise in the various states of affairs that make up the repetition. There is no first term to the series itself, however, as repetition takes
place in response to the drives rather than the ego and its object.
Now, what is interesting about this daim is that Deleuze is not here
rejecting the death instinct, but rather daiming that the error is with
Freud's interpretation of it. Deleuze makes the daim that the virtual
and actual objects 'inevitably become confused, the pure past thereby
assuming the status of a former present, albeit mythical, and reconstituting the illusion it was supposed to denounce, resuscitating the illusion of
an original and a derived, of an identity in the origin, and a resemblance
in the derived' (DR 109/135). This illusion, therefore, is that the origin
of the compulsion to repeat is in an actual, albeit potentially mythical
event. Once we succumb to this illusion, it is a short step to positing a
Freudian death drive. For Deleuze, the retention of the death drive will
be premised on a reinterpretation ofwhat death alllounts to. For Freud,
death is understood in terms of a mate rial repetition. Deleuze is instead
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96
97
98
410)
99
100
namely, the form of this discourse ... In fact, Eudoxus has no fewer presuppositions than Epistenzon, he simply has them in another, implicit or subjective form,
'priva te' and not 'public'; in the form of a natural capacity for thought which
ailows philosophy to daim to begin, and to begin without presuppositions. (DR
129-30/165)
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102
103
\'\Te will see that Deleuze presents a similar need for an encounter.
\'\That, therefore, is the difference between Deleuze and Feuerbach?
While Deleuze's concept of the image of thought is prefigured by
Feuerbach, the difference between them emerges when we consider
what it is that we encounter that provides a beginning to philosophy. For
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l05
106
see; it is hard, cold, and can be handled without clifficulty; if you rap it with your
lmuckles, it makes a sound. ln short, it has everything which appears necessary
for a body to be known as distinctly as possible. But even as 1 speak, 1 put the
wax by the fire, and look: the residual taste is eliminated, the smell goes away,
the colour changes, the shape is lost, and the size increases; it becomes liquid
and hot; you can harclly touch it, and if you strike it, it no longer makes a sound.
But does the same wax remain? It must be admitted that it does; no one denies
it, no one thinks otherwise. So what was it in the wax that 1 understood with
such distinctness? Evidently none of the features which 1 arrived at by means of
the senses; for whatever came under taste, smell, sight, touch or hem'ing has now
altered- yet the wax remains. (Descartes 1984a: 20)
Descartes' immediate point is that while we might daim that the objects
we find around us are more immediately known to us than our own ego,
in fact we do not perceive abjects at aIl, as is made dear by the fact that
aIl of the perceivable properties of a piece of wax can change while we
still continue to see it as the same piece of wax. If it isn't perception that
gives unity to objects, then what is it? Descartes continues his analysis by
bringing in the foIlowing example:
But then if 1 look out of the window and see men crossing the square, as 1 just
happen to have done, 1 normally say that 1 see the men themselves, just as 1
say that l see the wax. Yet do l see any more than hats and coats which could
conceal automatons? Ijudge that they are men. And so something 1 thought 1
was seeing with my eyes is in fact grasped solely by the faculty of judgement
which is in my mind. (Descartes 1984a: 21)
In this sense, it is the subject that is responsible for unifying the various
properties of the object into a coherent object, since the possibility of
error shows that the object is not given to us as such. For this reason,
even when we are dealing with objects outside of the subject, we are still
in a position whereby we only recog11ise them as objects in so far as they
are brought together by the thinking subject into a unity under the form
of an object. In this case too, therefore, we can note that we are in a position whereby what is perceived (or what we take to be important in what
is perceived) is a function of reason itself. The faculty of the subject that
is responsible for unifying the different sense modalities of the subject
by relating them to the structure of an object is, for Descartes, common
sense, or sensus cammunis. If we look at the example of misrecognition,
we can say that what leads us to posit the hats and coats as men is the
107
fact that different sense impressions are all in accordance. This accord
leads us to rnisrecognise them as properties of people. As Deleuze notes,
the concepts of cornrnon sense and recognition are therefore intimately
linked: 'An object is recognised, however, when one faculty locates it
as identical to that of another, or rather when all the faculties together
relate their given and relate themselves to a form of identity in the
object' (DR 133/169).
Common sense in fact refers to two kinds of commonality. On the one
hand, it allows different sense modalities to be related to one another,
and brought together into a judgement. On this reading, it literally
presents what is common to the senses. On the other hand, it is also intimately linked with the 'everybody knows' which was the first postulate
of the image ofthought. Ifwe return to the work oflVlerleau-Ponty, we
can see that the fact that consciousness is 'forgetful of the perspectivism
of my experience' (lVlerleau-Ponty 1962: 70) in positing objects as the
source of my perceptions allows the kind of objective world that makes
objective knowledge, and hence communication, possible. Referring
directly to Descartes' account in the second meditation of the central
role ofjudgement to perception, lVlerleau-Ponty writes that:
like the object, the ide a purports to be the sarne for everybody, valid in ail tirnes
and places, and the individuation of an object in an objective point of tirne and
space finaily appears as the expression of a universal positing power ... l now
refer to rny body only as an idea, to the universe as idea, to the idea of space and
the idea of time. Thus 'objective' thought (in Kierkegaard's sense) is forrned
being that of cornrnon sense and science - which finaily causes us to lose contact
with perceptual experience, of which it is nevertheless the outcorne andnatural
sequel. (l\1erleau-Ponty 1962: 71)
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109
110
1929: B 131-2). As Kant note d, however, it is not necessary for the '1
think' ahvays to accompany our representations, and we often just find
ourselves preoccupied with the world without any explicit reference to
ourselves. In fact, for Kant, co mm on sense is not this '1 think', which
is rather a result of the operation of common sense at a transcendental
level. Common sense is therefore provided by the transcendental unity
of apperception. In this sense, Kant differs from Descartes in that for
Descartes, conunon sense is provided by the cogito, whereas for Kant,
since the transcendental unity of apperception precedes experience to
make it possible, we have what Deleuze caUs a 'logical common sense'
(DR 137/1 73) that makes possible the analytical unity of the '1 think'.
We can further note that whereas Descartes proceeds from the axiom of
the cogito to common sense, and the recognition of the object through
judgement, for Kant, common sense and the notion of the object presuppose one another. Thus, as we saw, Kant daims that the subject
can only recognise itself as a self if it is able to distinguish itself from its
representations. This in turn is only possible if those representations are
taken as referring beyond themselves to the object. But the notion of an
object is in turn only possible as the result of the synthe tic activity of the
subject: Oit is the unity of consciousness that alone constitutes the relation
of representations to an object' (Kant 1929: B 137). Deleuze therefore
daims that what Kant has really provided is a corrective to Descartes'
project: 'Therefore the real (synthe tic) formula of the cogito is: l think
myself and in thinking myself, l think the object in general to which l
relate a represented diversity' (KCP 15-16/14).
VVe can now bring in the fourth postulate of the image of thought:
representation. We have already encountered representation in Chapter
1 of Difference and Repetition, where Deleuze dassified Aristotle's logic as a
type of representation. There, Deleuze daimed that:
There are four principal 'aspects' to reason, in so far as it is the medium of
representation: identity in the form of the undetemzined concept; analogy, in the
relationship between ultimate detenninable concepts; opposition, in the relations
between detenninations within concepts; resemblance, in the determined object of
the concept itself. (DR 29/37)
These four 'shackles' of representation mapped onto Aristotle's taxonomy of species and genera. They can also be mapped on to the various
moments of the transcendental deduction as foUows. First, in order to
have experience, we need to relate our different representations to a
III
112
Socrates argues that if we look, for instance, at the length of the finger,
we will find that it is long or short depending on what we are contrasting that length with. These properties are relative, and depend on other
f<:atures of the world (other fingers) for their determination. As such,
we cannot, even in perfect perceptual conditions, determine whether
something is short or long, as it will have both properties, depending
on ""hat we compare it to. As each object 'comes into being and passes
away' (Plato 1997b: 527b), even properties that are not necessarily relative, such as beauty, will at some moments apply to an object and at
other moments no longer apply. Thinking therefore ernerges because of
an inherent feature of the object: the contradictory status of the properties which we find within it. When the soul encounters an object of this
kind, it 'would then be puzzled, would look for an answer, would stir up
113
its understanding, and would ask what the one [object] itself is' (Plato
1997b: 524e). The senses themselves, therefore, 'summon' a form of
thinking that does not relate to the sensible, or even to the object that is
under the consideration of the sensible. For Deleuze, the nature of this
encounter that 'forces us to think' (DR 139/176) will be broader than
just sensible properties, and as examples of encounters, he suggests those
with 'Socrates, a temple, or a demon' (DR 139/176).
In order to answer the question of what thinking is, Deleuze turns to
Plato's account of anamnesis in the Phaedo. The Phaedo chronicles the
la st few hours of Socrates' life. Socrates seeks to assuage his friends' fears
about his impending death by showing that the philosopher is in fact
grateful for death, and its concomitant separation of the soul from the
body, 'because the body confuses the soul and does not allow it to acquire
truth and wisdom whenever it is associated with it' (Plato 1997 a: 66a).
Our concern will be not so much with this doctrine, but instead with the
doctrine of the Ideas, and the related doctrine of anamnesis. To begin
with, there is an extension of the critique of the sensible in the Phaedo. If
we consider a notion su ch as equality, we can note that two sticks can
appear to be equal in length, or two stones to be equal in size. '!\Te can
further note that in different circumstances, the length and size of these
sets of objects may appear to be unequal. In these cases, we therefore
become aware that objects that are equal are not themselves the source
of our notion of the Equal, as we think that the Equal itself must always
be equal to itself. Similarly, other properties that we encounter in the
world, such as justice, or beauty, are not encountered in objects that
are pUl'ely just, or purely beautiful. Rather, as the world is an imperfect
place, these objects amenable to sensation are always deficient cases of
justice or beauty. 'Our sense perceptions must surely rnake us realize that
aIl that we perceive through them is striving to reach that which is Equal
but faIls short of it' (Plato 1997 a: 75b). The implication of this is that as
weIl as the deficient sensory impression of equal or beautiful objects, we
are also given by these sensory impressions another object, namely that
in relation to which the object is se en to be deficient. Socrates takes this
object to be difierent in kind to a sensory object. It is for this reason that
he is dismissive of answers to questions su ch as 'what is beauty?' or 'what
is justice?' in earlier dialogues that define them in terms of empirical
objects. Rather, the deficiency of sensory experience relates us to Ideas.
At this point, there are two questions we need to address. First, how do
we gain access to Ideas, and second, what are Ideas?
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115
the shortest section (and least satisfactory form of relation) to the longest,
we first have types of knowledge concerning the visible world: images
such as shadows and reftections in water (Plato 1997b: 50ge), then
visible objects that these shadows and reftections are images of, such as
'the animaIs around us, aU the plants, and the whole dass of manufactured things' (Plato 1997b: 51 Oa). FoUowing this, we have the two kinds
ofknowledge that deal with the intelligible world. The first still proceeds
on the basis of iInages drawn from the visible world, but is not interested
in the determinate properties of the image itself. Geometry, for instance,
uses images, such as a triangle, to develop general truths about aIl triangles. It proceeds on the basis of hypotheses and uses images solely as
guides. The second intelligible understanding of the Ideas themselves
dispenses with any notion of an image of thought, and relates directly
to Ideas by means of recollection. Rather than having one object that
thinking relates to under different aspects, as in the common sense of
Descartes and Kant, we therefore have a whole series of objects. Each
of these objects is within the domain of a different faculty of thinking,
with imagination and opinion relating to objects of the visible world,
and thought and understanding relating to the two classes of object of
the intelligible world. These faculties do not converge on one object, but
instead simultaneously relate to two separate objects. Thus, to judge that
two sticks are equal to one another, we do not simply need the relation of
the fa culty of opinion to the sticks themselves, but also the relation of the
faculty of understanding to the Idea of the Equal, in order to recognise
the presence in the visible world of a deficient copy of the Ideas.
For Plato, an encounter with the sensible triggers the recollection
of something different in kind from the sensible itself. There is a communication that takes place in terms of difference. This bears a remarkable similarity to the account of the Bergsonian theory of memory that
we looked at in the previous chapter (2.4). There, the pure past was
brought into relation with the present by the future. In spite of this,
there was a fundamental difference in kind beh,yeen the h,yo moments,
as the present was understood in tenus of actuality, and the past was
understood in terms of virtuality. VVe can further note that, just as in the
case of Deleuze's account of the three syntheses in the previous chapter
where the present and the past were generated in parallel, such that
the past was not a past of passed presents here too we find that what is
recollected is something that is never experienced by the actual empirical individu al themselves, since it is prior to the soul's connection to the
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117
118
a totality. ""Te calI that sublime which is absolutely large' (Kant 1987:
25). Now, clearly, it is the case that, injact, the shapeless mountains that
we encounter, or the raging sea, are not absolutely large, as there could
be larger mountains, and more ferocious ston11S. For this reason, the
objects that generate the feeling of sublimity are not actually themselves
sublime, since even the size of the mountains is relative. Rather, the
feeling of sublimity is internaI, but is elicited by certain objects that are
appropriate to its presentation.
Extremely large objects can thus be suggestive of the notion of the
infinitely large. When we encounter a 'shapeless mountain mass', while
we may be able to determine their height mathematicalIy, through the
use of the understanding, we are un able to bring together the object into
a single intuition - to see it aIl at once. Either it is sim ply too big, and so
we apprehend the object through a series of moments that appears to
go on to infinity, or else the size of the object me ans that the parts of the
object that we began by apprehending faIl away from the imagination
before we are able to reach the final elements. On this basis, Kant gives
the following characterisation of the sublime:
Nature is thus sublime in those of its appearances, whose intuition brings with
them the idea of their infinity. Now the latter cannot happen, otherwi'le than
through the inadequacy of the greatest effort of our imagination in the estimation ofan object's mag11tude. (Kant 1987: 26)
119
We can see what kind of thing Deleuze has in mind when we look at
his account of the three syntheses of time in Chapter 2 of Difference and
Repetition. As we saw, Deleuze put forward there the daim that memory
and habit were different in kind, but could nonetheless communicate
with one another, with memory able to inform our practicallife through
the structure of habit. As we also saw, what allowed the communication between these faculties was not the legislation of one faculty in
particular, but rather the field of intensive difference, which in turn was
different from either memory or habit, but nonetheless was expressed
in terms of the virtual planes of co-existent memory, or the actual succession of impressions. Deleuze here therefore differs from Kant in that
Kant associa tes what is communicated with the Ideas of reason, whereas
Deleuze daims that we need to associate the Idea not with any particular faculty, not with, for instance, 'the pure cogitanda but rather [with]
those instances which go fron1 sensibility to thought and thought to
sensibility, capable of engendering in each case, according to their own
order, the limit- or transcendent-object of each faculty' (DR 146/183).
We will have to wait for the next chapter to see exactly what the nature
of these instances is.
(146-53/184-91)
The postulate of the negative or error is the first of the second set of
postulates. These postulates together present a model oflanguage found
in the image of thought that emerges from taking the proposition as
the primaI)' structure of expression. As we saw in thc previous chapter,
representation took the subject to be ready-made, and pre-existing the
120
operation of synthesis. It was also the case that the notion of the subject
and the notion of an object were interdependent. As we shall see, the
four remaining postulates of the image of thought aIl take knowledge to
relate to an already constituted field of objects. These four remaining
postulates are: the postulate of the negative, or of error, the postulate
of the logical function, or the proposition, the postulate of modality, or
solutions, and the postulate of the end, or ofknowledge (DR 167/207).
The first of these, the postulate of the negative, or error, is the daim
that the failure of thinking must be understood pUl'ely in terms of the
failure of the structure of recognition, that is, error is purely misrecognition. To see why representation might make this daim, we can return
to the example of Descartes. As we have seen, Descartes' aim is to
prove certain propositions that are dearly and distinctly perceived, and
therefore certain. In order to do so, in the Meditations, he instigates the
method of doubt: 'reason now leads me to think that I should hold back
my assent from opinions that are not completely certain and indubitable
just as carefully as l do from those which are patently false' (Descartes
1984a: 12). As Descartes makes dear here, it is ?(Jason that leads him to
introduce the method of doubt, and it is reason that is the arbiter of the
success of the operation. In dassical scepticism, the method of doubt
operates between the faculties to show that none of them can be given
primacy, so we may, for instance, use the fact that a stick looks bent in
water to show that there is a disparity benveen reason and the senses, and
so neither can be trusted. Descartes' use of scepticism is instead a method
for finding those propositions that borrow nothing from any faculty apart
from reason. The aim of methodological doubt is therefore to create a
space for reason to conduct its enquiries into the structure of the world,
since 'deduction or pure inference of one thing from another can never
be performed wrongly by an intellect which is in the least degTee rational'
(Descartes 1985b: 12). If the intellect is incapable of error, however, we
have the difficulty of explaining how error can and does occur, particularIy given Descartes' contention that we were created by a beneficent
and non-deceiving God. Descartes' solution to this central problem of
his method is to situate error in the relationship between the faculties.
That is, error is simply a failure of good sense. In the lHeditations, it is the
mismatch between the large domain of the will, which has no concern
over truth, and the sm aller domain of reason which leads to error. Here,
the willleads us to assent to daims that go beyond the truths that can be
deduced by reason. In this sense, the Meditations can be seen as a proce-
121
It is not the case that error has always been seen as a failure of good
sense caused by the interference of another faculty with reason. For
Kant, thinking is discursive, that is, it is about something. As we saw in
the previous chapter, Kant's daim was that thinking relied on the interrelation between fculties. Now, if this is the case, then for Kant, the
fculties themselves are capable of falling into error precisely when they
operate without reference to the other faculties. Thus, for Kant, reason
Falls into error when it mistakes its task of unifying knowledge for the
122
As we shall see in the next chapter, while Kant's theory of Ideas and
transcendental illusion is an important advance for Deleuze, representing something 'radically different from the extrinsic mechanism of error'
(DR 150/188), it ultimately fails to overturn the image of thought of
representation.
123
without words, and even in animaIs and infants who do not possess language.
Objeetively, the assertion, iftrue, 'indieates' a faet: iffalse, it intends to 'indicate'
a fact, but fails to do so. There are sorne assertions, narnely those whieh assert
present states of the speaker which he notices, in which what is 'expressed' and
what is 'indieated' are identieal; but in general these two are different. The 'signifieance' of a sentence is what it 'expresses'. Thus true and false sentences are
equally significant, but a string of words which cannot express any state of the
speaker is nonsensical. (Russell 1940: 171)
Russell here is making a distinction between the truth value of a proposition (whether it is true or false), and the meaning of a proposition.
Truth or falsity determine whether something is successfully inclicated
(in Russell's tenus) or designated (in Deleuze's terms) by a proposition.
Designation is simply a relation whereby either the structure of the
proposition minors a state of affairs in the world (and hence is true),
or does not (and hence is faIse). For Russell, truth and falsity cannot
capture the significance, or sense, of a proposition, because what a
proposition expresses is not a correspondence bet:\veen a state of affairs
and a proposition, but rather the beliefs of the speaker who asserts the
proposition. While whether a proposition succeeds in indicating a fact
or not depends on the truth or falsity of a proposition, since the sense
of a proposition depends on the psychological belief.'3 of the speaker, its
significance or lack thereof is not dependent on truth or falsity. A proposition can still 'make sense', even though it is false. Thus, we have to be
able to separate sense from truth.
Deleuze sees Russell's kind of account as essentially providing a transc endentaI model of the conditions of the possibility of a proposition
being true or false. In other words, it is an account of what counts as
a significant proposition. Nonetheless, Deleuze daims that this kind of
model of sense suffers from the same difficulties as Kant's transcendental
model of experience. We can note the following similarities between the
two accounts. First, sense is abstract and broader than the propositions
it relates to: 'the condition [sense] must retain an extension larger than
that which is conditioned [the true or false]' (DR 153/191). As Russell
notes, 'we may say that whatever is asserted by a significant sentence
has a certain kind of possibility' (Russell 1940: 170). That is, whereas
designation aims at an actual state of affairs, sense for Russell operates
according to possible states of affairs. Something is sigl1ificant if it cOl/ld
be the case. Second, and a consequence of this, sense merely repeats
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125
(DR 158/196)
126
127
128
Chapter 4 will give an account of the nature oflearning, and with it, an
account of the transcendental structure of the Idea that makes learning
possible.
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130
Ideas is 'only an idea' since our inability to determine these Ideas does
not mean that they do not relate to objects. In this sense, the Idea
appears to fulfil Deleuze's requirements for a notion of a problem that is
real, an 'indispensible condition of aIl practical employment of reason'
(Kant 1929: A328/B385), but is not reliant on the empirical content of
experience itself(the field of solutions). While Deleuze will take up many
of the features of this account, ultimately he will argue that Kant has
ti:tiled to properly escape fi'om the image of thought Deleuze presented
in Chapter 3. In order to demonstrate this, he introduces three categories: the indeterminate, the determinable and the determined.
First, the Idea itself is undetermined. That is, the object of the Idea
cannot be presented in a determinate fonn in intuition. Taking, for
instance, the Idea of God, which Kant considers to be the ground of
aU appearances, it is dear that we cannot know it, because the grounds
of appearance are not themselves appearances: 'Outside of this field,
[the categories] are merely titles of concepts, which we may admit, but
through which we can understand nothing' (Kant 1929: A696/B794).
It is nonetheless a concept that we can determine to some extent by
analogy with our own empirical intelligence. In doing so, however, we
only determine it 'in respect if tlze empl([)'nzent of our reason in respect to tlze
worlel' (Kant 1929: A698/B726). That is, the concept of God is determinable (we can specify what properties inhere in it) by analogy to the
empirical world, but on condition that we only use this Idea to allow us
to unify our understanding of the world further (by seeing the world as
ifit were created for an intelligible purpose, for instance). Furthermore,
the Idea is also present in empirical objects, in so far as we consider
them to be completely determined. Ifwe are going to consider empirical
objects as being completely specifiable in terms of intelligible properties,
Kant daims that we need the Idea ofGod. In order to specify something
completely in terms of the properties that it has, we need some kind of
account of aIl properties it is possible for an object to possess, so that
we can determine which of each pair of properties (the property and its
contrary) inheres in the object. 'The Ideal is, therefore, the archetype
(pmto!J'Pon) of aIl things, which one and aU, as imperfect copies (ec!)'Pa),
derive from it the material of their possibility, while approximating
to it in various degTees' (Kant 1929: A578/B606). Now, as Deleuze
notes, these three moments of the Idea together could be used to make
up a genetic account of actualisation. The Idea as undetermined provides a moment which differs in kind from the actual, and hence faIls
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132
In order to see why the calculus is important for Deleuze, it's necessary to outline in general what the calculus is. A first approximation is
that the calculus is a field of mathematics dealing with the properties
of points on curves (Boyer 1959: 6). As Boyer notes, this concern with
properties of points on curves is similar to a concern with the properties
of a body in motion, such as its velo city at a given moment in time. If we
wanted to determine the average velo city of a body in motion, we would
determine this by finding a ratio between two quantities, the distance
that the body has travelled in the time period (5), and the time period
itself (t). We could represent this, for instance, in the following form:
average velocity = /).5/ /).t, that is, the difference in displacement over the
period divided by the difference in time (with 11 symbolising difference).
This would give us an average velocity in terms of metres per second, or
miles per hour. While this might be effective for average velocities, the
problem emerges when we want to determine the velocity of the body
at a particular moment in time. When we are talking about a particular
moment, we are no longer talking about average velocity, but rather
now about instantaneous velo city. If a body is moving at constant speed,
th en the average and instantaneous velocities of the body will coincide,
but if a body is accelerating or decelerating, however, then its instantaneous velocity will be constantly changing, and so we cannot determine
it based on its average velocity.
Leibniz's solution to this dilemma was to suggest that if we take the
average velo city of the body over a time, beginning with the point we are
trying to determine the instantaneous velocity for, and slowly decrease
the slice oftime we are using to divide the distance travelled, the average
velo city will approach the instantaneous velocity. That is, the smaller the
segrnent oftime over which we determine the average velocity, the doser
it will be to the instantaneous velocity at a point. If we extend this idea,
and determine the average velo city over an infinitesimally smaIl stretch
of time, then, because this stretch of time is for aIl intents and pm'poses
0, the average velocity will actuaIly equal the instantaneous velo city.
Now, what we have been dealing with here is a relation between two
quantities, distance and time. One of the main concerns of mathematics
is with relations more generally, and the calculus in fact provides a way
of accounting for relations between varying quantities in general, that is,
for aIl kinds of continuous curves. We represent curves in tenus of mathematical equations, and so the differential calculus is a procedure we can
apply to mathematical equations. In this respect, the equation that gen-
133
erates the curve is known as the primitive function. When we apply the
calculus to the equation of a curve, we get what is known as the derivative, which is an equation that gives us the gradient of the curve at each
point (in the example of the body in motion, the velo city at each point).
For the average velocity between two points, we used the symbol b..s/ b..t,
where b..s indicates an arbitrary distance, and b..t represents the stretch of
time the body takes to travel that distance, but the calculus is not concerned with average velocities, which rely on finite differences, but with
infinitesimal differences, otherwise lmown as differentials. In order to
represent infinitesimal differences, Leibniz introduces the symbolism 4y/
dx. As we saw in Chapter 1, relations for Aristotle were defined in terms
of negation. The differential calculus provides the possibility of developing a the ory of relations that relies on reciprocal detennination of the
elements, 4)' and dx. Deleuze daims that 'there is a treasure buried in the
old so-called barbarie or pre-scientific interpretations of the differential
calculus' (DR 170/217). This treasure is covered over by two mistakes:
'it is a mistake to tie the value of the symbol dx to the existence of infinitesimals; it is equally a mistake to refuse it any ontological or gnoseological value in the name of a refusaI of the latter' (DR 170/217). In order
to understand why we might make these two mistakes, we need to look
further at what the term, dx, signifies. Now, as we saw, dx represents for
Leibniz an infinitesimal distance between two points. When we want to
use this to determine instantaneous velocity, however, we encounter a
contradiction. To see this, we can turn to the account of the infinitesimal
of L'Hpital, one of the earliest popularisers of the calculus:
PastuZate 1. Grant that two quantities, whose difference is an infinitely small
quantity, may be taken (or used) indifferently for each other: or (which is the
same thing) that a quantity, which is increased or decreased only by an infinitely
smaller quantity, may be considered as remaining the same. (L'Hpital 1969:
314)
This postulate is needed because dx must be seen as having a de terminate value in order to form a ratio, 4)1/ dt', but aiso has to have no
magnitude (=0) in order to capture the gradient at a point, rather than
across a length of the curve. Clearly, this is a fundamental difficulty,
since the consistency of mathematics is threatened by taking a variable simultaneously to have and to lack a magnitude. In this sense, it
appears that Deleuze is right in holding it to be a mistake to give the
differential a sensible magnitude, even if this were infinitely small, and
134
135
circurnference in itself. This is true for equations of ail curves, and finaily for
any variable function, so cailed because they give a continuous quantity and
its symbol. It is the individual curve or function which is represented, and not
the universal, which, accordingly, remains without a symbol, and has not been
considered mathematicaily by Descartes. (Bordas-Demoulin 1843: 133)
136
137
our faculty of thinking. Reason clemands of us therefore an infinite progression through which that which is thought is perpetually increased, the given,
however being decreased to an infinitesimal. (J.\!laimon 1791: 169)
Rather than seeing what is given as merely the passive matter of the
faculty of intuition, lVlaimon sees it simply as that which the intellect
cannot think. If we did not have a Iimited faculty of thought, but instead
had an infinite understanding, the entirety of what is for us given would
be thought, and so the given itself would disappear. To this extent,
lVlaimon's account is rather like Leibniz's, with the given empirical
object being a confused form of perception of the true nature of things.
Whereas for Leibniz, the difference between the thought of a finite being
and an infinite being was a difirence in degree (a greater intellect would
have no need to perceive conceptuai relations under the confused form
of space), for Maimon there is a difference in kind between the two kinds
of thinking. As we have seen, the infinitesimal cannot be given a sensible
interpretation without contradiction. Nonetheless, when we relate two
infinitesimals to each other in a differential function (4y/ d>.,), we derive a
formula that does have a sensible interpretation (the formula for the gradient of the points on a curve). The differential is thus like the Kantian
noumenon, which can be thought, but cannot be presented in intuition.
Maimon takes this mathematical interpretation of the differential, and
gives it a transcendentai interpretation, so the differential, dx, becomes a
symbol of the noumenal grounds for the synthesis of phenomena:
These clifferentials of objects are the so-called lZownena; but the objects themselves arising from them are the p/zenomena. \Vith respect to intuition = 0, the
differential of any such object is dx = 0, 4)' = 0 etc.; however, the: relations are
not 0, but can rather be given determinately in the intuitions arising from
them. (Maimon 2010: 32)
138
rules governing the way it arises, it can only think of it as given, that
is, through sensible intuition. Thus, rather than the extrinsic relation
between the faculties, lVlaimon shows how intuition emerges through
the finite intellect's inability to think the relations of differentials aU at
once. Instead of thinking the object as a completed synthesis, it must be
thought as a synthesis in process, as an 'arising' or 'Rowing'. Now, as
Guroult makes dear, the fact that we cannot simply think the object
means that we become subject to a transcendental illusion:
The imagination is thus never conscious of anything other than representations;
it therefore has, inevitably, the illusion that ail of the objects of consciousness
are representations; it is led by this to also consider the original object or the
complete synthesis as a representation. (Guroult 1929: 66)
It is this illusion that leads us to see problems in the sa me terms as solutions. We can therefore see in Maimon tvvo different modes of th in king.
One that opera tes in terms of intuition, and provides a philosophy of
conditioning, and another that provides a genetic model of thought that
attempts to trace the genesis of the given bad. to its differential roots.
We can now present the alternative the ory of the Idea. Rather than
seeing it as a relation between three moments, two ofwhich are extrinsic, the differential calculus relates the three moments intrinsically. It is
undetermined in that the differential, dx, cannot be given in intuition.
When it is put into a relation, su ch as 4)1/ dx, it becomes determinable, as
it specifies the complete range of values the function can take. Finally,
it is determined in tenns of specific values that the function takes at
particular moments (the instantaneous velo city of a particular point in
time in our prior example). Whereas the infinite understanding thinks
the curve as a whole, we can only think the process of generation of the
curve, equivalent to the actual evolution of the object in intuition. As
Guroult puts it, 'the differential is, then, the noumenon (that which is
simply thought by the intellect), the source of phenomena (which appear
in intuition)' (Guroult 1929: 60).
The final figure Deleuze introduces is Wronski. The mathematician,
J oseph-Louis Lagrange, tried to show that we could give an algebraic
interpretation of the calculus, representing it as an infinite series of
tenns using his notion of functions. In the introduction to his T7zeorie des
Fonctions Anab'tiques, he makes the daim that 'the Analysis which is popularly called transcendental or infinitesimal is at root only the Analysis of
primitive and derived functions, and that the differential and integral
139
Calculi are, speaking properly, only the calculation of these same functions' (LagTange, quoted in Grattin-Guinness 1980: 100-1). Lagrange's
daim that the calculus can be understood purely in terms of algebra
would, if successful, rem ove the need for the kind of 'barbaric' interpretation that Deleuze puts forward, since we would no longer need to give
a metaphysical interpretation of the differential. It is to save the possibility of a 'barbaric' interpretation that Deleuze introduces Wronski. As
with the other thinkers of the calculus discussed in this chapter, Wronski
holds that there is a fundamental distinction between the differential and
normal quantity:
It is this important transcendental distinction that is the crux of the metaphysics of Calculus. In effect, the finite quantities and indefinite quantities, that
is to say, infinitesimal quantities, belong to two entirely different, even heterogeneous, classes of knowledge: the finite quantities relate to the objects of
our cognition, and infinitesimal quantities relate to the generation of this same
cognition, so that each ofthese classes must have lmowledge ofproper laws, and
it is obviously in the distinction of these laws that the crux of the metaphysics of
infinitesimal amounts is found. (Hoen Wronski 1814: 35)
Now, while Lagrange believes that he has escaped from the need to
introduce infinitesimals by resorting to the (algebraic) indefinite, which
can be understood purely in algebraic terms, Wronski's daim is that the
indefinite itself cannot be understood without the infinitesimal. To bring
the infinitesimal into the domain of cognition, it has to be presented in
an intuition, which can be done purely as an indeterminate quantity.
The indeterminate quantity that is at the centre ofLagrange's method is
thus, for Wronski, still reliant on the differential.
In daiming that Lagrange's method still relies on the differential,
Wronski does not deny that, precisely because it is derived fr0l11 it, it is
still correct. In fact, Lagrange's method produces a series of diflerentials
which allow us to distinguish between two kinds of points on the line:
singular points and ordinary points. If we remember our initial example
of the calculus, relating distance to time gave us the velo city of a body.
If we differentiate this equation once more, we will obtain a relationship
between velocity and time, which is the acceleration of a body. Points on
this curve, such as where it is fiat, indicate singular features of the movement of the body, such as in this case the point at which it is travelling
at constant motion. In more abstract curves, points where the gradient
is 0/0, or is null or infinite, define points where the nature of the curve
140
changes. Potentiality thus defines the points at which the nature of the
relationship between the terms radically changes.
We can tie these three mornents together to develop an account of
the Idea where its three moments, the indeterminate, the determinable
and the determined, are intrinsic to it. As we saw when we looked at
Bordas-Dernoulin, the diflerentials themselves, 4)' and dx, are completely
undetermined with respect to representation, and hence to the field of
solutions. Nonetheless, when brought into relation with each other, they
give us an equation that is determinable. This equation gives us the rates
of change of a function at each point in time (or more correctly, for
any value of x). Such an equation, as Wronski shows, contains singular
points that determine the points on the curve where its nature radically
changes. That is, by specifying a value of x, we can determine the rate
of change at any point. Specifying a value of x, therefore de termines
the Idea. We therefore have a particular determined value (intuition), a
determinable equation that subsumes it (the concept), and a field of differentials themselves which engenders both the determinable and determination. The differential, as problem, therefore contains the solution
intrinsically, rather than simply being interpreted in terms of it. While
this account may seem abstract for now, as we shall see in the following
four sections, we can develop concrete examples of the Idea that operate
according to this schema.
The remainder of Deleuze's discussion of the difierential calculus
draws the consequences from this understanding of the calculus as
Idea. As Deleuze notes, 'the interpretation of the calculus has indeed
taken the form of asking whether infinitesimals are real or fictive' (DR
176/223). As Wronski's account makes dear, however, this question
has traditionally been interpreted in tenus of whether differentials can
be an object of (representational) cognition, or are fictions. Once we
recognise that they are of a different order to what they engender, 'the
first alternative - real or fictive? - collapses' (DR 178/225). Likewise,
Deleuze notes that the alternative between seeing the calculus as operating in terms of an infinitesimal, or modern finitist interpretations that
seek to dispense with the infinitesimal, is equally invalid. Deleuze's daim
is that both of these interpretations are ways of describing magnitudes,
but as these magnitudes operate within the domain of representation,
neither of these terms is adequate to the differential. Finally, as we have
seen, on Deleuze's reading, the emphasis is not on the primitive function, but on the differential, d'X, as constitutive of the primitive function.
141
(DR 178-9/226)
142
143
'spatio-temporal relations no doubt retain multiplicity, but lose interiority'. That is, the elements are not intrinsically related to one another, but
are simply related by occupying a certain space together. On the other
hand, 'concepts of the understanding retain interiority, but lose multiplicity' (DR 183/231). When we de termine a concept (man is a rational
animal, for instance), we do so by subsuming it under another. As such,
while they are intrinsically connected, they form a unity, rather than a
multiplicity. FinaIly, 'a differential relation, must be actualised in diverse
spatio-temporal relationslzips, at the same time as its elements are actually
incarnated in a variety of terms and fonns' (DR 183/231). That is, if
the Idea is to provide some kind of explanation of the structure of the
world, it must be applicable to more than one situation; it must capture
relations in more than one domain. AlI of these features can be found in
the differential calculus, but to explain how this account functions more
generaIly, Deleuze provides three examples ofldeas in non-mathematical fields: atomism as a physical Idea, the organism as a biological Idea,
and social Ideas.
144
the following account of how atoms enter into relations with one
another:
In this connection, 1 am anxious that you should grasp a further point: when the
atoms are being drawn downward through the void by theu: property ofweight,
at absolutely unpredictable times and places they deftect slightly from their
straight course, to a degree that could be described as no more than a shift of
movement. If they were not apt to swerve, ail would faIl downward through the
unfathomable void like drops of rain; no collisions between primai)' elements
would occur, and no blows would be effected, with the result that nature would
never have created anythu1g. (Lucretius 2001: 40-1)
It is through this swerve (clzamen) that atoms come into contact with one
another. Deleuze's analysis of this situation begins with the daim that
since the void provides no resistance, it is not the case that the atoms
simply have an undefined location. Rather, moving at the speed of
thought, they are strictly speaking 'non-localisable'. In this sense, they
operate much like the differential, dx, in that they are undetermined,
lacking one of the key characteristics of 'sensible form'. Second, they
can only be given in sensibility though a reciprocal relation formed
between them, just as it is only through the differential relation qy/
dx that differentials become determinate. In the case of atomism, this
reciprocal relation is provided by the clin amen, which allows a collection of atoms to take on sensible significance. Finally, as the atoms are
capable of forming diverse relationships amongst themselves, they can
be 'actualised in diverse spatio-temporal relationslzips' (DR 183/231).
Atomism therefore appears to me et Deleuze's criteria for the Idea. In
fact, however, Deleuze daims it fails to exemplify the Idea fully, because
the atom is still too tied to sensible determinations. Epicurus' account of
its nature is based on an analogy with sensible bodies: 'We must suppose
that the atoms do not possess any of the qualities belonging to perceptible things, except shape, weight and size, and aIl that necessarily goes
with shape' (Epicurus 1926: 31).
145
146
147
148
that level than the pre-Newtonian 'physicist' could osee' the law of attraction in
falling bodies, or the pre-Lavoisierian chemist could 'see' oxygen in 'dephlogisticated' air. Naturally, just as bodies were 'seen' to faU before Newton, the
'exploitation' of the majority of men by a minority was 'seen' before l\IIarx.
(Althusser and Balibar 2009: 181)
The Idea, in the lVlarxist sense, thus allows us to get away frorn the
anthropomorphic and historicist study of surface structures, and hence
to develop a science of society.
149
8
Figure 2: Conie sections
<E
bola
Ela
150
Each of these CUlves has different singular points (points where the
gradient is 0, null or infinite), despite the fact that all of the curves are
created from the same fundamental shape. In a non-mathematical field,
we can note that Geoffroy's comparative anatomy relies on the fact that
the same structure is to be found in the relations between the bones of
aIl animaIs. N evertheless, the singular points will vary within species, so
the same bones that attach the jaw to the skuIl in fish are found in the
inner ear in mammals. Deleuze explains the final dimension of variety,
that of depth, with an example fi'om the mathematical theory of groups.
He gives the example of 'the addition of real numbers and the composition of displacements' in this context (DR 187/236). As the structuralist
rnathematical collective, Bourbaki, note d, the addition of real numbers
and the composition of displacements traditionaIly belong to two very
different fields of mathematics, since one involves discrete units, and one
continuous measurement:
quite apart fi:om applied mathematics, there has a1ways existed a duali'3m
between the origins of geometry and of arithmetic (certainly in their elementary
aspects), since the latter was at the start a science of dis crete magnitude, while
the former has always been a science of continuous extent; these 1:\'\10 aspects
have brought about two points of view which have been in opposition to each
other since the discovery of irrationals. (Bourbaki 1950: 221-2)
151
152
exhibit. Depending on how the elements are related to one another, different states of affairs will be generated.
Clearly, if an Idea is to be understood as forming a multiplicity of
interpenetrating elements, then it cannot have the same nature as states
of affairs. Elements in states of affairs are determined in an opposite
manner to the interpenetrative structure of perplication, namely by
determining their limits (what they are not). Furthermore, we can see
that just as problems were immanent to their solutions, the genetic
conditions for states of affairs (Ideas) are simultaneous with states of
affairs themselves. Thus, for Epicurus, atoms co-existed with the sensible
objects that they constituted, and for Althusser, the mode of production
co-existed with the actual relations that it determined. We thus have two
series that differ in kind: actual events that occur within the world, and
the ideal events of 'sections, ablations, adjunctions' that engender them
(DR 188/237).
l want to jump ahead somewhat now, to introduce the related discussion of the Idea and possibility. We have already seen that the Idea
can give rise to different actual situations; so, for instance, Geoffroy's
unit y of composition provides the rules for generating the anatomical
structure of different animaIs, and Marx's mode of production gives the
sh"ucture underlying different real social organisations. Deleuze defines
the structure of the Idea as being virtual. Now, Deleuze introduces three
daims about the nature of the virtual that need to be explored. It is 'real
wid10ut being actual, differentiated without being differenciated, and
complete without being entire' (DR 214/266). l want to go through
these different daims, contrasting them with the structure of possibility,
which appears at first glance to be a dosely aligned concept. In fact,
Deleuze daims that 'the only danger in aU this is that the virtual cou Id
be confused with the possible' (DR 211/263).
What does it mean to say that the virtual is real without being actual?
If we return to the notion of possibility, we can ask, what happens when
something which is merely possible is realised? \I\Te can begin by following Kant in noting that there is no difference in structure between a
possible object and a real object: 'A hundred real thalers do not contain
the least coin more than a hundred possible thalers' (Kant 1929: A599/
B629). Rather, the difference is purely in the existential status of the two
objects. In order to distinguish a hundred real thalers from a hundred
possible thalers, we need to note that the former exist whereas the latter
do not. Possibility is therefore distinguished from actuality in terms of
153
existence. Now, the virtual is instead 'Real without being actual, ideal
without being abstract' (DR 208/260). Throughout this chapter, we
have se en that Ideas are difierent in kind from actual states of affairs,just
as differentials differ from actual numbers. In this sense, we do not need
to distinguish possibility from actuality in tenus of re a lity, as they can be
distinguished by this difference in kind itself. Nlore than this, however,
the virtual is real to the extent that it provides the structure responsible
for the genesis of the qualities we find in actual entities. 'The reality of
the virtual is structure' (DR 209/260). It provides a complete account
of the structure of the actual state of affairs that results from it, and is no
less a real part of the object than the actual object itself. In this regard,
Deleuze notes that it is 'complete vvithout being entire' (DR 214/266).
Deleuze's point is that the virtual does not rely on any reference to
the actual, although in fact it is always found to be associated with the
object which it engenders. In this sense, it escapes from the limitation of
possibility we discussed in the previous chapter. There, we saw that the
concept of possibility could not give us the sense of an object, because
it merely reduplicated it at a higher transcendent al level of analysis.
As such, a possible object is not complete, since it is dependent on the
notion of a real object to which we add the concept of non-being. The
completeness of the virtual is th us what allows us to understand it as
giving the sense of a proposition, even though it is not whole, since
'every object is double' (DR 209/261).
Finally, the virtual is differentiated without being differenciated. That
is, it operates according to an entirely different procedure of determination to that of the possible. As Deleuze puts it, 'one [the possible] refers to
the form of identity in the concept, whereas the other designates a pure
multiplicity in the Idea which radically exdudes the identical as a prior
condition' (DR 211-12/263). We saw that Chapter 1 of DijJrence and
Repetition deals at length vvith the daim that in order to de termine something through the properties it possesses, we need some kind of concept
of identity. This is because we describe an object by ascribing predicates
to a subject (we differenciate it). The other procedure of determination
generates structural properties by bringing into relation with each other
elements which are in themselves undetermined (they are differentiated,
in the sense of the differentials we looked at in 4.2). Deleuze characterises these two modes of organisation in terms of Leibniz's distinctions
between the dear and confused, and the distinct and obscure. \'\Te saw
in Chapter 1 that Leibniz's understanding of the world ultimately traces
154
it back to the notion of possibility, as God chooses the best of aIl possible
worlds. Nevertheless, in his daim that perception of spatio-temporal
objects is a confused perception of conceptual relations, we have an
important insight into the relationship between virtuality and actuality.
In the .New Essqys on Human Understanding, Leibniz puts forward the daim
that perception of objects is based upon microperceptions below the
threshold of the senses. In support of this theory, he gives the following
analogy:
To give a clearer example of these minute perceptions which we are unable to
pick out from the crowd, 1 like to use the example of the roaring noise of the sea
which impresses itself on us wh en we are standing on the shore. To hear this
noise as we do, we must hear the parts which make up this whole, that is the
noise of each wave, although each of these little noises makes itself known only
when combined confusedly with ail the others, and would not be noticed if the
wave which made it were by itself. (Leibniz 1997: 54)
155
156
of the problem and ... the correlative genesis of cases of solution' (DR
190/239). The two examples Deleuze gives of learning in this context,
learning to swim and learning a foreign language (DR 192/214), are
both favourite examples of Bergson. Bergson's formulation of the
swimming example is as follows:
If we had never se en a man swim, we might say that swirnrning is an impossible
thing, inasrnuch as, to learn to swirn, we must begin by holding ourselves up in
the watel' and, consequently, all'eady lmow how to swirn. Reasoning, in fact,
always nails us down to the solid gl'ound. But if, quite simply, I thl'ow myself
into the water without far, I rnay keep rnyself up weil enough at first by rnerely
struggling, and gradually adapt rnyselfto the new environment: I shall thus have
learnt to swim. So, in theory, there is a kind of absurdity in trying to know otherwise than by intelligence; but if the risk be frankly accepted, action will perhaps
eut the knot that reasoning has tied and will Ilot unloose. (Bergson 1998: 192)
157
In this case, the faculty of speech is rendered possible by the virtual multiplicity, which gives the rules for actual speech production. If we relate
the structure of speech to the Idea, we can see that it contains each of its
moments. The phonemes are undetermined, but able to enter into determinable relations. These relations describe the expressiveness of the language. In turn, an individu al speech act corresponds to the integration
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160
the Platonic account quite dosely. Whereas for Plato, Deleuze daims,
this process leads to a ground in an apodictic principle, for Deleuze, it
instead leads to an ungTound in the problem. This difference between
grounds and ungrounds ultimately simply relates to the fa ct that apodictic principles have the same structure as the system of propositions
they ground (they are amenable to the structure ofjudgement). On the
contrary, the problem differs in kind from the solutions it engenders. As
such, it cannot ground solutions by providing a principle that we know
to be true, because truth is a function of judgement, and the problem
is different in kind to judgements. Thus, rather than a ground, it serves
as an 'ungTOlll1d', destabilising the vision of the world as amenable to
judgement in its entirety. Rather than invoking 'the moral imperative of
predetermined rules' (DR 198/248), Deleuze instead therefore invokes
the notion of the dice throw and decision:
It is rather a question of a throw of the dice, of the whole sky as open space and
of throwing as the only rule. The singular points are on the die; the questions
are the dice themselves; the imperative is to throw. Ideas are the problematic
combinatiolls which result from throws. (DR 198/248)
The imperative is the problematic instance within the state of affairs (the
throw), that points beyond itself, through the question (the dice itselfj,
to the problem that engenders the state of affairs and the problematic
instance itself (the combination on the die). The Ideas result from this
pro cess as the result of our going beyond the state of affairs to find its
conditions. The remaining moment of the analogy to explain is the significance of the points on the dice themselves. We can explain this by
introducing the moment of decision. As we saw in the first case oflearning, we move to the sub-representationallevel by combining 'adjunct
fields', or similar cases, to reach the problem (in Bergson's example,
we relate walking to swimming). Now, depending on which cases we
corn bine to form the problem, our understanding of it will differ. How
we relate together different encounters, and which encounters we relate,
will give a different emphasis to the problem (a different set of singularities), and hence to our Ideas. If the relation of different adjunct fields
gives us different Ideas, then how is it that a given throw is able to 'affirm
the whole of chance' (to provide an objective Idea) (DR 198/248)?
vVhen we looked at the example of the conic section (4.7), we saw that
depending on how we took a section on the cone, we would derive a
different curve, and with it, a different set of singularities. Each of these
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162
in the sense that it is not extensive being, in the same way that the differential was not actual (it did not have a magnitude) without on that basis
not existing (it was, in Wronski's terms, an intensive quantity). As we
have seen, Deleuze takes problems to be interpenetrative multiplicities
which determine aH possible actual states of the object. In this sense, the
problem does not contain any negation. Learning and solving problems
involve a move from the actual state of affairs to the Idea and back again
to a different possible solution. They th us involve differentiation to determine the Idea fllowed by diflrenciation to reach an alternative solution. Now, as Deleuze notes, 'the negative appears neither in the process
of differentiation nor in the process of differenciation' (DR 207/258).
VVe can see that differentiation does not le ad us to posit the negative,
as differentiation involves contracting together actual states of affairs to
form an affirmation. Similarly, differenciation is the process whereby we
extract a state of affairs from the Idea, and as such is also an affirmation
of the Idea. How does negation therefore occur? Once again, Deleuze's
answer is that it is the result of taking the problem to be structured like
a proposition. To make this clear, we can turn to another exarnple from
Bergson:
If 1 choose a volume in my library at random, 1 may put it back on the shelf
after glancing at it and say, 'This is not verse.' Is this what 1 have really seen in
turning over the leaves of the book'? Obviously not. 1 have not seen, 1 Hever shall
see, an absence of verse. 1 have se en prose. But as it is poetry 1 want, 1 express
what 1 find as a function of what 1 am looking for, and instead of saying, 'This
is prose,' 1 say, 'This is not verse.' ln the same way, if the faney takes me to read
prose, and 1 happen on a volume ofverse, 1 shall say, 'This is not prose,' thus
expressing the data of my perception, which shows me verse, in the language of
my expeetation and attention, which are fixed on the ide a of prose and will hear
of nothing else. (Bergson 1998: 221)
163
As Deleuze notes, at the he art of the issue is the daim that opposition
and limitation are interchangeable (DR 203/253), or in other words,
that negation (this is not that) is the way in which something is determined. It should be noted that the issue here is not one of whether
negation actually exists, but of the determination of the problematic,
regardless of whether this determination is taken to be real or logical.
Central to this critique is therefore a different theory of determination
that operates through the reciprocal determination of differentials,
rather than determining objects (either real or conceptual) through limitation and negation. Negation thus only appears when we understand
aIl determination as determination through opposition: 'Forms of the
negative do indeed appear in actual tenns and real relations, but only
in so far as these are cut off from the virtuality which they actualise, and
from the movement of their actualisation' (DR 207/258).
164
165
These dynamisms are not purely spatial, however, and Deleuze takes
up Geoffroy's suggestion that the differences between organisms can be
understood by the relative speeds of the different processes that operate
within the embryo. As such, the embryo constitutes its own tin.1e, which
is defined by the differential relations of these processes. In fact, as
Deleuze suggests, because we are talking about relationships between
distances and time, at the level of the spatio-temporal dynamism, we
cannot separate the dimensions of space and time themselves:
Consider the following example, concerning sterility and fecundity (in the case
of the female sea-urchin and the male annelid): problem - will certain paternal
chromosomes be incorporated into new nuclei, or will they be dispersed into the
protoplasm? question - will they arrive soon enough? (DR 217/270)
166
167
168
223/281]). Carnot's work shows that if the input and output energies
of an engine were equal, the efficiency of the engine would drop to
zero. Thus, difference is fundamentally implicated in 'everything which
happens and everything which appears' (DR 222/280). In line with
Deleuze's distinction between the transcendent al and the empirical,
Deleuze draws from this the principle that 'every phenomenon Hashes in
a signal-sign system' (DR 222/280).just as the difference in the intensity
oftemperature gives rise to work, Deleuze's daim is that more generaIly,
differences in intensity manifest themselves as qualities in the phenomenal world. If this were the final result of thermodynamics, then dearly
it would provide a model of physics commensurate with Deleuze's
metaphysics. Deleuze daims, however, that thermodynamics betrays its
own principle of difference through the introduction of entropy, and the
concomitant equalisation of differences.
If we return to Carnot's engine, we can see that useful work cannot be
done with total efficiency by the engine (except in the impossible situation of a difference between absolute zero and an infinite temperature).
VVhat happens to the heat that isn't converted into work by the engine?
WeIl, this energy is introduced into the output reservoir as heat (just as a
ste am engine heats the environment as weIl as moving the train). Thus,
in the process of doing work, the system reduces the difference between
the two temperatures. It is possible to reverse this process within the
system itselfby doing work (a refrigerator, for instance, is able to reduce
the temperature of objects placed within it), but this work itself will not
be totally efficient. vVe can see this in the case of the refi'igerator if we
take into account its environment. In order to create a temperature
differential, it requires a How of energy from outside of it. So while
the refrigerator allows heat to How fi'om bodies at low temperature to
bodies at higher temperatures, this is only as a result of an interaction
with its environment whereby energy is supplied to it by equalising a
temperature differential elsewhere (the power station, for instance). In
this case, a temperature differential is maintained in the system because
the system exchanges heat with its environment (it is what is known as
an open system); but if we look at the universe as a whole as a system,
we can see that in this case, there is no further environment with which
it can exchange energy (it is a dosed system). Now, given the first law of
thermodynamics, which states that there is a fixed quantity of energy in
the world, then, over time, as various processes in the universe do work,
more energy will be lost as heat as a result of inefficiency. EventuaIly,
169
Thus, organised systems tend to faH into disorder over time as the
intensive differences that allow structure and useful work to take place
give way to a disordered field lacking in any organising differences in
intensity.
Finally, why is this model considered by Deleuze to be a transcendental illusion? As Deleuze notes, the theOl'y of thermodynamics is a
partial truth, but it becornes a transcendent al illusion when we attach
'the feeling of the absolu te to [this] partial [truth]' (DR 226/284). This
partial truth opera tes within the framework of 'forms of energy which
are already localised and distributed in extensity, or extensities already
qualified by forms of cnergy' (DR 223/281). As such, it assumes the
differences in intensity as already given as preformed. \l\That is missing
170
While thermodynamics provides an account of processes affecting preconstituted systems, qualities and extensities, it does not account for the
emergence of these systems, qualities and extensities in the first place.
:Nluch of the remainder of the chapter will attempt to show how intensity
is central to this process of constitution.
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172
v\Thile representation attempts to derive the field of depth from the two
given dimensions, thus characterising depth itself as an axis of extended
space, lVlerleau-Ponty reverses this procedure. That is, rather th an
seeing depth as derived from the given dimensions, he sees it as that by
which the given dimensions of extensity are given to us. Depth is not
merely breadth seen from another angle, but rather is something difTerent in kind that, by making possible a field of autonomous but interrelated objects, also makes possible the system of extensive distances taken
as foundational by representation.
Once depth is understood in this way, we can no longer cail it a third dimension.
ln the first place, if it were a dimension, it would be the first one; there are forms
and definite planes only if it is stipulated how far from me their different parts
are. But a first dimension that contains ail the others is no longer a dimension,
at least in the ordinary sense of a cettaz relatJnship according to which we make
measurements. Depth thus understood is, rather, the experience of the reversibility of dimensions, of a global 'locality' - everything in the same place at the same
time, a locality from which height, width, and depth are abstracted, of a voluminosity we express when we say that a thing is there. (lVlerleau-Ponty 1964: 180)
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174
175
the extensum and the spatium as a whole are radically different. V\Thile
his presentation focuses on the mathematics of cardinal and ordinal
numbers, in the background of this discussion is Bergson's account of
two multiplicities. Deleuze daims that intensity has 'three characteristics' (DR 232/291). These are that it 'includes the unequal in itself (DR
232/291), it 'affirms difference' (DR 234/293), and it 'is an implicated,
enveloped, or "embryonised" quantity' (DR 237/297). In this section, l
want to go through these three characteristics.
In what sense does intensity 'indude the unequal in itself'? To explain
this point, l will follow the analysis provided by DeLanda (2002: 73-4).
As we have seen, one of the key differences betvveen intensive and
extensive quantities is that the latter can be added without changing
their nature. As Deleuze notes, this difference reflects one of the key
features of extensive magnitudes: that they can be measured numerically, and that these measurements are comparable (or commensurate)
with one another. Now, if we look just at the natural numbers (0, l, 2,
3 ... ), we find that frequently we come across magnitudes that cannot
be expressed in these terms. For instance, provided we remain with the
natural numbers, we cannot divide 7 by 2, as the result is not itself a
natural number. The obvious solution to this difficulty is to introduce
another order of numbers that does allow us to relate these two quantities to each other, in this case, fractions. Similarly, we will discover that
fractions do not allow aIl quantities to be related to one another, leading
to the instigation of a new order of numbers: real numbers (such as -Y2
or n). In each case, we have an incommensurability between quantities
that cannot be cancelled within the order of numbers themselves, but
only by instigating a new order of numbers. As Deleuze notes, as weIl
as proceeding From natural numbers to fractions and real numbers, we
can also ask if there is an order From yvhich natural numbers themselves
proceed. Now, we can make a distinction between cardinal numbers
(one, two, three ... ) and ordinal numbers (first, second, third ... ).
Whereas cardinal numbers can be constructed out of basic numerical
units, and so we can construct identities between them (for instance, that
the difference between one and three is equal to the difference between
two and four), ordinal nmnbers just give us a sequence without requiring
that the difIerence between the elements is the same in each case (thus,
the difirence between first and third does not have to be the same as
the difference between second and fourth). Now, in a technical sense, we
can talk about distance in relation to ordinal numbers, in that they form
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177
178
Qualities, on the other hand, are not divisible. It makes no sense to talk
of dividing rationality, or animality, for instance. Now, intensity is not
like quality, in that it can be divided. It is not composed of equal elements, however, but is rather a sequence of asymmetrical relations, such
as we find with the ordinal numbers (it is asymmetrical in that second is
defined by being 'in between' first and third, but first and third are not
'in between' second). Thus, 'a temperature is not composed of other
temperatures, or a speed of other speeds' (DR 237/297). If an intensive
multiplicity is not simply constituted from pre-existing elements, then
division is true division, leading to a change in the nature of what is
divided. Here we can turn to Bergson's alternative form of multiplicity.
For Bergson (at least at this stage ofhis philosophical development), this
alternative form of organisation is that which we find in our conscious
179
The two different notions of multiplicity can be mapped onto the extensive and intensive in a relatively straightforward manner:
Therefore there are two types of multiplicity: one is called multiplicity of
juxtaposition, numerical multiplicity, distinct multiplicity, actual multiplicity,
material multiplicity, and for predicates it has, we will see, the following: the
one and the multiple at once. The other: multiplicity of penetration, qualitative
multiplicity, confused multiplicity, virtual multiplicity, organizecl multiplicity,
and it rejects the predicate of the one as weIl as that of the same. (L 00100/70)
180
related to the Idea. In answering this question, we will also have to deal
with the problem of individuation, or the emergence of the subject from
an a-subjective field of intensity.
181
ism, in that it presents a field of elements that are different in kind from
the characteristics we find in the organism to which it relates. Despite
the fact that DNA differs in structure from the structure of the organism,
there is still a temptation to understand it in terms of those structures.
Thus, as the biologist Susan Oyama writes, 'though we aIl know that
there are no hooves or noses in the genes, the accepted formulation
is that the genes that are literally passed on make hooves and noses in
ontogenesis' (Oyama 2000: 43). Seeing a direct relationship between the
Idea and the extensive form that it determines in fact rests on the same
model of synthesis we saw in Kant's philosophy. The Idea here would be
akin to the active subject that manipulates passive extensive matter into
form, and the differenciation of the Idea would be the simple expression
ofits structure. To turn to Oyama once again, we can see that this model
of active synthesis is indeed widespread in genetic theory:
The discovery of DNA and its confirmation of a gene theOl'y that had long
been in sem'ch of its material agent offered an enormously attractive apparent
solution to the puzzle of the origin and perpetuation of living form. A material
object housed in every part of the organism, the gene seemed to bridge the gap
between inert matter and design; in fact, genetic ifomzation, by virtue of the
meanings of information as 'shaping' and as 'animating,' promised to supply just
the cognitive and causal functions needed to make a heap of chemicals into a
being. (Oyama 2000: 14)
Deleuze himself notes that seeing Ideas as solely responsible for the
constitution of the world is a potentialmisstep in the philosophy of difference that we are prone to:
In fact any confusion between the
Instead of the structure of the organism being governed by the operation of Ideas on passive extensity, Deleuze instead argues that it is
governed by the interplay between the Idea and the field of intensity:
'Individuation is the act by which intensity de termines differential relations to become actualised, along the Enes of differenciation and within
the qualities and extensities it creates' (DR 246/308).
The process by which intensity generates extensity is governed by a
182
fourfold structure which Deleuze describes as 'differentiation-individuation-dramatisation-differenciation' (DR 251/313). As the first category
suggests, differentiation is the moment of the calculus~ in particular, the
wider calculus of the Ideas that we looked at in the previous chapter.
At this level, we are not dealing with anything resembling the kinds of
entities we encounter in sensibility, hence Deleuze refers to this moment
as being structured by 'pre-individual singularities' (DR 246/308).
The second moment is the moment of intensity. As we saw, intensity is
understood as a difference between two potentials. It is this difference
between potentials which allows work to be done in the thermodynamic
model of intensive quantities. To return to the example of the cell, we
not only have the nucleus, which contains the genetic material, but also
the cytoplasm, which appears to be a homogeneous field. N onetheless,
we find that the cytoplasm contains chemical gradients that determine
differences between points within the egg. These differences set up
potentials similar to the differences in temperature which allow the
thermodynamic engine to function. This field of potentials is what
Deleuze caIls the 'field of individuation': 'An intensity forming a wave
of variation throughout the protoplasm distributes its difference along
the axes and from one pole to another' (DR 250/312). The interaction
of these two moments Deleuze caIls 'dramatisation'. If we return to the
archetypaimodei of the Idea, colour, we can see that the Idea can be
actualised in a variety offorms, each ofwhich exclu des the actualisation
of other fonns. If we actualise the Idea of colom', it will have to take the
form ofa particular colour. Similarly, ifwe actualise the Idea of the unity
of com position, we will get a particular animal. It is the field of intensities
which determines which form is actualised by determining the speed of
development of various parts of the organism according to the distribution of intensities within the egg. Thus, the field of intensity determines
how the relations between elements are determined in extensity. As
Deleuze noted in Chapter 4, this process of dramatisation relies on
movements by the embryo that are topological - that is, understood in
non-metric rather than metric terms. While these movements are possible within the intensive field of constitution, the y are not possible within
the constituted field of extensity: 'Embryology already displays the truth
that there are systematic vital movements, torsions and drifts, that only
the embryo can sustain: an adult would be torn apart by them' (DR
118/145). While it l11ight be claimed that DNA differs from the unity of
composition, in that it specifies one particular form or species, in fact, we
183
can note that here too, the milieu in which the genetic material expresses
itself is fundamental to the form generated:
Development seems to involve dynamics as weil as chemical computation.
'I\Then the developing frog embryo turns itself inside out during gastrulation,
it looks just like a \riscous fluid, flowing in an entirely natural manner. Sorne
of the information required to make this process work rnay be specified by the
laws of fluids, not by DNA. Brian Goodwin sees development as a combination of natural free-flow dynamics and DNA-programmed intervention to
stabilize a particular dynamic form. vVhy should nature waste effort programming the shape of the organism into DNA if the laws of physics will pro duce it
free of charge? It's like programming into DNA the fact that salt crystals must
be cubical. For example, the eye a shape that puzzled both Darwin and his
detractors is dynamically very natural. Rudimentary eyes can occur naturally
without any special DNA coding. Natural selection can then refine the rudimental)' eye into something more sophisticated, but it is the dynamics that gives
selection a he ad start. (Stewart and Cohen 2000: 294-)
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185
delayed in the egg, to such a degree that the principle of indiscernibles would
indeed have the formula given it by Lucretius: no n'Vo eggs or grains of wheat
are identical. These conditions, we believe, are fully satisfied in the order of
implication of intensities. (DR 252/314)
This condition is met by the fact that intensity is not constructed from
pre-existing equal units, as extensity is. Rather, Deleuze's claim that 'the
world is an egg' makes explicit that the entire sjJatium is implicated in the
potentialities of each individual egg, although different aspects of it are
implicated to different degrees. As each occupies a different position in
the sjJatium, each expresses the sjJatium diflerently.
At this point, we can note the fundamental difference between Ideas
and intensity. When we looked at Descartes' method at the opening to
Chapter 3, we saw that Descartes based his method on clear and distinct
ideas. The lack of separation between these two ternIS is, for Deleuze, a
fundamental failing of representation:
the weakness of the theOl)' of representation, from the point of view of the logic
ofknowledge, was to have established a direct proportion between the clear and
the distinct, at the expense of the inverse proportion which relates these two
logical values: the entire image of thought was compromised as a result. (DR
253/315)
Now, as we saw in the previous chapter (4.8), the terms clear and distinct
do not need to be associated with one another. If we consider the noise
of the sea, we can conceive of it clearly, in that we can recognise it.
Nonetheless, we do not perceive the differences which make it up (the
noise of the individual drops of water that make it up and are below our
threshold of perception). In this case, our perception of the noise of the
sea is both clear and confused. If we instead focus on the noise of the
individual waves, we can conceive of these distinctly, even though we
cannot fOrIn a clear ide a of them as they are too small to perceive. Thus,
in this case, we either focus on the waves, which are distinct, but obscure,
or the sea, which we perceive clearly but confusedly. Similarly, the pure
Idea, is distinct, in that it is completely determined. Nonetheless, in so
far as it is only in relation to a field of intensity that it can determine
lzow it relates to an actual organism (whether it will instantiate a bison
or a giraffe), it is obscure. Conversely, intensity expresses some relations
clearly only at the expense of other aspects of the Idea which, while
still present in the organism, are only present confusedly, on the basis
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187
188
departing from the subjects which give effect to the Other-structure, we return
as far as this structure in itself~ thus apprehending the Other as No-one, then
continue further, following the bend in sufficient reason until we reach those
regions where the Other-structure no longer functions, far from the objects
and subjects that it conditions, where singlarities are free to be deployed or
distributed within pure Ideas, and individuating factors to be distributed in pure
intensity. In this sense, it is indeed true that the thinker is necessarily solitary and
solipsistic. (DR 282/352)
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190
rather than seeing Diffrence and Repetition as the beginning of a new phase
in Deleuze's development, it might be better to see Diffrence and RejJetition
as the last (at least until his late book on Leibniz) ofhis great works on the
history of philosophy, and a work itself of the history of philosophy. It
is in his later collaborations with Flix Guattari that Deleuze draws out
the implications of DijJrence and RejJetition, in order to attempt to develop
a philosophy that thinks in terms of 'multiplicities for themselves' (TRl\1
362) rather than 'difference in itself. There, Deleuze replaces the logic
of genealogical enquiry and selection with a thinking in terms of the
rhizome and horizontal connections. As he puts it in conversation with
Claire Parnet: 'In my earlier books, l tried to describe a certain exercise
of thought; but describing it was not yet exercising thought in that way
... 'J\Tith Flix, aH that became possible, even if we failed' (D 16-1 7/13).
Not everyone follows Deleuze in moving beyond Difference and Repetition
however, and we can also note that its hybrid nature, as a text in the
'old style' that opens onto the later work, is also its strength. Dijjrence
and RejJetition provides a point of transition, but also a point of engagement for those who wish to critique Deleuze, and for those who wish
to deploy his own critique within the debates betvveen more traditional
philosophical approaches.
2. Study Aids
Glossary
Actualisation: the process whereby Ideas are incarnated in actual tenus.
(4.12,5.5)
Clear-Confused: A Leibnizian expression Deleuze uses to characterise
the structure of the actual. We can either understand the world in
terms of the pre-individual singularities that constitute it, in which
case we understand it distinctly (we understand its basic determinations) but obscurely (our analysis is not on the level ofhow the world is
actually given to us), or we can understand it as constituted, in which
case we understand it clearly (our analysis is in terms of the given) ,
but confusedly (our analysis does not separate out the genetic factors
responsible for the nature of the given). These two languages are
mutually exclusive. (4.8)
Cogito: An argument (Cogito Ergo Sum: l think, therefore, l am) used by
Descartes for the existence of a thinking substance. Also often used to
describe the thinking substance itself. (2.6, 3.1)
Common Sense: A faculty that connects together determinations of different faculties by relating them to an abstract object. Deleuze holds
this to be the second postulate of the dogmatic image of thought. (3.3)
Dark Precursor: The 'differenciator of difference' that relates together
disparate series, thus producing fields of individuation. (2.8)
Depth: lVlerleau-Ponty's term for the horizon that allows the visible (perspectival) world to be constituted. Deleuze understands this in tenus of
intensity, and also posits pure depth as the spatium. (5.3)
Determination: A property belonging to an object that allows us to
distinguish it from other objects.
Difference: Difference is represented in terms of negation (x differs from y
if x is not y). Diffrence and Repetition presents the project of discovering
192
Study Aids
193
Intensity: In terms of thermodynamics, this refers to an intensive property, such as tempe rature or pressure that allows work to be performed. In De1euze's terms, it is a non-metric field of difIerences that
differs in kind when divided. (5.4)
Judgement: In 10gical terms, the attribution of a determination or property to an object. (1.1)
Larval subject: A systematic collection of passive syntheses which
together constitute a self. (2.3)
lVIultiplicity: A variety. This can either be an actual multiplicity, which
is made up of a set of elements subsumed under a unity (the one and
the many), or a virtual multiplicity, where the unity is constituted by
the elements themselves. (5.4)
N omadic Distribution: A conception of the foundations of the world of
representation that sees those foundations as having a different kind
of structure to the world itself. (1.6)
Passive Synthesis: A process whereby elements are drawn together and
organised that constitutes, rather than presupposes, a self. (2.2)
Problem: Deleuze describes two kinds of problems. The first, drawn from
solutions, coyer over difference. (3.9) The second are difIrent in kind
from their solutions, and give rise to the actual. Problems are objective
structures, and occur in amongst others, psychological, biological and
social milieus. (4.1, 4.10)
Question: The question emerges from an encounter (an imperative), and
relates thought to Ideas. For Plato, the question is, '\Vhat is x?', for
Deleuze, the key questions are 'how many', 'how', 'in which cases'?
(4.10)
Repetition: Deleuze introduces two forms ofrepetition. 'Bare' repetition is
our normal conception of repetition, whereas 'dothed repetition' is different in kind from this form ofrepetition, and is responsible for it. (0.4)
Representation: A way of characterising the world, relying on the concepts of identity, analogy, opposition and resemblance, that attempts
to guarantee the subordination of difference to identity. (0.5, 1.1,3.4)
Sedentary Distribution: A conception of the foundations of the world of
representation that sees those foundations as having the same kind of
structure as the world itself. (1. 6)
Simulacrum: An image that does not rely on a prior iclentity. (1.11, 1.12)
Spatium: The field ofintensity taken as a whole. (5.3,5.4)
Univocity: The daim that the bcing of everything is said in the same
sense. (1.3-1. 7)
194
Further Reading
The variety of thinkers Deleuze refers to in DijJrence and Repetition is
overwhelming. The aim of this section is to give some of the key reference points Deleuze relies on in the various sections, as an aid to further
reading. The list is not comprehensive by any means, and largely tracks
the reading of DijJrence and Repetition given in this book. Similarly, l have
only listed texts available in English. The vast majority of these texts
are thought provoking pieces in their own right, however, and l would
advise the reader to spend time reading them beyond the bounds of theu'
relevance to Diffrence and Repetition. l have also listed sorne other texts
on Deleuze that might be of use in approaching DijJrence and Repetition.
\Vhile there is much excellent scholarship on Deleuze's philosophy, here
l want to focus on those texts which concern thernselves principally with
DijJrence and Repetition itself.
Study Aids
195
one of the few books on Deleuze to attempt to assess the veracity of his
arguments.
196
Study Aids
197
198
4.2) Few of the sources Deleuze refers to, apart from Maimon 2010, are
available in English. Boyer 1959 gives a de cent account of the history
of the calculus, focusing on its conceptual development. Deleuze's
approach to the calculus is also heavily inftuenced by Lautman 20 Il.
4.4) The tvvo principal sources are Epicurus 1926 and Lucretius 2001.
See LS 266-79/303-20 for an extended discussion by Deleuze of
ancient atomism.
4.5) Hardly any of Geoffroy or Cuvier's works have been translated into
English. Appel 1987 and Coleman 1964 provide good sources for the
debate. See also ATP '3. 10,000 B.C.: The Geology of MoraIs (Who
Does the Earth Think It Is?)', for a further account by Deleuze (with
Guattari) of the Cuvier-Geoffroy debate.
4.6) See Althusser 2005: Chapter 3, for the difference between Hegelian
and J\!Iarxist dialectics. See also Althusser and Balibar 2009, particularly
Chapter 8.
4.7) For the relation of depth, see Bourbaki 1950.
4.8) Deleuze here relies on Bergson's critique of possibility in Bergson
1992: 73-86, and his analysis of essence in Bergson 1992: 187-216. For
Kant on possibility, see Kant 1929: A592-603/B620-631.
4.9) Deleuze relates the difference between knowledge and learning to
Plato's analogy of the divided line (Plato 1997b: 509d-513e). Bergson
1998: 192 gives his account of swimming.
4.10) Nietzsche discusses the dice throw in Nietzsche 2006b: 'Before
Sunrise'.
4.11) Deleuze here borrows from the discussion of order and disorder in
Bergson 1998: Chapter 3.
4.12) The reading for (5.5) covers this section. DeLanda 2002 ties in the
dynamic systems approach to Deleuze's work.
Study Aids
199
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205
Index
absurd, 13
abyss, 21-3
accident, 25
actualisation, 163-6, 191
actuality, 164
Althusser, Louis, 146-8, 152
analogy, 10-11,23,29-32,37,110-11,
117, 144-5; see also paronymy
Ansell Pearson, Keith, 194
Aquinas, Saint Thomas, 31-2, 37,
40
Aristotle, 23-30, 31, 37, 38,40,41,42,
47,53,97-9,110,125,145,151,
177
atomism, 16-17, 143-4
attribute, 35-6
Bergson, Henri, 8, 64, 65-72, 115-16,
151, 156, 162-3, 176-80
Blanchot, Maurice, 95, 159, 161
blockage, conceptual, 15, 16
Boltzmann, Ludwig, 166, 169, 170
Bordas-Demoulin, 134-6, 140
Bryant, Levi, 194
calculus, differential, 131-42, 182
Carnot, Nicolas, 167-8
Carroll, Le\vis, 189
Czanne, Paul, 172-3
Clausius, Rudolph, 167
clear-confused, 153-4, 185-6, 191
common sense, 97,103-12,114-16,
121, 124, 169, 191
comprehension, conceptual, 14-17
concepts, creation of, 103
contemplation, 64-5
Cuvier, Georges, 1L14-6
Index
extensio, 173
extensity see space, extensive
o:tenS1l1l7, 173, 179, 192
207
infinity
Aquinas' conception of; 32, 40-1
Hegel's conception of, 45-7
Scotus' conception of, 32-5
Spinoza's conception of: 37
see also representation: infinite
intensity, 32-4, 37-8,50-3, 83, 85,
95-6, 159, 166-71, 173-86, 193
judgement, 21-3, 38,42-4,48-9,57-8,
61-2,96-7, 124, 193
Kant, Immanuel, 55-68, 70, 72-7,
82-3,90-1,96-7, 104, 108-11,
117-19,123-4, 126-31,136-7,
142, 152, 181
incongruent counterparts, 16-21,
55-6,58,109
morallaw, 9-13, 81
sublime, 117-19
transcendental deduction, 58-62, 76,
109, 110
see also illusion: transcendenta1
illusion; para10gism
Kierkegaard, S0ren, 11-14,47, 107
Klee, Paul, 172-3
Lagrange, joseph-Louis, 138-9
lm'val subject, 65, 193
law, 7-9, 13-14,41,67,78-80, 109; see
also Kant, Immanuel: morallaw
learning, 128, 155-9, 162
Leibniz, Gottfried \J\Tilhelm, 15, 17, 18,
19,21,44,48-50,75,132-3,136,
137, 153-4, 185
Lenin, Vladimir; 156-7
limit, 34, 40-2,44-5,52, 152, 163
Lucretius, 143-4, 185
Maimon, Salomon, 134, 136-8
Marx, Karl, 146-8
memory, 13-14,52,66-72,82-3,85-6,
111-12, 115-16, 119, 180
Merleau-Ponty, Maurice, 50-3, 107,
170-4, 186-7
multiplicity, 142-3, 178-9, 193
narcissistic ego, 87-8
negation, 41-2, 50-3, 119-22, 161-3,
177
208
quale, 173
qualitas, 173
question, 125 159-61, 193
reality principle, 84, 91
recognition, 14, 104-8, 110-11,
116-17, 120-1
repetition, 7-18,21,55-6,62,71-2,
82-4,88-90,93-6,193
representation, 14-15,21-3,40-1,
51-3,55,57,60-2,70-1,83-4,
92-3,96-7, 102-3, 117, 138,
185-7
infinite, 43-50, 99, 108-11, 193
repression, 16, 84
resemblance, 8-9, 26, 66-7, 82
rhizome, 189-90
Rosenberg, Harold, 78-80
Russell, Bertrand, 122-5
Ruyer, Raymond, 165
Saint-Hilaire, Geofii'oy, 144-6, 150,
152, 164-5, 180
science, 8-9
sedentary distribution, 40-3, 116,
193
sense, 122-5, 127
Shakespeare, William see Hamlet
sign, 36, 65, 88, 92
simulacrum, 189, 193
singularity, 139-40, 149-50, 156-7,
160-l, 182
solutions, 125-31, 140, 142, 152, 156,
160, 162
Sophocles, 78
space, extensive, 17-21, 50, 142,
169-82, 192
spatio-temporal dynamism, 164-5
spatium, 173, 175-6, 179, 183, 185,
193
species, 15-16
Aristotelian, 24-6, 30, 47
biological, 101, 164, 182, 184speech, 157-8
Spinoza, 35-8,43,46-7, 82, 136
structuralism, 146-8
stupidity, 121
theology, 30-5
thermodynamics, 166-70, 173, 174,
176, 182
transcendental empiricism, 52-3
transcendent al illusion see illusion:
transcendental illusion
trauma, 86-7
unground, 159-60,174
univocity, 30-43, 46, 193
vice-diction, 155-6
virtual object, 91-4
virtuality, 150-4, 164, 179-80, 194
Williams,]ames, 194-5