THE FOLD
Leibniz and the Baroque
Gilles Deleuze
Foreword and translation by Tom Conley
A
continuum
Contents
Continuum
The Tower Building
11 York Road
London
SE1 7NX
15 East 26th Street
Suite 1703
New York
NY 10010
www.continuumbooks.com
Translator's foreword: A plea for Leibniz
ix
First published in Great Britain 1993 by The Athlone Press,
Reprinted 2001
Reprinted 2003, by Continuum
This edition, 2006
a) The Regents of the University of Minnesota 1993
-
First published in France as
Le ph: Leibniz et he baroque
(ii") Les Editions de Minuit, Paris
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British library
ISBN 0 8264 9076X
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted in any form or by any
means, electronic, mechanical, photocopying or otherwise, without
prior permission in writing from the publisher.
I The Fold
The pleats of matter
3
The fold that goes to infinity — The Baroque home — the lower
floor: matter, elastic forces, springs — Organism and plastic
forces — Organic folds — Why another floor is needed, a
problem of the animal soul — The elevation of reasonable
souls, and its organic and inorganic consequences
2
The folds in the soul
15
Inflection — Singularities — Baroque mathematics and variation: the irrational number, the differential quotient, the
family of curvatures — The new status of the object —
Perspectivism: variation and point of view — The new status
of the subject — From inflection to inclusion — The subdivision
— The monad, the world, and the condition of closure
3 What is Baroque?
30
The room without windows — The inside and the outside, the
high and the low — Heidegger, MaHarm& and the fold —
Baroque light — The search for a concept — The six esthetic
qualities of the Baroque — Modern or abstract art: textures and
folded forms
1
II Inclusions
4
Typeset by BookEns Ltd, Royston, Herts.
Printed and bound in China
1
45
Sufficient reason
47
Events or predicates — The four classes of beings, the genres of
predicates, the nature of subjects, the modes of inclusions, the
case of infinity, the corresponding principles — Leibniz's
CONTENTS
CONTENTS
mannerism — The predicate is not an attribute — The five
criteria of substance — Styles and depth — The play of
principles
5 Incompossibility, individuality, liberty 67
Incompossibility or the divergence of series — The Baroque
narrative — Preindividual and individual singularities — The
play of the Baroque world — Optimism, the world's misery,
and Mannerism — The question of human liberty — A
phenomenology of motifs — Inclusion of the predicate and
the living present — Leibniz and Bergson: movement as it
happens — Baroque damnation
6 What is an event? 86
Whitehead the successor — Extension, intensity, the individual — Prehensions and monads — Eternal objects — The
concert — Modern Leibnizianism: suppression of the condition
of closure, and the neo-Baroque
HI
Having
a
Body
9
The new harmony 139
Baroque clothing and matter clothed — The fold to infinity:
painting, sculpture, architecture, and theatre — The unity of
the arts — The world as a cone: allegory, emblem, and device —
Leibniz's concettism — Music or higher unity — Harmonics: the
monad as number — Theory of accords — The two aspects of
harmony: spontaneity and concertation — Harmony, melody,
and Baroque music
Notes
159
Index
193
95
7 Perception in the folds 97
The requirement of having a body — First stage of deduction:
from the world to perception in the monad — Minute
perceptions: the ordinary and the remarkable — Differential
relations — Recapitulation of singularities — Psychic mechanism and hallucinatory perception — Dusts and folds in the soul
— Second stage: from perception to the organic body — What
does perception look like? — Organs and vibrations: the
physical mechanism of excitation — Pleats of matter — The
status of calculus
114
8 The two floors
The two halves: the ones and the others, the 'each' and
'every' — Mathematics of halves — The role of the extrema —
Virtual-present, possible-real: the event — Leibniz and Husserl:
the theory of appurtenances — Body and soul: appurtenance
inverted, provisional appurtenances — Domination and
vinculum — The three species of monads: dominant, dominated, defective — Crowds, organisms, and heaps — Force —
Private and public — Where does the fold go?
vi
vii
Translator's foreword
A plea for Leibniz
Soon after finishing what would bear the title of The Art of the West, an
esthetic history of the High Middle Ages, Henri Focillon theorized the
experience of his research in Vie des formes. 1 Reflecting on the emergence
of the Romanesque and Gothic styles, Focillon confronts dilemmas facing
all historians of the Middle Ages and ancien regime. How do styles develop,
and why do they differ so markedly? Do they succeed one another or
share pertinent traits? Do esthetic styles convey, in a broader sense, the
notion of particular 'manners of thinking'? Can styles be periodized and,
if so, what are the ideological motivations betraying the historical
schemes that also tend to produce them?
In the context of French literary and esthestic history in the aftermath
of the First World War, Focillon departs from traditions of esthetic and
literary botany that date to Sainte-Beuve and Auguste Comte. For them,
tables, categories, genealogical trees, and lines of phyla could map out
great mnemonic systems. They would soon program the ways the French
nation would construct its patrimony. Students of these paradigms would
forever recall the grids, fill them with appropriate facts and traits, and
thus be 'informed' by schemes of knowledge. 2 To the contrary, Focillon
notes that the Romanesque and Gothic, two dominant and contrastive
styles, often inflect each other. They crisscross and sometimes fold vastly
different sensibilities into each other. The historian is obliged to
investigate how the two worlds work through each other at different
speeds and, in turn, how they chart various trajectories on the surface of
the European continent.
ix
TRANSLATOR'S FOREWORD
In Vie des formes, Focillon rethought the logic of evolution that had
been bequeathed to the twentieth century. On the one hand, a
remarkably firm tradition of inquiry, observation, and historicization
came with positivism. Yet, on the other, the really creative positivists of
the nineteenth century — Balzac, Hugo, and Proust — built works whose
mass, fragmentary totality, and changing effects impugned the tabled
symmetries that their scientific counterparts had invented. The history of
the Romanesque and Gothic appeared, in the eyes of Focillon, no less
massive in its overall effects than the poems and novels of nineteenthcentury literary masters.
At certain points, Focillon's overview of the Middle Ages resembles a
mix of technical history and organic chemistry. Forms move back and
forth, disappear, recur, or bring out new shapes when they are
superimposed or interconnected. Gothic maidens at Reims indeed 'smile'
where Romanesque peasants at Vezelay had been staring, exorbitantly
and aghast, at the onslaught of the Second Coming. Both styles
experience a Baroque phase. Romanesque buildings, and sculptures on
tympana and capitals, with their solemn aura, share features that can be
identified best by categories whose descriptives belong to a later period. 3
In a similar vein, the textured effects of 'irreality' in the flamboyant in the
fifteenth century tend to narrate the entire history of the adventure of the
ogive, and flow into the life of culture in general.
Through the theory gained from his observations, in Vie des formes
Focillon calls into question the rationale of periodization. With figures
borrowed from biology, he bends many of the schematic lines of
positivistic forebears. At the same time, adapting Wilhelm Worringer's
notion of the 'Gothic' as what signifies a will for movement running
through the entire Middle Ages, Focillon assails the gap that existed, in
the entre-deux-guerres, between French and German culture. He writes of a
history of art composed of differently paced but intermingling phases. An
'experimental' beginning seeks solutions to problems that a 'classical'
moment discovers and exploits. A 'radiating' (rayonnant) period refines
the solutions of the former to a degree of preciosity, while a 'Baroque'
phase at once sums up, turns upon, contorts, and narrates the formulas of
all the others.
The Baroque thus does not comprise what we associate with Bernini,
Borromini, or Le Brun. 'The Baroque state reveals identical traits existing
as constants within the most diverse environments and periods of time.
Baroque was not reserved exclusively for the Europe of the last three
x
TRANSLATOR'S FOREWORD
centuries any more than classicism was the unique privilege of
Mediterranean culture.' 4 'Baroque' designates a trope that comes from
the renewed origins of art and has stylistic evidence that prevails in
culture in general. Under its rubric are placed the proliferation of mystical
experience, the birth of the novel, intense taste for life that grows and
pullulates, and a fragility of infinitely varied patterns of movement. It
could be located in the protracted fascination we experience in watching
waves heave, tumble, and atomize when they crack along an unfolding
line being traced along the expanse of a shoreline; in following the curls
and wisps of color that move on the surface and in the infinite depths of a
tile of marble; or, as Proust described, when we follow the ramifying and
dilating branches of leaves piled in the concavity of the amber depths of a
cup of tea.
Gilles Deleuze appears to share these same sensations in his dazzling
reading of Leibniz. The Fold tells indirectly of the reincarnation of the
Franco-German philosopher through the Baroque, as understood by
Focillon in its broadest and most influential way, that radiates through
different histories, cultures, and worlds of knowledge. Deleuze's work
may be the first and most daring venture to take the Baroque, in the
specific figure of the fold, through the history of art, science, costume,
mathematics, lyric, and philosophy. The Fold might also stand as one of
the most personal, sensuous, and original of all of Deleuze's writings. At
the same time its breadth might also strike readers as difficult and opaque.
At first glance, the book is disarming. The implied reader is taken to be as
familiar as the author is with atomic theory, differential calculus, classical
and contemporary painting and music, and with the history of logic. Yet
the pleasure Deleuze affords comes with the confidence he invests in the
reader: the work is composed as if spoken to a friend relaxing on a sofa by
a window of a small apartment, on a second or third floor, that overlooks
a large city. Without pretension Deleuze speaks of marvelously difficult
equations in differential calculus, biological and fractal models, of the
performance of the music of Pierre Boulez, and of esthetic history. The
book's tone flatters us at the same time it dismantles — without posture or
grandiloquence — some of the most shopworn beliefs we have inherited
about the texture of our physical world. In what remains of this preface I
should like to touch on what Deleuze appears to be doing with Leibniz,
and how his affiliation with the philosopher affects what we discern
about contemporary issues.
TRANSLATOR'S FOREWORD
Deleuze argues that while the Baroque has been a disputed term in the
fine arts, esthetic history, and music, it has not been associated with
either a philosophy or a philosopher apt or complex enough to embody
and theorize its principles. For Deleuze, Leibniz happens to be the
philosopher of the Baroque. Leibniz is so contemporary that the ensemble
of his research on science and mathematics, or his treatments of
contradiction, belief, music, and theology help to explain — or unfold —
what we know about the world at the end of the twentieth century.
The experience of the Baroque entails that of the fold. Leibniz is the
first great philosopher and mathematician of the pleat, of curves and
twisting surfaces. He rethinks the phenomenon of 'point of view,' of
perspective, of conic sections, and of city planning. Included in the
category of things folded are draperies, tresses, tessellated fabrics, ornate
costumes; dermal surfaces of the body that unfold in the embryo and
crease themselves at death; domestic architecture that bends upper and
lower levels together while floating in the cosmos; novels that invaginate
their narratives or develop infinite possibilities of serial form; harmonics
that orchestrate vastly different rhythms and tempos; philosophies that
resolve Cartesian distinctions of mind and body through physical means —
without recourse to occasionalism or parallelism — grasped as foldings;
styles and iconographies of painting that hide shapely figures in ruffles
and billows of fabric, or that lead the eye to confuse different orders of
space and surface.
Now in The A rt of the W est, Focillon remarks that the age of the
'Baroque Gothic' witnessed the birth of the mystical experience. It is
characterized, as other thinkers have since shown in greater detail, by an
individual's account of his or her voyage to and from an ineffably
universal event, which set the body in a trance, and which has left marks,
scars, or other physical evidence that confirm the individual's tale of
passage. 5 The mystical venture convinces because no language can be
said to represent what it means. It is tantamount, in part, to what
Deleuze, by means of Leibniz, Henri Michaux, and Gaetau Clerambault,
might call an event: it may not have an empirical or historical basis, but it
happens to be the virtual sensation of a somatic moment of totalization
and dispersion. In the novel or poetry, it can be felt as a seriality of
epiphany. Its scientific analogies might include the thoughts of infinity
that come with the view of the world in which all of its visible objects are
moving aggregates of infinite numbers of atoms and molecules. In the
vision of Alfred North Whitehead, a philosopher inspired by Leibniz, an
TRANSLATOR'S FOREWORD
event can be seen in the duration that produces the site of a pyramid, an
avalanche of snow, or the jagged edge of rifts in a block of ice. For
Deleuze, an event unfolds from the union of our perception and the
duration of a fan — of the kind Mallarme describes in his occasional verse —
that unites and disperses a word (an event) and an object (an eventail)
when it swirls the atmosphere.
These rarefied areas of sensation constitute a mystical and mathematical dimension of the Baroque. Leibniz, declares Deleuze, stands as the
first philosopher able to deal with the experience of events and the world
of atomic dynamics. Deleuze himself appears to be mystical insofar as
much of The Fold — especially in the arguments that develop from
sufficient reason, incompossibility, perception, and the apportioning of
space (in chapters 4 through 8) — develops through absolute identity with
Leibniz. A reader often notices an indirect discourse that melds with the
movement of the New Essays on Human Understanding or the correspondence with Arnauld. Deleuze, whose voice translates better than any the
experience of contemporary time, is harmonized with that of the FrancoGerman philosopher at the threshold of the Enlightenment. As we listen
to Deleuze, in the intimacy of the Baroque home in which The Fold
appears to be taking place (figure 1 in the first chapter), we perceive
philosophical and ethical dilemmas on the horizon of our lives.
Reincarnation of Leibniz follows a pattern of force. Deleuze has often
identified with philosophers of the past — not always the most renowned —
in order to confront political and ethical issues of the present. When he
wrote on Nietzsche in the early 1960s, Deleuze was Nietzsche: he
launched a transvaluation of a culture, mired in existentialism, that had
not completely assimilated the effects of its colonial history. He then
became Spinoza and Bergson at a time when intellectuals collectively
cried for a 'return' to Freud. To extend and modify the canon of
philosophical writing, he wrote on Kafka, Melville, and, later, Francis
Bacon. Yet Leibniz has always been a powerful force in all of Deleuze's
writing, and at this stage of the philosopher's career The Fold comes as no
surprise. The earlier writings (especially Logique du sens) often mention
Leibniz with admiration, or use the Monadologie to recall the complexity
of scientific theory in the ancien regime, but they never develop into
identification with Leibniz's signature.
A truism of French intellectual history states that for national and
philosophical reasons every postwar thinker, from Jean Hippolyte to
Jacques Derrida, must contend with Hegel. Deleuze had resisted the
TRANSLATOR'S FOREWORD
totalizing effects of the dialectic by aligning himself at once with Cartesian
and left-wing political traditions. He made moves that showed how, by
way of Spinoza, a more complex, fragmented, and prismatic philosophy
antedated Hegel and could not be supplanted by systematic dialectics. In
this light the study of Leibniz implies that an extraordinarily delicate
filigree of concepts, winding through organic and inorganic worlds, has to
be retrieved. Leibniz is thus also a philosopher of habitat and ecology. His
myriad connections and series of concepts are not held in a prescribed
order or a unifying system. Multiplicity and variety of inflections produce
'events,' or vibrations, 'with an infinity of harmonics or submultiples.'
Movement of a concept that has bearing upon a subject's impressions of
the physical world does not elevate according to a spiral plan, which
belongs to philosophy, but radiates or ramifies everywhere in the
geography of experience, such that we can imagine movement of light
and sound, together, as folds of ethereal matter that waft and waver.
An exquisitely sensuous view of the world is obtained through the
curved shapes that Leibniz creates with calculus, and from manifestations
of folds that we follow in modern art and poetry. Deleuze implies that if a
chronology of the history of philosophy is mapped over the kinds of
vibrations and events developed from the Gothic period until now,
something goes awry. Leibniz is not merely a chapter in the history of
mathematics, cognition, or logic. The relation of monadic thinking to our
sense of the world cannot be discounted; the movement of his reasoning
shares many common traits with what theorists of science, musicians,
and artists are now making of habitat.
Leibniz, he implies, develops a philosophy that bridges the preSocratics, Lucretius, and neo-Einsteinian thinkers. In light of earlier work
(Proust et les signes) and his most recent writing (Qu'est-ce que la philosophie?
with Felix Guattari), The Fold joins philosophy to the ecology of
hypothetical experience. In his study of In Search of Lost Time. Deleuze
noted that Proust's mission bore a Platonic label. The quest would restore
art and lead to an enduring and redemptive idea. But what the text seeks
to redeem is riddled from within by a stylistic practice that scatters
everything that would comprise a 'whole' or a 'unity.' Yet since the work
is finished in its incompletion, 'there must be a unity which is the unity of
that multiple piece, of that multiplicity, as in all of those fragments.' 6
Deleuze's stress on the partitive shows how Proust's great project of a
total novel betrays a 'communication that would not be posited as a
principle, but would result from the play of [textual] machines and their
xiv
TRANSLATOR'S FOREWORD
detached pieces, of their unconnected parts' (196). It is Leibniz who
inspires this observation, since the seventeenth-century philosopher 'first
posed the problem of communication resulting from closed units or from
what cannot be attached' (196). By means of Leibniz's innovation, which
marks the limits of communication, the subject is enveloped in the
predicate, just as Proust's intention is folded into his effect. Inclusion of
the subject in the predicate implies that the world makes up a chaotic
cosmos or chaosmos. By way of Leibniz's logic, Deleuze is able to conceive
of artworks composed of units that are neither logical nor organic, 'that is,
neither based upon pieces as a long unity or a fragmented totality; nor
formed or prefigured by those units in the course of a logical development
or of an organic evolution' (191). As in Focillon's vision of a 'life of forms'
that mixes biological and serial figures in its description of the Baroque
phase, or in the giddy effects of partial things in the novel that betray
Proust's intentions, a hierarchy of organic and inorganic things no longer
holds. 'Life' is invested into brute matter insofar as it, too, is perpetually
moving, metamorphosing, or emigrating from one condition to another.
All of a sudden, by way of the relation of atomic theory to that of the
monad, an ideology of hierarchies of life begins to totter. When organic
and inorganic materials are differentiated not by a wall but by way of a
vector (early in chapter 1). There ensues an ethical problem about how
we are to apprehend the world. That humans stand as triumphant
subjects among inert objects no longer holds. They no longer own things
as they had in the world of possessive individualism. Now it must be
asked how humans select and designate what they call 'living' or 'inert.'
If organic life cannot be easily demarcated from inorganic matter, it
behoves subjects to look at all matter from a different angle. Leibniz
points toward an ethics that appends the science of ecology. In his turn,
Deleuze suggests that an at once abstract and tactile sense of matter must
figure at the crux of any social practice.
In more recent work that follows the implications of The Fold, Deleuze
(and Felix Guattari) promote conceptual activity that will move in the
direction of a 'geophilosophy.' Entailed is a revolution of 'absolute
deterritorialization.' 7 The authors do mean that philosophy advocates the
collapse of national boundaries or a return to diversities of economic or
ethnic worlds, but that the totalitarian aspect of liberal democracy
(spurred by the demise of the Soviet Union and the prospect of the
European Economic Community) has to be atomized, at least in one
stage, by the labor of conceptual thinking. They suggest that philosophy
TRANSLATOR'S FOREWORD
can acquire agency by the use of a monadic sensibility when it addresses
issues of habitat and thinking.
In Qu'est-ce que la philosophie, a geopolitics of deterritorialization is
advanced. The authors speculate that Greek philosophy is something that
originates with migrants who arrive on the Aegean peninsula and,
through their example, initiate a collective sense of immanence. Ulysses,
not Robinson Crusoe, is the ruseful plebian, the everyman who inhabits
urban space, and who gives rise to a conceptual process in which are
planted the seeds of its own demise. When it commodifies concepts,
marketing seeks to co-opt philosophy. Deterritorialization, and its
obverse, reterritorialization, implicitly tie monadic thinking to the art of
displacement and transformation.' A stick is, in its turn, a deterritorialized
branch' (p. 66). Those who conceive of organic and inorganic matter from
this point of view tend to be geophilosophers. Their activity 'slides' on the
surface of the world, as on a wave. A 'surfer,' the geophilosopher moves
along the crest of turbulence, on the shoulders of waves that envelop
mind, energy, and matter, and that diffuse them into the atmosphere.
Allusive as the politics of geophilosophy may be, some of its clearest
manifestations are found at the end of The Fold. In the final chapter,
Deleuze ties Leibniz's concept of 'new harmony' to Baroque and
contemporary music. 8 He picks up, however, the strands of his discussion
on the Baroque home that he had elaborated in the first and third
chapters. By virtue of the radiation of musical waves that move in and
about monads, the world is made up of 'divergent series,' and thus
resembles an infinity of pleats and creases of unified and dispersed matter.
All of a sudden the distinctions that were used to elaborate Leibniz's
vision of space — in which the monad is composed of two 'floors,'
including first, an upper, private, intimate area (that would be a stage for
a chamber ensemble) and, second, a lower, public level where masses
circulate — are no longer sustained. The sentences break off from the
music of monadic harmony and decor; they turn to issues of habitat.
The last question that Deleuze poses involves what it means to live in
the world. Our experience of a shrinking globe inflects the vision of the
monad, since compressions of time and space modify 'the difference of
inside and outside and of public and private' (p. 137). Thus, contemporary artists and musicians in the line of Leibniz transform monadology into
nomadology. They are emigrant thinkers who deterritorialize accepted
notions of space. Like the shift of the opposition of organic and inorganic
matter into tonal flow and flux, the movement from an order of ethereal
TRANSLATOR'S FOREWORD
and private space over a teeming public world (or 'fishbowl') indicates
how the geophilosophy will operate. The two worlds must fold into each
other. The political implication is that the 'upper floor' of the first world
must refuse a distinction with second, third, or fourth worlds by (a)
rethinking the difference of organic and inorganic forms and (b) by
reducing the speed of its movement to harmonize with that of the 'lower'
world.
Leibniz had mediated what historians study in terms of social
contradiction of the ancien regime with an activity that 'folds, unfolds,
and refolds' matter, space and time. Contemporary artists, also
geophilosophers and students of revolutions, are impelled to work in
the same fashion. Their activity accounts for the shrinkage of the world,
its increased organic mass, and consequent impoverishment of biological
variety. Forms, like modes of folding, disappear. The political strategy of
The Fold continually bends our dilemmas back onto Leibniz's fascination
with infinite and curvilinear forms. Leibniz opens a window onto our
world: Deleuze appears to use Leibniz's concept of harmonics to advocate
the possibility of infinity to be thought within the restricted limits of our
habitat. A process without spatial development is implied by the nonHegelian tenor of the last clause in the book: plier, diplier, replier. Thus
Deleuze argues for rediscovery of other styles (manieTes) of folding the
space of life. If philosophy can theorize the shrinking limits in which we
live, Leibniz exemplifies a system that does not flatten nature to a concept
or world-picture. The searing irony is that Leibniz refuses simplification
so at the very time his work indicates how the technology of capitalism
can be developed. 9 By counterexample, the infinity of the fold locates
where and how the world has since become compressed. Now if the fold
traverses all matter, its movement allows us to conceive ways of
inhabiting the world with tactical resourcefulness. Its very abstraction —
for what indeed is the fold? — allows for elaboration of sensibilities not
under the yoke of liberal democracy.
It may be that Deleuze's imagination of the fold harbors an impractical
and unfounded optimism in respect to what can be conceived in our
history of accelerated compression of time and space. The politics of the
fold would seem to be so chimerical that Deleuze and Guattari could be
likened to two 'spiritual automata,' Quixote and Sancho, who venture in
an intimate infinity of philosophical space far from the stress that human
life and social contradiction impose on the globe. It is licit to wonder if the
work withdraws into an interdisciplinary monad.
TRANSLATOR'S FOREWORD
Seen thus, The Fold and Qu'est-ce que la philosophie would be
hypothetical approaches to problems — population, habitat, displacement,
geocide — that require urgent and practical commitment. Habitat, it must
be countered, includes conceptual virtue. And since they beg reaction of
this kind, these works can also be said to orient philosophy to the future
of the planet in ways that pragmatic means have yet to conceptualize. In
fact, The Fold finds the clearest expression of its politics in the ways that a
utopian thought — and by utopia can be meant Leibniz's fancifully lucid
invention of the monad — joins the labors of philosophy.
Leibniz is political because he is utopian. His theories of curvature,
movement, and point of view cannot be localized. Deleuze and Guattari
note that a 'utopia is not separated from infinite movement: Utopia
designates absolute deterritorialization, yet always at the critical point
where the latter is attached to the relatively present milieu, and especially
with forces that are the fabric of this milieu.' 10 The pleats and hems of the
ideal Baroque home thus do not merely refer to a 'nowhere,' as if
prompting a mirror-reading of Samuel Butler's Erewhon, but also to a
'now-here' that is present whenever and wherever the concept of its
space is taken up.
In this sense Leibniz's theories are not specifically 'objects' but, in
Deleuze's lexicon, Baroque territories. They pertain to a nature endowed
with forces that Leibniz describes by tracking the motion of infinite
folding, or by investigation of the caverns and crannies of porous shapes
opened in the twists of stone, fossils, and metamorphic rocks. These are
territories of contemplation for the mind, but they are not to be abused
while it 'lives and thinks in a state of self-contained reflection' (p. 99). A
similar politics emerges from Deleuze's comparison of Descartes's and
Leibniz's views on extension. For the former, the material world can be
mapped out from the axis of the thinking subject, in rectilinear fashion,
and can be divided into discrete units. The resulting geography resembles
the order and process of the quincunx, a two-dimensional system of
gridding and squaring that places a center (the ego) at the intersection of
the diagonals of a surrounding square. When the self moves into space, it
transforms one of the corners of the square or rectangle of its periphery
into the site of a new center, around which new extremities are
established, and so forth, until space is conquered." For the latter,
neither the self nor the world can work so schematically. Everywhere the
subject swirls in the midst of forces they exert stress that defines the
individual body, its elasticity, and its bending motions in volumes that
xviii
TRANSLATOR'S FOREWORD
produce movement in and of extension. The subject lives and reinacts its
own embryonic development as a play of folds (endo-, meso-, and
ectoderm) rather than as a battleground pitting the self against the world.
By way of Leibniz's critique of Cartesian space the author pleads for tact
of body and environment.
The Fold makes its sensibility manifest through its turns of style. The
sentences are simple, and the transparency of their expression often
beguiling. They are built less from the verb or the tension of the subject
and predicate than along the path of its logical 'seams' on the edges or
pleats of each sentence. Many start with what appear to be conversational
modes, with c'est, c'est bien, ce n'est plus, c'est que, or c' est qu'il y a. ... These
beginnings promise less than the philosophically charged incipit, es gibt, or
the French i/ y a, 'there is,' 'what is ... is the fact that,' etc., that tend to
identify the writer with a hidden authority invested with the power to
judge and control those who read or listen. Deleuze employs c'est as a
connector, as a unit that can link concepts into serial chains that attach to
any number of other sentences. The construction stages the process — also
dear to Leibniz — that conflates subject and predicate. Cast thus, Deleuze's
sentences articulate the problem of inclusion and connection of different
lexical constructions. Vocables and phrastic units are apt to ramify. The
concept itself 'becomes a subject' in conformity with each level of
grammatical parts and wholes. Leibniz's logic marks a break, Deleuze
argues (in 'Sufficient Reason,' chapter 4), with the classical conception of
the subject as a rational being. By using terms linked by the copula to be,
and by varying on c'est, Deleuze does not shirk responsibility for elegance
of argument or stylistic clarity: following Leibniz, he summons the
distinction of subject and predicate that grounds Cartesian reason. The
continuity of style in The Fold keeps the one — either subject or predicate —
from being an attribute of the other.
At the same time, transparency is gained in the apparent simplicity of
the sentence. Different and simultaneous movements of logic and style
develop within the syntax of each phrastic unit. In this sense, Focillon's
description of Baroque 'syntax' in medieval art is not without parallel to
the style of either Leibniz or Deleuze. Baroque forms, notes the art
historian, 'live with passionate intensity a life that is entirely their own.
... They break apart even as they grow; they tend to invade space in
every direction, to perforate it, to become as one with all its
possibilities: 12 Deleuze's style promotes confusion of form and sign, but
paradoxically, in ways such that the overall effect does not draw attention
xix
TRANSLATOR'S FOREWORD
to itself. The sentence signifies its content, but the content is seriated to
conform to the rhythm of the argument.
With some exception, Deleuze's sentences tend to be short, simple,
and pellucid. In their concatenation, they break open and recombine,
inviting the reader to isolate given clauses and reconnect them, to
produce mobile effects where verbal groups jump into or recur in other
clauses. The implied movement mimes what the author finds in the play
of fixity and passage in Leibniz's taste for simultaneous mobility and
closure of concepts. Once again, the manner confirms what Deleuze
observes about the sufficiency of Leibnizian reason: an 'extraordinary
philosophical activity which consists of the creation of principles,' where
there are 'two poles, one toward which all principles are folding
themselves together, the other toward which they are all unfolding, in
the opposite way.' The double movement betrays what Deleuze calls 'the
extreme taste for principles,' far from favouring division into compartments, that 'presides over the passage of beings, of things, and of concepts
under all kinds of mobile partitions' (p. 58).
The geometrical shapes of Deleuze's sentences reproduce the serialities
of which he writes. Leibniz manifests a vision of the world with
consequences that exceed the correlation of philosophy with the
beginnings of industrial technology. At the beginning of the eighteenth
century, the idea of a stamp (or an impression promoting the effect of
individual style) 'imposed a law of constancy on the production of
objects. With the fold a fluctuation or deviation from a norm replaces the
permanence of a law, when the object assumes its place in a continuum
of variation.' The object acquires a new status when it refers no longer to
a spatial conception of molding, but a 'temporal modulation' or a
'continuous variation of matter' (chapter 2). The object is not withdrawn
from the mold that forms it. A 'continuous temporal molding' of
serialized objects replaces a paradigm of spatiality by another, of temporal
order. So, too, is the tenor of Deleuze's style. Deleuze notices that
Leibniz's mathematics of continuity and modulation change utterly our
ideas about the object and event, but all the while they conform to an
order of preformation.
Deleuze's diction tends to replicate this standard for transformation.
The sentences do not reflect a law, but vary on their implicit norm. They
are declarative; often composed of two or three independent clauses
connected by a colon or conjunctions; unlike a classical concept, they do
not seek to recall the origin of a signatory stamp. Attention is shunted
TRANSLATOR'S FOREWORD
away from their composition to the logical process that makes their
linkage appear as an unfolding of ideas and shapes. Modulation therefore
becomes a criterion of style. Consequently, the verbal material does not
set forth to tell a narrative, based on Aristotelian poetics (exposition,
movement toward a 'plot-point,' and resolution), that would tend to
reach a kernel truth in the story of Leibniz and the Baroque. Nor does
Deleuze, as might Jacques Derrida, construct an elaborate system of
textual defense that produces a surface of tantalizing involutions, or
expressions of foreplay, which defer a gripping conclusion that inverts or
twists the exposition. Instead, each chapter establishes a modulated flow,
as it were, of concept-sentence-units, which flatten illusion that generally
accompanies the rhetoric of argument or narrative. The chapters can be
read in any order; their conclusions are enveloped everywhere in the
'machinic' manner of the text.
The French edition is composed of long paragraphs that envelop the
themes listed serially in the table of contents. Most of the material follows
— but not always — the order he places under each chapter-heading. The
logic of the argumentation is carefully outlined. If the table of contents is
not studied beforehand, the organization of materials can appear dense or
chaotic. To attenuate that impression, I have taken the liberty of inserting
breaks in the text that roughly follow the themes listed in the summary. I
have also divided many of the paragraphs into smaller units. Whereas the
specialist of philosophy may have no difficulty following the development
of Deleuze's reasoning, readers of different backgrounds may find the
added space helpful for pause and reflection. Otherwise, I have stayed as
close as possible to the order and rhythm of the arguments.
Wherever possible, I have quoted English translations of Leibniz from
standard and available editions. The way that the German, French, and
English editions of Leibniz are used in The Fold is outlined in the Preface
to the Notes.
For this translation I wish to thank Biodun Iginla, of the University of
Minnesota Press, who encouraged its undertaking; Brian Massumi for his
magnificent example of A Thousand Plateaus and timely advice about this
project; Ann Klefstad and Mary Byers for their alert reading and
emendations; John Aubrey, of the Newberry Library, who solved many
bibliographical riddles. Their assistance has been invaluable. The
blemishes the reader will find are solely the fault of the translator.
Part I
THE FOLD
1
The pleats of matter
The Baroque refers not to an essence but rather to an operative function,
to a trait. It endlessly produces folds. It does not invent things: there are
all kinds of folds coming from the East, Greek, Roman, Romanesque,
Gothic, Classical folds. ... Yet the Baroque trait twists and turns its folds,
pushing them to infinity, fold over fold, one upon the other. The
Baroque fold unfurls all the way to infinity. First, the Baroque
differentiates its folds in two ways, by moving along two infinities, as
if infinity were composed of two stages or floors: the pleats of matter, and
the folds in the soul. Below, matter is amassed according to a first type of
fold, and then organized according to a second type, to the extent its part
constitutes organs that are 'differently folded and more or less
developed.' 1 Above, the soul sings of the glory of God inasmuch as it
follows its own folds, but without succeeding in entirely developing
them, since 'this communication stretches out indefinitely.' 2 A labyrinth
is said, etymologically, to be multiple because it contains many folds. The
multiple is not only what has many parts but also what is folded in many
ways. A labyrinth corresponds exactly to each level: the continuous
labyrinth in matter and its parts, the labyrinth of freedom in the soul and
its predicates. 3 If Descartes did not know how to get through the
labyrinth, it was because he sought its secret of continuity in rectilinear
tracks, and the secret of liberty in a rectitude of the soul. He knew the
inclension of the soul as little as he did the curvature of matter. A
'cryptographer' is needed, someone who can at once account for nature
and decipher the soul, who can peer into the crannies of matter and read
into the folds of the soul.'
3
THE PLEATS OF MATTER
THE FOLD
Clearly the two levels are connected (this being why continuity rises
up into the soul). There are souls down below, sensitive, animal; and
there even exists a lower level in the souls. The pleats of matter surround
and envelop them. When we learn that souls cannot be furnished with
windows opening onto the outside, we must first, at the very least,
include souls upstairs, reasonable ones, who have ascended to the other
level ('elevation'). It is the upper floor that has no windows. It is a dark
room or chamber decorated only with a stretched canvas 'diversified by
folds,' as if it were a living dermis. Placed on the opaque canvas, these
folds, cords, or springs represent an innate form of knowledge, but when
solicited by matter they move into action. Matter triggers 'vibrations or
oscillations' at the lower extremity of the cords, through the intermediary
of 'some little openings' that exist on the lower level. Leibniz constructs a
great Baroque montage that moves between the lower floor, pierced with
windows, and the upper floor, blind and closed, but on the other hand
resonating as if it were a musical salon translating the visible movements
below into sounds up above. 5
It could be argued that this text does not express Leibniz's thought, but
instead the maximum degree of its possible conciliation with Locke. The
text also fashions a way of representing what Leibniz will always affirm: a
correspondence and even a communication between the two levels,
between the two labyrinths, between the pleats of matter and the folds in
the soul. A fold between the two folds? And the same image, that of veins
in marble, is applied to the two under different conditions. Sometimes the
veins are the pleats of matter that surround living beings held in the mass,
such that the marble tile resembles a rippling lake that teems with fish.
Sometimes the veins are innate ideas in the soul, like twisted figures or
powerful statues caught in the block of marble. Matter is marbled, of two
different styles.
WOlfflin noted that the Baroque is marked by a certain number of
material traits: horizontal widening of the lower floor, flattening of the
pediment, low and curved stairs that push into space; matter handled in
masses or aggregates, with the rounding of angles and avoidance of
perpendiculars; the circular acanthus replacing the jagged acanthus, use
of limestone to produce spongy, cavernous shapes, or to constitute a
vortical form always put in motion by renewed turbulence, which ends
only in the manner of a horse's mane or the foam of a wave; matter tends
to spill over in space, to be reconciled with fluidity at the same time fluids
themselves are divided into masses. °
4
dosed private room,
decorated with a 'drapery
diversified by folds'
common rooms, with
'several small openInge the five senses
The Baroque House (an allegory)
Huygens develops a Baroque mathematical physics whose goal is
curvilinearity. With Leibniz the curvature of the universe is prolonged
according to three other fundamental notions: the fluidity of matter, the
elasticity of bodies, and motivating spirit as a mechanism. First, matter
would clearly not be extended following a twisting line. Rather, it would
follow a tangent.' But the universe appears compressed by an active force
that endows matter with a curvilinear or spinning movement, following
an arc that ultimately has no tangent. And the infinite division of matter
causes compressive force to return all portions of matter to the
surrounding areas, to the neighbouring parts that bathe and penetrate
the given body, and that determine its curvature. Dividing endlessly, the
parts of matter form little vortices in a maelstrom, and in these are found
even more vortices, even smaller, and even more are spinning in the
concave intervals of the whirls that touch one another.
Matter thus offers an infinitely porous, spongy, or cavernous texture
without emptiness, caverns endlessly contained in other caverns: no
matter how small, each body contains a world pierced with irregular
passages, surrounded and penetrated by an increasingly vaporous fluid,
the totality of the universe resembling a 'pond of matter in which there
exist different flows and waves.' 8 From this, however, we would not
conclude, in the second place, that even the most refined matter is
perfectly fluid and thus loses its texture (according to a thesis that Leibniz
imputes to Descartes). Descartes's error probably concerns what is to be
found in different areas. He believed that the real distinction between
5
THE FOLD
parts entailed separability. What specifically defines an absolute fluid is
the absence of coherence or cohesion; that is, the separability of parts,
which in fact applies only to a passive and abstract matter. 9 According to
Leibniz, two parts of really distinct matter can be inseparable, as shown
not only by the action of surrounding forces that determine the
curvilinear movement of a body but also by the pressure of surrounding
forces that determine its hardness (coherence, cohesion) or the
inseparability of its parts. Thus it must be stated that a body has a degree
of hardness as well as a degree of fluidity, or that it is essentially elastic,
the elastic force of bodies being the expression of the active compressive
force exerted on matter. When a boat reaches a certain speed a wave
becomes as hard as a wall of marble. The atomistic hypothesis of an
absolute hardness and the Cartesian hypothesis of an absolute fluidity are
joined all the more because they share the error that posits separable
minima, either in the form of finite bodies or in infinity in the form of
points (the Cartesian line as a site of its points, the analytical punctual
equation).
That is what Leibniz explains in an extraordinary piece of writing: a
flexible or an elastic body still has cohering parts that form a fold, such
that they are not separated into parts of parts but are rather divided to
infinity in smaller and smaller folds that always retain a certain cohesion.
Thus a continuous labyrinth is not a line dissolving into independent
points, as flowing sand might dissolve into grains, but resembles a sheet of
paper divided into infinite folds or separated into bending movements,
each one determined by the consistent or conspiring surroundings. 'The
division of the continuous must not be taken as of sand dividing into
grains, but as that of a sheet of paper or of a tunic in folds, in such a way
that an infinite number of folds can be produced, some smaller than
others, but without the body ever dissolving into points or minima." ° A
fold is always folded within a fold, like a cavern in a cavern. The unit of
matter, the smallest element of the labyrinth, is the fold, not the point
which is never a part, but a simple extremity of the line. That is why parts
of matter are masses or aggregates, as a correlative to elastic compressive
force. Unfolding is thus not the contrary of folding, but follows the fold up
to the following fold. Particles are 'turned into folds,' that a 'contrary
effort changes over and again.'" Folds of winds, of waters, of fire and
earth, and subterranean folds of veins of ore in a mine. In a system of
complex interactions, the solid pleats of 'natural geography' refer to the
effect first of fire, and then of waters and winds on the earth; and the
6
THE PLEATS OF MATTER
veins of metal in mines resemble the curves of conical forms, sometimes
ending in a circle or an ellipse, sometimes stretching into a hyperbola or a
parabola. I2 The model for the sciences of matter is the 'origami,' as the
Japanese philosopher might say, or the art of folding paper.
Two consequences result that provide a sense of the affinity of matter
with life and organisms. To be sure, organic folds have their own
specificity, as fossils demonstrate. But on the one hand, the division of
parts in matter does not go without a decomposition of bending
movement or of flexions. We see this in the development of the egg,
where numerical division is only the condition of morphogenic movements, and of invagination as a pleating. On the other hand, the
formation of the organism would remain an improbable mystery, or a
miracle, even if matter were to divide infinitely into independent points.
But it becomes increasingly probable and natural when an infinity of
indeterminate states is given (already folded over each other), each of
which includes a cohesion at its level, somewhat like the improbability of
forming a word by chance with separate letters, but with far more
likelihood with syllables or inflections.' 3
In the third place, it is evident that motivating force becomes the
mechanism of matter. If the world is infinitely cavernous, if worlds exist
in the tiniest bodies, it is because everywhere there can be found 'a spirit
in matter,' which attests not only to the infinite division of parts but also
to progressivity in the gain and loss of movement all the while
conservation of force is realized. The matter-fold is a matter-time; its
characteristics resemble the continuous discharge of an 'infinity of windmuskets.' 14 And there still we can imagine the affinity of matter for life
insofar as a muscular conception of matter inspires force in all things. By
invoking the propagation of light and the 'expulsion into luminosity,' by
making an elastic, inflammable, and explosive spirit from animal spirits,
Leibniz turns his back on Cartesianism. He renews the tradition of Van
Helmont and is inspired by Boyle's experimentation. 15 In short, to the
extent that folding is not opposed to unfolding, such is also the case in the
pairs tension-release and contraction-dilation (but not condensationrarefaction, which would imply a void).
The lower level or floor is thus also composed of organic matter. An
organism is defined by endogenous folds, while inorganic matter has
exogenous folds that are always determined from without or by the
7
THE FOLD
surrounding environment. Thus, in the case of living beings, an inner
formative fold is transformed through evolution, with the organism's
development. Whence the necessity of a preformation. Organic matter is
not, however, different from inorganic matter (here, the distinction of a
first and a second matter is irrelevant). Whether organic or inorganic,
matter is all one; but active forces are not the only ones exerted upon it.
To be sure, these are perfectly material or mechanical forces, where
indeed souls cannot be made to intervene: for the moment, vitalism is a
strict organicism. Material forces, which account for the organic fold,
have only to be distinguished from the preceding forces, and be added to
it; they must suffice, where they are exerted, to transform raw matter into
organic matter. In contrast to compressive or elastic forces, Leibniz calls
them 'plastic forces.' They organize masses but, although the latter
prepare organisms or make them possible by means of motivating drive, it
is impossible to go from masses to organisms, since organs are always
based on these plastic forces that preform them, and are distinguished
from forces of mass, to the point where every organ is born from a
preexisting organ. 18 Even fossils in matter are not explained by our
faculty of imagination; when, for example, we see that the head of Christ
we fancy in the spots on a wall refers to plastic forces that wind through
organisms that already exist.
If plastic forces can be distinguished, it is not because living matter
exceeds mechanical processes, but because mechanisms are not sufficient
to be machines. A mechanism is faulty not for being too artificial to
account for living matter, but for not being mechanical enough, for not
being adequately machined. Our mechanisms are in fact organized into
parts that are not in themselves machines, while the organism is infinitely
machined, a machine whose every part or piece is a machine, but only
'transformed by different folds that it receives."' Plastic forces are thus
more machinelike than they are mechanical, and they allow for the
definition of Baroque machines. It might be claimed that mechanisms of
inorganic nature already stretch to infinity because the motivating force is
of an already infinite composition, or that the fold always refers to other
folds. But it requires that each time, an external determination, or the
direct action of the surroundings, is needed in order to pass from one level
to another; without this we would have to stop, as with our mechanisms.
The living organism, on the contrary, by virtue of preformation has an
internal destiny that makes it move from fold to fold, or that makes
machines from machines all the way to infinity. We might say that
8
THE PLEATS OF MATTER
between organic and inorganic things there exists a difference of vector,
the latter going toward increasingly greater masses in which statistical
mechanisms are operating, the former toward increasingly smaller,
polarized masses in which the force of an individuating machinery, an
internal individuation, is applied. Is this Leibniz's premonition of several
aspects that will come true only much later? 18 No doubt, for Leibniz,
internal individuation will only be explained at the level of souls: organic
interiority is only derivative, and has but one container of coherence or
cohesion (not of inherence or of 'inhesion'). It is an interiority of space,
and not yet of motion; also, an internalization of the outside, an
invagination of the outside that could not occur all alone if no true
interiorities did not exist elsewhere. It remains the case that the organic
body thus confers an interior on matter, by which the principle of
individuation is applied to it: whence the figure of the leaves of a tree,
two never being exactly alike because of their veins or folds.
Folding-unfolding no longer simply means tension-release, contractiondilation, but enveloping-developing, involution-evolution. The organism
is defined by its ability to fold its own parts and to unfold them, not to
infinity, but to a degree of development assigned to each species. Thus an
organism is enveloped by organisms, one within another (interlocking of
germinal matter), like Russian dolls. The first fly contains the seeds of all
flies to come, each being called in its turn to unfold its own parts at the
right time. And when an organism dies, it does not really vanish, but folds
in upon itself, abruptly involuting into the again newly dormant seed by
skipping all intermediate stages. The simplest way of stating the point is
by saying that to unfold is to increase, to grow; whereas to fold is to
diminish, to reduce, 'to withdraw into the recesses of a world.' 19 Yet a
simple metric change would not account for the difference between the
organic and the inorganic, the machine and its motive force. It would fail
to show that movement does not simply go from one greater or smaller
part to another, but from fold to fold. When a part of a machine is still a
machine, the smaller unit is not the same as the whole. When Leibniz
invokes Harlequin's layers of clothing, he means that his underwear is
not the same as his outer garments. That is why metamorphosis or
'metaschematism' pertains to more than mere change of dimension:
every animal is double — but as a heterogenous or heteromorphic
creature, just as the butterfly is folded into the caterpillar that will soon
unfold. The double will even be simultaneous to the degree that the ovule
is not a mere envelope but furnishes one part whose other is in the male
9
THE FOLD
element. 2° In fact, it is the inorganic that repeats itself, with a difference
of proximate dimension, since it is always an exterior site which enters
the body; the organism, in contrast, envelops an interior site that contains
necessarily other species of organisms, those that envelop in their turn the
interior sites containing yet other organisms: 'Each portion of matter may
be conceived as a garden full of plants, and as a pond full of fish. But
every branch of each plant, every member of each animal, and every drop
of their liquid parts is in itself likewise a similar garden or pond.' 2I Thus
the inorganic fold happens to be simple and direct, while the organic fold
is always composite, alternating, indirect (mediated by an interior site). 22
Matter is folded twice, once under elastic forces, a second time under
plastic forces, but one is not able to move from the first to the second.
Thus the universe is neither a great living being, nor is it in itself an
Animal: Leibniz rejects this hypothesis as much as he rejects that of a
universal Spirit. Organisms retain an irreducible individuality, and
organic descendants retain an irreducible plurality. It remains that the
two kinds of force, two kinds of folds — masses and organisms — are strictly
coextensive. There are no fewer living beings than parts of inorganic
matter. 23 Clearly an exterior site is not a living being; rather, it is a lake, a
pond, or a fish hatchery. Here the figure of the lake or pond acquires a
new meaning, since the pond — and the marble tile — no longer refer to
elastic waves that swim through them like inorganic folds, but to fish that
inhabit them like organic folds. And in life itself the inner sites contained
are even more hatcheries full of other fish: a 'swarm.' Inorganic folds of
sites move between two organic folds. For Leibniz, as for the Baroque, the
principles of reason are veritable cries: Not everything is fish, but fish are
teeming everywhere. ... Universality does not exist, but living things are
ubiquitous.
It might be said that the theory of preformation and duplication, as
observations made through the microscope confirm, has long been
abandoned. The meaning of development or evolution has turned topsyturvy, since it now designates epigenesis — the appearance of organs and
organisms neither preformed nor closed one within the other, but formed
from something else that does not resemble them: the organ does not
arch back to a preexisting organ, but to a much more general and less
differentiated design. 24 Development does not go from smaller to greater
things through growth or augmentation, but from the general to the
special, through differentiations of an initially undifferentiated field
either under the action of exterior surroundings or under the influence of
10
THE PLEATS OF MATTER
internal forces that are directive, directional, but that remain neither
constitutive nor preformative. However, insofar as preformism exceeds
simple metric variations, it tends to be aligned with an epigenesis to the
extent epigenesis is forced to hold to a kind of virtual or potential
preformation. The essential is elsewhere; basically, two conceptions share
the common trait of conceiving the organism as a fold, an originary
folding or creasing (and biology has never rejected this determination of
living matter, as shown nowadays with the fundamental pleating of
globular protein). Preformism is the form in which this truth of the
seventeenth century is perceived through the first microscopes. It is
hardly surprising that from then on the same problems are found in the
sense of epigenesis and preformation.
Thus can all types of folding be called modifications or degrees of
development of a same Animal in itself? Or are there types of irreducible
foldings, as Leibniz believes in a preformist perspective, and as Cuvier and
Baer also contend from an epigenic standpoint? 25 Certainly a great
opposition subsists between the two points of view. With epigenesis the
organic fold is produced, is unearthed, or is pushed up from a relatively
smooth and consistent surface. (How could a redoubling, an invagination,
or an intubation be prefigured?) Now with preformism an organic fold
always ensues from another fold, at least on the inside from a same type
of organization: every fold originates from a fold, plica ex plica. If
Heideggerian terms can be used, we can say that the fold of epigenesis is
an Einfalt, or that it is the differentiation of an undifferentiated, but that
the fold from preformation is a Zweifalt, not a fold in two — since every
fold can only be thus — but a 'fold-of-two,' an entre-deux, something
'between' in the sense that a difference is being differentiated. From this
point of view we cannot be sure if preformism does not have a future.
Masses and organisms, masses and living beings thus fill the lower level.
Why then is another storey needed, since sensitive or animal souls are
already there, inseparable from organic bodies? Each soul even seems apt
to be localized in its body, this time as a 'point' in a droplet, that subsists
in a part of the droplet when the latter is divided or diminished in
volume: thus, in death the soul remains right where it was, in a part of
the body, however reduced it may be. 26 Leibniz states that the point of
view is in the body. 27 Surely everything in the body works like a
machine, in accord with plastic forces that are material, but these forces
explain everything except for the variable degrees of unity to which they
11
THE FOLD
bring the masses they are organizing (a plant, a worm, a vertebrate ...).
Plastic forces of matter act on masses, but they submit them to real unities
that they take for granted. They make an organic synthesis, but assume
the soul as the unity of synthesis, or as the 'immaterial principle of life.'
Only there does an animism find a connection with organicism, from the
standpoint of pure unity or of union, independently of all causal action. 28
It remains that organisms would not on their account have the causal
power to be folded to infinity, and of surviving in ashes, without the
unity-souls from which they are inseparable, and which are inseparable
from them. Here is the great difference that makes Leibniz break away
from Malebranche: not only is there a preformation of bodies, but also a
preexistence of souls in fertile seeds. 29 Life is not only everywhere, but
souls are everywhere in matter. Thus, when an organism is called to
unfold its own parts, its animal or sensitive soul is opened onto an entire
theater in which it perceives or feels according to its unity, independently
of its organism, yet inseparable from it.
But — and here is the whole problem — what happens with bodies, from
the time of Adam's seed that envelops them, that are destined to become
humans? Juridically, one might say that they carry in a nutshell 'a sort of
sealed act' that marks their fate. And when the hour comes for them to
unfold their parts, to attain a degree of organic development proper to
man, or to form cerebral folds, at the same time their animal soul
becomes reasonable by gaining a greater degree of unity (mind): 'The
organized body would receive at the same time the disposition of the
human body, and its soul would be raised to the stage of a reasonable
soul, but I cannot decide here if it occurs through an ordinary process or
an extraordinary work of God.' 3° Then in every event this becoming is an
elevation, an exaltation: a change of theater, of rule, of level or of floors.
The theater of matter gives way to that of spirits or of God. In the Baroque
the soul entertains a complex relation with the body. Forever indissociable from the body, it discovers a vertiginous animality that gets it tangled
in the pleats of matter, but also an organic or cerebral humanity (the
degree of development) that allows it to rise up, and that will make it
ascend over all other folds.
The reasonable soul is free, like a Cartesian diver, to fall back down at
death and to climb up again at the last judgment. As Leibniz notes, the
tension is between the collapse and the elevation or ascension that in
different spots is breaching the organized masses. We move from funerary
12
THE PLEATS OF MATTER
figures of the Basilica of Saint Laurence to the figures on the ceiling of
Saint Ignatius. It might be claimed that physical gravity and religious
elevation are quite different and do not pertain to the same world.
However, these are two vectors that are allotted as such in the distinction
of the two levels or floors of a single and same world, or of the single and
same house. It is because the body and the soul have no point in being
inseparable, for they are not in the least really distinct (we have already
seen it for the parts of matter). From this moment on any localization of
the soul in an area of the body, no matter how tiny it may be, amounts
rather to a projection from the top to the bottom, a projection of the soul
focalizing on a 'point' of the body, in conformity with Desargues's
geometry, that develops from a Baroque perspective. In short, the
primary reason for an upper floor is the following: there are souls on the
lower floor, some of whom are chosen to become reasonable, thus to
change their levels.
Movement, then, cannot be stopped. The reciprocation of the
Leibnizian principle holds not only for reasonable souls but also for
animal or sensible souls themselves: if two really distinct things can be
inseparable, two inseparable things can be really distinct, and belong to
two levels, the localization of the one in the other amounting to a
projection upon a point ('I do not think that we can consider souls as
being in points, perhaps we might say ... that they are in a place through
a connection'). As degrees of unity, animal souls are already on the other
floor, everything being accomplished mechanically in the animal itself at
the lower level. Plastic or machinic forces are part of the 'derivative
forces' defined in respect to the matter that they organize. But souls, on
the contrary, are 'primitive forces' or immaterial principles of life that are
defined only in respect to the inside, in the self, and 'through analogy
with the mind.' We can nonetheless remember that these animal souls,
with their subjugated organism, exist everywhere in inorganic matter.
Thus in its turn inorganic matter reverts to souls whose site is elsewhere,
higher up and that is only projected upon it. In all probability a body —
however small — follows a curvilinear trajectory only under the impulsion
of the second species of derivative forces, compressive or elastic forces
that determine the curve through the mechanical action of the
surrounding bodies on the outside: isolated, the body would follow the
straight tangent. But still, mechanical laws or extrinsic determinations
(collisions) explain everything except the unity of a concrete movement,
no matter how irregular or variable it may be. Unity of movement is an
13
THE FOLD
affair of the soul, and almost of a conscience, as Bergson will later
discover. Just as the totality of matter arches back to a curving that can no
longer be determined from the outside, the curvilinear course followed by
a given body under the impetus of the outside goes back to a 'higher,'
internal and individuating, unity on the other floor, that contains the
'law of curvilinearity,' the law of folds or changes of direction. 31 The same
movement is always determined from the outside, through collisions,
insofar as it is related to derivative force, but unified from the inside, to
the degree it is related to primitive force. In the first relation, the curve is
accidental and derived from the straight line, but in the second it is
primary, such that the motive force sometimes is mechanically explained
through the action of a subtle surrounding, and sometimes is understood
from the inside as the interior of the body, 'the cause of movement that is
already in the body,' and that only awaits the suppression of an obstacle
from the outside. 32
Hence the need for a second floor is everywhere affirmed to be strictly
metaphysical. The soul itself is what constitutes the other floor or the
inside up above, where there are no windows to allow entry of influence
from without. Even in a physical sense we are moving across outer
material pleats to inner animated, spontaneous folds. These are what we
must now examine, in their nature and in their development. Everything
moves as if the pleats of matter possessed no reason in themselves. It is
because the Fold is always between two folds, and because the betweentwo-folds seems to move about everywhere: Is it between inorganic
bodies and organisms, between organisms and animal souls, between
animal souls and reasonable souls, between bodies and souls in general?
14
2
The folds in the soul
Inflection is the ideal genetic element of the variable curve or fold.
Inflection is the authentic atom, the elastic point. That is what Klee
extracts as the genetic element of the active, spontaneous line. It testifies
to his affinity for the Baroque and for Leibniz, and opposes him to
Kandinsky, a Cartesian, for whom angles are firm, for whom the point is
firm, set in motion by an exterior force. For Klee, however, the point as a
'nonconceptual concept of noncontradiction' moves along an inflection.
It is the point of inflection itself, where the tangent crosses the curve.
That is the point-fold. Klee begins with a succession of three figures.' The
first draws the inflection. The second shows that no exact and unmixed
figure can exist. As Leibniz stated, there can never be 'a straight line
without curves intermingled,' nor any 'curve of a certain finite nature
unmixed with some other, and in small parts as well as large,' such that
one 'will never be able to fix upon a certain precise surface in a body as
one might if there were atoms.' 2 The third marks the convex side with
shadow, and thus disengages concavity and the axis of its curve, that now
and again changes sides from the point of inflection.
Bernard Cache defines inflection — or the point of inflection — as an
intrinsic singularity. Contrary to 'extrema' (extrinsic singularities,
maximum and minimum), it does not refer to coordinates: it is neither
high nor low, neither right nor left, neither regression nor progression. It
corresponds to what Leibniz calls an 'ambiguous sign.' It is weightless;
even the vectors of concavity still have nothing to do with a vector of
gravity since the axes of the curve that they are determining oscillate
around it. Thus inflection is the pure Event of the line or of the point,
15
THE FOLDS IN THE SOUL
THE FOLD
V
Gothic arch
the Virtual, ideality par excellence. It will take place following the axes of
the coordinates, but for now it is not yet in the world: it is the World
itself, or rather its beginning, as Klee used to say, 'a site of cosmogenesis,'
'a nondimensional point' 'between dimensions.' An event that would
await an event? That is how the inflection already moves through virtual
transformations, that is (for Cache), three transformations. 3
The first are vectorial, or operate by symmetry, with an orthogonal or
tangent plane of reflection. They work according to optical laws,
transforming inflection at a turning point, in an ogive, or pointed arch.
The ogive expresses the form of a moving body that espouses the
configuration of lines of flowing liquid, and the return, the profile of the
depth of a valley when waters are brought together following the line of a
single course.
The second set of transformations is projective: such transformations
convey the projection, on external space, of internal spaces defined by
'hidden parameters' and variables or singularities of potential. Rene
Thorn's transformations refer in this sense to a morphology of living
matter, providing seven elementary events: the fold; the crease; the
dovetail; the butterfly; the hyperbolic, elliptical, and parabolic umbilicus. 4
Finally, the inflection in itself cannot be separated from an infinite
variation or an infinitely variable curve. Such is Koch's curve, obtained
16
point of return
Gothic scansion: gothic arch and return
by means of rounding angles, according to Baroque requirements, by
making them proliferate according to a law of homothesis. 3 The curve
passes through an infinite number of angular points and never admits a
tangent at any of these points. It envelops an infinitely cavernous or
porous world, constituting more than a line and less than a surface
(Mandelbrot's fractal dimension as a fractional or irrational number, a
nondimension, an interdimension). 6 Nonethelesss homothesis causes
variation to coincide with a change of scale, as in the case of the length of
a geographical gradient. Everything changes when fluctuation is made to
intervene in the place of internal homothesis. It is no longer possible to
determine an angular point between two others, no matter how close one
is to the other; but there remains the latitude to always add a detour by
making each interval the site of a new folding. That is how we go from
fold to fold and not from point to point, and how every contour is blurred
to give definition to the formal powers of the raw material, which rise to
the surface and are put forward as so many detours and supplementary
folds. Transformation of inflection can no longer allow for either
symmetry or the favored plane of projection. It becomes vortical and is
produced later; deferred, rather than prolonged or proliferating: the line
17
THE FOLD
THE FOLDS IN THE SOUL
effectively folds into a spiral in order to defer inflection in a movement
suspended between sky and earth, which either moves away from or
indefinitely approaches the center of a curve and at each instant 'rises
skyward or risks falling upon us.' 7 But the vertical spiral neither retains
nor defers inflection without also promoting it and making it irresistible,
in a transversal sense: a turbulence that is never produced on its own,
whose spiral follows a fractal mode by which new turbulences are
inserted between the initial ones. 8 Growing from other turbulences, in
the erasure of contour, turbulence ends only in watery froth or in a
flowing mane. Inflection itself becomes vortical, and at the same time its
variation opens onto fluctuation, it becomes fluctuation.
The definition of Baroque mathematics is born with Leibniz. The object of
the discipline is a 'new affection' of variable sizes, which is variation itself.
To be sure, in a fractional number or even in an algebraic formula,
variability is not considered as such, since each of the terms has or must
have a particular value. The same no longer holds either for the irrational
number and corresponding serial calculus, or for the differential quotient
and differential calculus, in which variation becomes presently infinite.
The irrational number is the common limit of two convergent series, of
which one has no maximum and the other no minimum. The differential
quotient is the common limit of the relation between two quantities that
are vanishing. But we can remark that in both cases the presence of a
curved element acts as a cause. The irrational number implies the descent
of a circular arc on the straight line of rational points, and exposes the
latter as a false infinity, a simple undefinite that includes an infinity of
lacunae; that is why the continuous is a labyrinth that cannot be
represented by a straight line. The straight line always has to be
intermingled with curved lines.
C
Between the two points A and B — no matter in what proximity they may
be — there always remains the possibility for carrying out the right
isosceles triangle, whose hypotenuse goes from A to B, and whose
18
summit, C, determines a circle that crosses the straight line between A
and B. The arc of the circle resembles a branch of inflection, an element of
the labyrinth, that from an irrational number, at the meeting of the
curved and straight lines, produces a point-fold. It is identical in the case
of the differential quotient, with the point-fold A that retains the relation
c
e
when these two magnitudes vanish (that, too, is the relation between a
radius and a tangent that fits the angle in C). 9 In short, there will always
be an inflection that makes a fold from variation, and that brings the fold
or the variation to infinity. The fold is Power, as we see in the irrational
number that appears by way of an extraction from a root, and in the
differential quotient that appears by way of the relation of a magnitude
and a power, as a condition of variation. Force itself is an act, an act of the
fold.
When mathematics assumes variation as its objective, the notion of
function tends to be extracted, but the notion of objective also changes
and becomes functional. In some especially important mathematical
writings, Leibniz posits the idea of families of curves depending upon one
or several parameters: 'Instead of seeking the unique straight tangent in a
unique point for a given curve, we can go about seeking the tangent
curve in an infinity of points with an infinity of curves; the curve is not
touched, it is touching, the tangent no longer either straight, unique, or
touching, but now being curvilinear, an infinite, touched family' (the
problem of the inverse of tangents). I° There exists thus a series of curves
19
THE FOLD
that not only imply constant parameters for each and every curve, but the
reduction of variables to a 'single and unique variability' of the touching
or tangent curve: the fold. The goal is no longer defined by an essential
form, but reaches a pure functionality, as if declining a family of curves,
framed by parameters, inseparable from a series of possible declensions or
from a surface of variable curvature that it is itself describing.
This new object we can call objectile. As Bernard Cache has demonstrated,
this is a very modern conception of the technological object: it refers
neither to the beginnings of the industrial era nor to the idea of the
standard that still upheld a semblance of essence and imposed a law of
constancy ('the object produced by and for the masses'), but to our
current state of things, where fluctuation of the norm replaces the
permanence of a law; where the object assumes a place in a continuum
by variation; where industrial automation or serial machineries replace
stamped forms. The new status of the object no longer refers its condition
to a spatial mold — in other words, to a relation of form-matter — but to a
temporal modulation that implies as much the beginnings of a
continuous variation of matter as a continuous development of form.
In modulation 'a pause never intervenes for withdrawal from the mold
because the circulation of the source of energy amounts to a permanent
withdrawal; a modulator is a continuous temporal mold ... Molding
amounts to modulating in a definitive way; modulating is molding in a
continuous and perpetually variable fashion."' Can we not affirm that
modulation is what Leibniz is defining when he states that the law of
series posits curves as 'the trace of the same line' in a continuous
movement, continually touched by the curve of their convergence? His is
not only a temporal but also a qualitative conception of the object, to the
extent that sounds and colors are flexible and taken in modulation. The
object here is manneristic, not essentializing: it becomes an event.
If the status of the object is profoundly changed, so also is that of the
subject. We move from inflection or from variable curvature to vectors of
curvature that go in the direction of concavity. Moving from a branching
of inflection, we distinguish a point that is no longer what runs along
inflection, nor is it the point of inflection itself; it is the one in which the
lines perpendicular to tangents meet in a state of variation. It is not
exactly a point but a place, a position, a site, a 'linear focus,' a line
emanating from lines. To the degree it represents variation or inflection, it
20
THE FOLDS IN THE SOUL
can be called point of view. Such is the basis of perspectivism, which does
not mean a dependence in respect to a pregiven or defined subject; to the
contrary, a subject will be what comes to the point of view, or rather what
remains in the point of view. That is why the transformation of the object
refers to a correlative transformation of the subject: the subject is not a
subject but, as Whitehead says, a 'superject.' Just as the object becomes
objectile, the subject becomes a superject. A needed relation exists
between variation and point of view: not simply because of the variety of
points of view (though, as we shall observe, such a variety does exist), but
in the first place because every point of view is a point of view on
variation. The point of view is not what varies with the subject, at least in
the first instance; it is, to the contrary, the condition in which an eventual
subject apprehends a variation (metamorphosis), or: something = x
(anamorphosis). 12 For Leibniz, for Nietzsche, for William and Henry
James, and for Whitehead as well, perspectivism amounts to a relativism,
but not the relativism we take for granted. It is not a variation of truth
according to the subject, but the condition in which the truth of a
variation appears to the subject. This is the very idea of Baroque
perspective.
It might, however, be claimed that point of view explodes with the
proximity of concavity: does there not exist a contradiction between
continuity of infinite variation and the discontinuity of viewpoint? Is this
not the same contradiction between the law of continuity and the
principle of indiscernibles that many authors (following Kant) denounce
in Leibniz? The question is moot if, from the outset, we try to not
combine continuity and contiguity.' 3 Although they are not contiguous,
singularities, or unique points, belong fully to continuousness. Points of
inflection make up a first kind of singularity in space, and constitute
envelopes in accord with indivisible relations of distance. But neither one
nor the other contradicts the continuous. There are as many points of
view — whose distance in each case is indivisible — as inflections in
inflection, whose length increases. Continuity is made up no less of
distances between points of view than of the length of an infinity of
corresponding curves. Perspectivism is clearly a pluralism, but it thus
implies by its name distance and not discontinuity (certainly no void is
21
THE FOLD
given between two points of view). Leibniz can define extension (extensio)
as 'continuous repetition' of the situs or position - that is, of point of view:
not that extension is therefore the attribute of point of view, but that the
attribute of space (spatium), an order of distances between points of view,
is what makes this repetition possible."
Point of view on a variation now replaces the center of a figure or a
configuration. The most famous example is that of conic sections, where
the point of the cone is the point of view to which the circle, the ellipse,
the parabola, and the hyperbola are related as so many variants that
follow the incline of the section that is planned ('scenographies'). All
these figures become so many ways by which a 'flat projection' is
mapped out. And this projection is not exactly the circle, which it would
be only under the privilege of an old conception of perspective. Rather,
it is the objectile that now declines or describes relations of curves: those
of the second degree, in which the circle plays a role. This objectile or
projection resembles an unfolding. But unfolding is no more the
contrary of foldings than an invariant would be the contrary of
variation. It is an invariant of transformation. Leibniz will designate it
by an 'ambiguous sign." 5 It is effectively enveloped in variation, just as
variation is enveloped in point of view. It does not exist outside of
variation, just as variation does not exist outside of point of view. That is
why, at the basis of this new theory of conic sections, Desargues called
the relation or the law enveloped by a variation 'involution' (for
example, a triangle that is supposed to turn around an axis, the
dispositions of the points defined on the axis by the projection of three
summits and by the prolongation of the three sides)."
Michel Serres has analyzed superlatively both the consequences and
the presuppositions of the new theory of conic sections: in a world of
infinity, or of variable curvature that has lost notion of a center, he
stresses the importance of setting point of view in the place of the missing
22
THE FOLDS IN THE SOUL
center; of the new optical model of perception, and of geometry in
perception, that casts aside tactile notions, contact and figure, in favor of
an 'architecture of vision'; of the status of the object, which now exists
only through its metamorphoses or in the declension of its profiles; of
perspectivism as a truth of relativity (and not a relativity of what is true).
In each area point of view is a variation or a power of arranging cases, a
condition for the manifestation of reality: thus the alternating series of
conics, beginning with the summit of the cone (a finite point, an infinite
straight line, a finite circle, an infinite parabola, a finite ellipse, an infinite
hyperbola), or rather the series of powers to the second degree from the
apex of the arithmetical triangle, and for every area the need to assign the
point of view without which truth could not be proven, that is, to arrange
series of variations or determine each case. 17 In all these areas Leibniz
constructs the 'table' of cases that refers to point of view as jurisprudence
or the art of judgment. It comprises the need to find the correct point of
view - or rather, the best - without which disorder or even chaos would
reign. When we mentioned Henry James it was with respect to Leibniz's
idea about point of view as the secret of things, as focus, cryptography, or
even as the determination of the indeterminate by means of ambiguous
signs: what I am telling to you, what you are also thinking about, do you
agree to tell him about it, provided that we know what to expect of it.
about her, and that we also agree about who he is and who she is? As in a
Baroque anamorphosis, only point of view provides us with answers and
cases.
We have gone from variable curvature to the origin of curvature (from
the concave side), from variation to point of view, from the fold to
envelopment, in a word, from inflection to inclusion. The transition
cannot be discerned, somewhat like a right angle that is not measured by
a great arc but by a tiny arc situated close to the summit: it is at the
summit 'that the angle or the inclination of the two lines is found.' 18 We
would nonetheless hesitate to say that visibility is located in point of
view. We would need a more natural intuition to allow for this passage to
the limit. Thus it is a very simple intuition: Why would something be
folded, if it were not to be enveloped, wrapped, or put into something
else? It appears that here the envelope acquires its ultimate or perhaps
final meaning: it is no longer an envelope of coherence or cohesion, like
an egg, in the 'reciprocal envelopment' of organic parts. Nor even a
mathematical envelope of adherence or adhesion, where a fold still
23
THE FOLD
envelops other folds, as in the enveloping envelope that touches an
infinity of curves in an infinity of points. It is an envelope of inherence or
of unilateral 'inhesion': inclusion or inherence is the final cause of the fold,
such that we move indiscernibly from the latter to the former. Between
the two, a gap is opened which makes the envelope the reason for the
fold: what is folded is the included, the inherent. It can be stated that
what is folded is only virtual and currently exists only in an envelope, in
something that envelops it.
From now on it is not exactly point of view that includes; or at least, it
does so only as an agent, but not of a final cause or a finished act
(entelechia). Inclusion or inherence has a condition of closure or
envelopment, which Leibniz puts forward in his famous formula, 'no
windows,' and which point of view does not suffice to explain. When
inclusion is accomplished, it is done so continuously, or includes the
sense of a finished act that is neither the site, the place, nor the point of
view, but what remains in point of view, what occupies point of view,
and without which point of view would not be. It is necessarily a soul, a
subject. A soul always includes what it apprehends from its point of view,
in other words, inflection. Inflection is an ideal condition or a virtuality that
currently exists only in the soul that envelops it. Thus the soul is what has folds
and is full of folds.
Folds are in the soul and authentically exist only in the soul. That is
already true for 'innate ideas': they are pure virtualities, pure powers
whose act consists in habitus or arrangements (folds) in the soul, and
whose completed act consists of an inner action of the soul (an internal
deployment). 19 But this is no less true for the world: the whole world is
only a virtuality that currently exists only in the folds of the soul which
convey it, the soul implementing inner pleats through which it endows
itself with a representation of the enclosed world. We are moving from
inflection to inclusion in a subject, as if from the virtual to the real,
inflection defining the fold, but inclusion defining the soul or the subject,
that is, what envelops the fold, its final cause and its completed act.
Whence the distinction of three kinds of points as three kinds of
singularities. 20 The physical point is what runs along inflection or is the
point of inflection itself: it is neither an atom nor a Cartesian point, but an
elastic or plastic point-fold. Thus it is not exact. On the one hand, it is
important to note that it devalorizes the exact point while, on the other, it
leads the mathematical point to assume a new status that is rigorous
without being exact. On one side, the exact point is effectively not a part
24
THE FOLDS IN THE SOUL
of extension, but a conventional extremity of the line. On the other side,
the mathematical point in turn loses exactitude in order to become a
position, a site, a focus, a place, a point of conjunction of vectors of
curvature or, in short, point of view. The latter therefore takes on a
genetic value: pure extension will be the continuation or diffusion of the
point, but according to the relations of distance that define space
(between two given points) as the 'place of all places.' However, if the
mathematical point thus stops being the extremity of the line in order to
become the point of focus, it is nonetheless a simple 'modality.' It is in the
body, in the thing extended. 21 But in this way, as we have seen, it is only
the projection of a third point in the body. That is the metaphysical point,
the soul or the subject. It is what occupies the point of view, it is what is
projected in point of view. Thus the soul is not in a body in a point, but is
itself a higher point and of another nature, which corresponds with the
point of view. The point of inflection, the point of position, and the point of
inclusion will thus be distinguished.
Everyone knows the name that Leibniz ascribes to the soul or to the
subject as a metaphysical point: the monad. He borrows this name from
the Neoplatonists who used it to designate a state of One, a unity that
envelops a multiplicity, this multiplicity developing the One in the
manner of a 'series.' 22 The One specifically has a power of envelopment
and development, while the multiple is inseparable from the folds that it
makes when it is enveloped, and of unfoldings when it is developed. But
its envelopments and developments, its implications and explications, are
nonetheless particular movements that must be understood in a universal
Unity that 'complicates' them all, and that complicates all the Ones.
Giordano Bruno will bring the system of monads to the level of this
universal complication: the Soul of the world that complicates everything. Hence Neo-Platonic emanations give way to a large zone of
immanence, even if the rights of a transcendent God or an even higher
Unity are formally respected.
Explication-implication-complication form the triad of the fold,
following the variations of the relation of the One-Multiple. 23 But if we
ask why the name 'monad' has been associated with Leibniz, it is because
of the two ways that Leibniz was going to stabilize the concept. On the
one hand, the mathematics of inflection allowed him to posit the
enveloping series of multiples as a convergent infinite series. On the other
hand, the metaphysics of inclusion allowed him to posit enveloping unity
as an irreducible individual unity. In effect, as long as series remained
25
THE FOLD
finite or undefined, individuals risked being relative, called upon to melt
into a universal spirit or a soul of the world that could complicate all
series. But if the world is an infinite series, it then constitutes the logical
comprehension of a notion or of a concept that can now only be
individual. It is therefore enveloped by an infinity of individuated souls of
which each retains its irreducible point of view. It is the accord of singular
points of view, or harmony, that will replace universal complication and
ward off the dangers of pantheism or immanence: whence Leibniz's
insistence upon denouncing the hypothesis, or rather the hypostasis, of a
Universal Spirit that would turn complication into an abstract operation
in which individuals would be swallowed up. 24
All this remains obscure. For if, by pushing to its limit a metaphor
sketched by Plotinus, Leibniz makes of the monad a sort of point of view on
the city, must we understand that a certain form corresponds to each point
of view? 25 For example, a street of one form or another? In conic sections,
there is no separate point of view to which the ellipse would return, and
another for the parabola, and another for the circle. The point of view, the
summit of the cone, is the condition under which we apprehend the group
of varied forms or the series of curves to the second degree. It does not
suffice to state that the point of view apprehends a perspective, a profile
that would each time offer the entirety of a city in its own fashion. For it
also brings forth the connection of all the related profiles, the series of all
curvatures or inflections. What can be apprehended from one point of view
is therefore neither a determined street nor a relation that might be
determined with other streets, which are constants, but the variety of all
possible connections between the course of a given street and that of
another. The city seems to be a labyrinth that can be ordered. The world is
an infinite series of curvatures or inflections, and the entire world is
enclosed in the soul from one point of view.
The world is the infinite curve that touches at an infinity of points an infinity
of curves, the curve with a unique variable, the convergent series of all series. But
why then is there not a single and universal point of view? Why does
Leibniz so strongly deny 'the doctrine of a universal spirit'? Why are there
several points of view and several irreducible souls, an infinity? We can
consider the series of the twelve sounds: the series can undergo in turn
many variations that are both rhythmic and melodic, but that also follow
the contrary, or retrograde, movement. With greater reason an infinite
series, even if the variable is unique, cannot be separated from an infinity
of variations that make it up: we necessarily take it in accord with all
26
THE FOLDS IN THE SOUL
possible orders, and we favor this or that partial sequence at this or that
time. That is why only one form — or one street — recovers its rights, but
only in respect to the entire series.
As an individual unit each monad includes the whole series; hence it
conveys the entire world, but does not express it without expressing more
clearly a small region of the world, a 'subdivision,' a borough of the city, a finite
sequence. Two souls do not have the same order, but neither do they have
S
the same sequence or the same clear or enlightened region. It might even
be stated that insofar as it is filled with folds that stretch to infinity, the
soul can always unfold a limited number of them inside itself, those that
make up its subdivision or its borough. 26 A definition of individuation
remains to be clarified: if only individuals exist, it is not because they
include the series in a certain order and according to a given region; it is
even the inverse that holds.
Thus for the moment we only have a nominal definition of the
individual. The definition suffices all the same to show that there
necessarily exists an infinity of souls and an infinity of points of view,
although each included soul and each point of view may grasp the
infinitely infinite seriality. Each grasps or includes it in a different order
and from the standpoint of a different borough. If we return to the
elementary schema of the two foci of inflection, we see that, in truth,
each of them is a point of view on inflection in general, but that it is in an
inverse order (a retrograde movement) and in accord with an opposed
subdivision (one of the two branches).
But why is it necessary to depart from the world or the serial order? If
not, the theme of the mirror and of point of view would lose all meaning.
We move from inflections of the world to inclusion in its subjects: how
can this be possible since the world only exists in subjects that include it?
In this respect the first letters to Arnauld specify the conciliation of the
two essential propositions. On the one hand, the world in which Adam
committed sin exists only in Adam the sinner (and in all other subjects
who make up this world). On the other hand, God creates not only Adam
the sinner but also the world in which Adam has committed sin. In other
words, if the world is in the subject, the subject is no less for the world. God
produces the world 'before' creating souls since he creates them for this
world that he invests in them. In this very way the law of infinite
seriality, the 'law of curvatures,' no longer resides in the soul, although
seriality may be the soul, and although curvatures may be in it.
27
THE FOLDS IN THE SOUL
THE FOLD
It is in this sense too that the soul is a 'production,' a 'result.' The soul
results from the world that God has chosen. Because the world is in the
monad, each monad includes every series of the states of the world; but,
because the monad is for the world, no one clearly contains the 'reason'
of the series of which they are all a result, and which remains outside of
them, just like the principle of their accord. 27 We thus go from the world
to the subject, at the cost of a torsion that causes the monad to exist
currently only in subjects, but that also makes subjects all relate to this
world as if to the virtuality that they actualize. When Heidegger tries to
surpass intentionality as an overly empirical determination of the
subject's relation to the world, he envisions how Leibniz's formula of
the monad without windows is a way to get past it, since the Dasein, he
says, is already open at all times and does not need windows by which an
opening would occur to it. But in that way he mistakes the condition of
closure or concealment enunciated by Leibniz; that is, the determination
of a being-for the world instead of a being-in the world. 28 Closure is the
condition of being for the world. The condition of closure holds for the
infinite opening of the finite: it 'finitely represents infinity.' It gives
soul? Is a realization in matter also required, because the folds of this
matter might happen to reduplicate the folds in the soul? We cannot yet
be sure, although the preceding chapter invites us to believe it.
Monads
The World
the world the possibility of beginning over and again in each monad. The
world must be placed in the subject in order that the subject can be for
the world. This is the torsion that constitutes the fold of the world and of
the soul. And it is what gives to expression its fundamental character: the
soul is the expression of the world (actuality), but because the world is
what the soul expresses (virtuality). Thus God creates expressive souls
only because he creates the world that they express by including it: from
inflection to inclusion. Finally, in order that the virtual can be incarnated
or effectuated, is something needed other than this actualization in the
28
29
WHAT IS BAROQUE?
3
What is Baroque?
Monads 'have no windows, by which anything could come in or go out.'
They have neither 'openings nor doorways." We run the risk of
understanding the problem vaguely if we fail to determine the situation.
A painting always has a model on its outside; it always is a window. If a
modern reader thinks of a film projected in darkness, the film has
nonetheless been projected. Then what about invoking numerical images
issuing from a calculus without a model? Or, more simply, the line with
infinite inflection that holds for a surface, like the lines of Pollock's or
Rauschenberg's painting? More exactly, in Rauschenberg's work we
could say that the surface stops being a window on the world and now
becomes an opaque grid of information on which the ciphered line is
written. 2 The painting-window is replaced by tabulation, the grid on
which lines, numbers, and changing characters are inscribed (the
objectile ).
Leibniz is endlessly drawing up linear and numerical tables. With
them he decorates the inner walls of the monad. Folds replace holes. The
dyad of the city-information table is opposed to the system of the
window-countryside. 3 Leibniz's monad would be just such a grid — or
better, a room or an apartment — completely covered with lines of
variable inflection. This would be the camera obscura of the New Essays,
furnished with a stretched canvas diversified by moving, living folds.
Essential to the monad is its dark background: everything is drawn out of it,
and nothing goes out or comes in from the outside.
In this sense, it would be pointless to imagine overly modern
situations unless they can help us understand what the Baroque had
30
really entailed. For ages there have been places where what is seen is
inside: a cell, a sacristy, a crypt, a church, a theater, a study, or a print
room. The Baroque invests in all of these places in order to extract from
them power and glory. First of all, the camera obscura has only one small
aperture high up through which light passes, then through the relay of
two mirrors it projects on a sheet the objects to be drawn that cannot be
seen, the second mirror being tilted according to the position of the
sheet. 4 And then transformational decors, painted skies, all kinds of
trompe l'oeil that adorn the walls: the monad has furniture and objects
only in trompe l'oeil. Finally, the architectural ideal is a room in black
marble, in which light enters only through orifices so well bent that
nothing on the outside can be seen through them, yet they illuminate or
color the decor of a pure inside. (Is it not the Baroque manner, such as
this, that inspires Le Corbusier in the Abbey of La Tourette?) The
Leibnizian monad and its system of light-mirror-point of view-inner
decor cannot be understood if they are not compared to Baroque
architecture. The architecture erects chapels and rooms where a crushing
light comes from openings invisible to their very inhabitants. One of its
first acts is in the Studiolo of Florence, with its secret room stripped of
windows. The monad is a cell. It resembles a sacristy more than an atom:
a room with neither doors nor windows, where all activity takes place on
the inside.
The monad is the autonomy of the inside, an inside without an
outside. It has as its correlative the independence of the façade, an outside
without an inside. Now the façade can have doors and windows — it is
riddled with holes — although there may be no void, a hole being only the
site of a more rarefied matter. The doors and windows of that matter open
or even close only from the outside and onto the outside. To be sure, the
organic matter already sketches an interiorization, but a relative one, that
is always ongoing and forever unfinished. It is because a fold passes
through living material in order to allot to the absolute interiority of the
monad the metaphysical principle of life, and to make the infinite
exteriority of matter the physical law of phenomena. We have two
infinite sets, whereby the one never rejoins the other: 'Since infinite
division of exteriority is extended endlessly and remains open, we are
required to exit from the outside in order to posit an inner punctual
unity.... The physical, natural, phenomenal, contingent world is plunged
entirely in the infinite repetition of open linkages: in this way it is not
metaphysical. The world of metaphysics is beyond, and closes repetition
31
THE FOLD
... the monad is this fixed point that infinite partition never attains, and
that closes infinitely divided space.' 5
Baroque architecture can be defined by this severing of the facade from
the inside, of the interior from the exterior, and the autonomy of the
interior from the independence of the exterior, but in such conditions
that each of the two terms thrusts the other forward. WOWlin states as
much in his own way ('It is precisely the contrast between the
exacerbated language of the façade and the serene peace of the inside
that constitutes one of the most powerful effects that Baroque art exerts
upon us'), although he may be misled in thinking that the excess of inner
decoration ends up by jostling the contrast, or that the absolute inside in
itself is peaceful. Likewise, Jean Rousset defines the Baroque through the
severing of the facade from the inside, although he also believes that
decoration may risk making the inside 'explode.' Yet the inside remains
perfectly integral from the point of view, or in the mirror, that oversees its
decoration, no matter how complicated it might be. A new kind of link, of
which pre-Baroque architecture had no inkling, must be made between
the inside and outside, or the spontaneity of the inside and the
determination of the outside. 'What necessary and direct relation can
be found between the inside of Saint Agnes and its facade? ... Far from
being adjusted to the structure, the Baroque façade only tends to thrust
itself forward,' while the inside falls back on itself, remains closed, and
tends to be offered to the gaze that discovers it entirely from one point of
view, 'a little coffin containing the absolute.' 6
What makes the new harmony possible is, first, the distinction
between two levels or floors, which resolves tension or allots the division.
The lower level is assigned to the façade, which is elongated by being
punctured and bent back according to the folds determined by a heavy
matter, forming an infinite room for reception or receptivity. The upper
level is closed, as a pure inside without an outside, a weightless, closed
interiority, its walls hung with spontaneous folds that are now only those
of a soul or a mind. This is because, as Mifflin has shown, the Baroque
world is organized along two vectors, a deepening toward the bottom,
and a thrust toward the upper regions. Leibniz will make coexist, first, the
tendency of a system of gravity to find its lowest possible equilibrium
where the sum of masses can descend no further and, second, the
tendency to elevate, the highest aspiration of a system in weightlessness,
where souls are destined to become reasonable. The coexistence
32
WHAT IS BAROQUE?
resembles Tintoretto's paintings. That one is metaphysical, dealing with
souls, or that the other is physical, entailing bodies, does not impede the
two vectors from comprising a similar world, a similar house. And not
only are they distributed as a function of an ideal line which is actualized
on one level and realized on another; a higher analogy endlessly relates
the one to each other.
Domestic architecture of this kind is not a constant, either of art or of
thinking. What is Baroque is this distinction and division into two levels
or floors. The distinction of two worlds is common to Platonic tradition.
The world was thought to have an infinite number of floors, with a
stairway that descends and ascends, with each step being lost in the upper
order of the One and disintegrated in the ocean of the multiple. The
universe as a stairwell marks the Neoplatonic tradition. But the Baroque
contribution par excellence is a world with only two floors, separated by a
fold that echoes itself, arching from the two sides according to a different
order. It expresses, as we shall see, the transformation of the cosmos into
a 'mundus.'
Among the apparently Baroque painters, Tintoretto and El Greco
shine, and are incomparable. And yet they have in common this same
Baroque trait. The Burial of Count Orgaz is, for instance, divided in two by a
horizontal line. On the bottom bodies are pressed leaning against each
other, while above a soul rises, along a thin fold, attended by saintly
monads, each with its own spontaneity. In Tintoretto the lower level
shows bodies tormented by their own weight, their souls stumbling,
bending and falling into the meanders of matter; the upper half acts like a
powerful magnet that attracts them, makes them ride astride the yellow
folds of light, folds of fire bringing their bodies alive, dizzying them, but
with a 'dizziness from on high': thus are the two halves of the Last
Judgment.'
The severing of the inside from the outside in this way refers to the
distinction between the two levels, but the latter refers to the Fold that is
actualized in the intimate folds that the soul encloses on the upper level,
and effected along the creases that matter brings to life always on the
outside, on the lower level. Hence the ideal fold is the Zweifalt, a fold that
differentiates and is differentiated. When Heidegger calls upon the
Zweifalt to be the differentiator of difference, he means above all that
differentiation does not refer to a pregiven undifferentiated, but to a
Difference that endlessly unfolds and folds over from each of its two sides,
33
THE FOLD
and that unfolds the one only while refolding the other, in a coextensive
unveiling and veiling of Being, of presence and of withdrawal of being. 8
The 'duplicity' of the fold has to be reproduced from the two sides that it
distinguishes, but it relates one to the other by distinguishing them: a
severing by which each term casts the other forward, a tension by which
each fold is pulled into the other.
The fold is probably Mallarme's most important notion, and not only
the notion but, rather, the operation, the operative act that makes him a
great Baroque poet. Illrodiade is already the poem of the fold. The fold of
the world is the fan or 'l'unanime pli' (unanimous fold). At times the
open fan makes all particles of matter, ashes, and fog rise and fall. We
glimpse the visible through the mist as if through the mesh of a veil,
following the creases that allow us to see stone in the opening of their
inflections, 'fold after fold,' revealing the city. The fan reveals absence or
withdrawal, a conglomeration of dust, hollow collectivities, armies and
hallucinating assemblies. Ultimately the fold pertains to the sensitive side
of the fan, to sensitivity itself, stirring up the dust through which it is
visible, and exposing its own inanity. And at others, from the other side of
the fan that is now closed ('le sceptre des rivages roses ... ce blanc vol
ferme que to poses') [the scepter of the rosy shores ... this white closed
flight you pose], the fold no longer moves toward pulverization, it
exceeds itself or finds its finality in an inclusion, 'tassement en epaisseur,
offrant le minuscule tombeau, certes, de l'Sme' [thick layerings, offering
the tiny tomb, surely, of the soul].
The fold is inseparable from wind. Ventilated by the fan, the fold is no
longer made of matter through which we see, but of the soul in which we
read 'plis jaunes de la pensee' [yellow folds of thought], the Book or the
monad with multiple leaves. Now it contains every fold, since the
combinations of its pages are infinite; but it includes them in its closure,
and all its actions are internal. However, these are not two worlds: the
fold of the newpaper, dust or mist, inanity, is a fold of circumstance that
must have its new mode of correspondence with the book, the fold of the
Event, the unity that creates being, a multiplicity that makes for
inclusion, a collectivity having become consistent.
For Leibniz, these were not the folds of the fan, but veins in marble.
And on one side there are all these creases of matter following which we
behold living matter in the microscope, collectivities through the folds of
dust that they are stirring up, armies and flocks, greenery seen through
blue and yellow dust, inanities or fictions, swarming holes that endlessly
34
WHAT IS BAROQUE?
feed our disquiet, our boredom, or our giddiness. And then, on the other
side, there are these folds in the soul, where inflection becomes inclusion
(just as Mallarme writes that folding becomes a layering): we're no longer
seeing, we're reading. Leibniz begins to use the word 'to read' at once as
the inner act in the privileged region of the monad, and as the act of God
in all of the monad itself. 9
It is well known that the total book is as much Leibniz's dream as it is
Mallarme's, even though they never stop working in fragments. Our
error is in believing that they did not succeed in their wishes: they made
this unique Book perfectly, the book of monads, in letters and little
circumstantial pieces that could sustain as many dispersions as combinations. The monad is the book or the reading room. The visible and the
legible, the outside and the inside, the facade and the chamber are,
however, not two worlds, since the visible can be read (Mallarme's
journal), and the legible has its theater (both Leibniz's and Mallarme's
theaters of reading). Combinations of the visible and the legible make up
'emblems' or allegories dear to the Baroque sensibility. We are always
referred to a new kind of correspondence or mutual expression, an entr'
expression, fold after fold.
The Baroque is inseparable from a new regime of light and color. To
begin, we can consider light and shadows as 1 and 0, as the two levels of
the world separated by a thin line of waters: the Happy and the
Damned.' ° An opposition is no longer in question. If we move into the
upper level, in a room with neither door nor window, we observe that it
is already very dark, in fact almost decorated in black, 'fuscum
subnigrum.' This is a Baroque contribution: in place of the white chalk
or plaster that primes the canvas, Tintoretto and Caravaggio use a dark,
red-brown background on which they place the thickest shadows, and
paint directly by shading toward the shadows." The painting is
transformed. Things jump out of the background, colors spring from
the common base that attests to their obscure nature, figures are defined
by their covering more than their contour. Yet this is not in opposition to
light; to the contrary, it is by virtue of the new regime of light. Leibniz
makes the point in the Profession de foi du philosophe: 'It slides as if through
a slit in the middle of shadows.' Should we be given to understand that it
comes from a vent, from a thin opening, angled or folded, by
intermediary mirrors, the white consisting 'in a great number of small
reflecting mirrors'?
35
THE FOLD
More exactly, since monads have no openings, a light that has been
'sealed' is lit in each one when it is raised to the level of reason. A
whiteness is produced through all the tiny inner mirrors. It makes white,
but shadow too: it makes the white that is confounded with the
illuminated area of the monad, that soon becomes obscure or shades
toward the dark background, the fuscum, whence things emanate 'by
means of shadows and fairly strong and well-handled colors.' As with
Desargues, we only have to invert perspective or to place 'the luminous in
place of the eye, the opaque in place of the object, and shadow in place of
the projection.' I2 WOlfflin has summarized the lessons of this progressivity of light that grows and ebbs, and that is transmitted by degrees. It is
the relativity of clarity (as much as of movement), the inseparability of
clarity from obscurity, the effacement of contour — in short, the
opposition to Descartes, who remained a man of the Renaissance, from
the double point of view of a physics of light and a logic of the idea.
Clarity endlessly plunges into obscurity. Chiaroscuro fills the monad
following a series that can move in either of two directions: at one end is a
dark background and at the other is light, sealed; when it is lit, the monad
produces white light in an area set aside, but the white is progressively
shaded, giving way to obscurity, to a thicker and thicker shadow, as it
spreads toward the dark background in the whole monad. Outside of the
series we have God on one side, who said let there be light, and with it
the white-mirror, but on the other side the shadows or absolute
blackness, made up of an infinity of holes that can no longer reflect the
received rays. An infinitely spongy and cavernous matter ultimately
contains all of these holes." Does the line of light — or fold of the two
levels — pass between the shadows and the dark background being
withdrawn from it? Ultimately, yes, insofar as the lower level is now no
more than a cave hollowed out by caves, and matter, forced back under
the waters, is almost reduced to nothing. But concrete matter is above, its
holes already filled with an increasingly vaporous matter, such that the
fold of the two levels appears to be the common limit of two kinds of full
folds.
Germany's entry on the philosophical scene implies the entire German
soul that, according to Nietzsche, comes forward less as something 'deep'
than full of folds and pleats. I4 How can a portrait be made of Leibniz's
person without marking the extreme tension of an open façade and a
hermetic inner volume, each being independent of the other and both
36
WHAT IS BAROQUE?
regulated by a strange preestablished connection? It is an almost
schizophrenic tension. Leibniz comes forward in Baroque strokes. 'As a
German type Leibniz is more interesting than Kant: simple-minded, full
of noble words, ruseful, supple, malleable, a mediator (between
Christianism and mechanistic philosophy), and in his own heart having
enormous audacity, sheltered under a mask and courteously intrusive,
modest in appearance. ... Leibniz is dangerous, a good German who
needs façades and philosophies of facades, but bold and basically
mysterious in the extreme.' I5 The courtly wig is a façade, an entry, like
the vow to hurt no one's established feelings, and the art of presenting his
system from one point of view or another, in such and such a mirror,
following the apparent intelligence of a correspondent or of an opponent
knocking on his door, while the System itself is up above, turning about
itself, ceding absolutely nothing to the compromises, down below, whose
secret he keeps, taking, on the contrary, 'the best of all sides' in order to
deepen or to make another fold in the room with closed doors and with
sealed windows, the room in which Leibniz is confined when he states,
'Everything is always the same, with degrees of perfection excepted.'
The best inventors of the Baroque, the best commentators have had
their doubts about the consistency of the notion, and have been
bewildered by the arbitrary extension that, despite themselves, the
notion risked taking. The Baroque was seen as being restricted to one
genre (architecture), or to an increasingly restrictive determination of
periods and places, or yet again to a radical disavowal: the Baroque never
existed. It is nonetheless strange to deny the existence of the Baroque in
the way we speak of unicorns or herds of pink elephants. For in this case
the concept is given, while in the case of the Baroque the question entails
knowing if a concept can be invented that is capable (or not) of
attributing existence to it. Irregular pearls exist, but the Baroque has no
reason for existing without a concept that forms this very reason. It is
easy to call the Baroque inexistent; it suffices not to propose its concept.
We thus have to go back and wonder if Leibniz is the Baroque
philosopher par excellence or if his work forms a concept capable of
making the Baroque exist in itself. In this respect, those who have
compared Leibniz to the Baroque have often done so in the name of too
broad a concept, such as Knecht with his 'coincidence of opposites.'
Christine Buci-Glucksmann proposes a much more interesting criterion, a
dialectics of seeing and gazing, but this criterion might in turn be too
restrictive, allowing only the definition of an optical fold. 16 For our
37
THE FOLD
purposes the criterion or operative concept of the Baroque is the Fold,
everything that it includes, and in all its extensiveness.
Fold after fold: if the Baroque can be stretched beyond its precise
historical limits, it appears to us that it is always by virtue of this
criterion, which inspires us to recall Michaux when he writes of La vie
dans les plis (Life in the folds), or Boulez when he looks to Mallarme and
composes 'Fold after Fold,' or Hantal when he constructs a method from
folding. And if, in the other direction, we return to the past, why would
we not find the Baroque already, for instance, in Uccello? Because he is
not satisfied with painting blue and pink horses, and lances arched as if
they were strokes of light directed on all points of the sky, he endlessly
draws 'mazocchi, that are wooden circles covered with cloth that is placed
on the head, so that the folds of the remaining fabric turn about the
whole face.' He comes up against his contemporaries' incomprehension
because 'the power of sovereignly developing all things and the strange
series of hoods with folds seem to him more revealing than the
magnificent marble figures of the great Donatello.'" Thus a Baroque
line would move exactly according to the fold, and that would bring
together architects, painters, musicians, poets, and philosophers. To be
sure, it might be argued that the concept of the fold also remains too
broad: If we restrict ourselves to the plastic arts, what period and what
style would fail to recognize the fold as a trait of painting or of
sculpture? It is not only in clothing, but includes the body, rocks,
waters, earth, and line. Baltrugaitis generally defines the fold by
severing but a severing that casts forth each of the divided terms next
to the other. In this way he defines the Romanesque fold by the
severing-casting forth of figuration and of geometry. 18
Cannot the Oriental fold also be defined by what is void and what is
full? And all the others will have to be defined, one after the other,
through comparative analysis. Uccello's folds are not really Baroque
because they are held in solid, polygonal, inflexible — even if ambiguous —
geometrical structures. Should we wish to maintain the working relation
of the Baroque and the fold, we shall therefore have to show that the fold
remains limited in the other cases, and that in the Baroque it knows an
unlimited freedom whose conditions can be determined. Folds seem to be
rid of their supports — cloth, granite, or cloud — in order to enter into an
infinite convergence, as in El Greco's Christ in the Mountolive Garden (that
of the National Gallery). Or then, notably in The Baptism of Christ, the
counter-fold of the calf and knee, the knee as an inversion of the calf,
38
WHAT IS BAROQUE?
confers on the leg an infinite undulation, while the seam of the cloud in
the middle transforms it into a double fan. ...
These are the same traits, taken in their rigor, that have to account for the
extreme specificity of the Baroque, and the possibility of stretching it
outside of its historical limits, without any arbitrary extension: the
contribution of the Baroque to art in general, and the contribution of
Leibnizianism to philosophy.
1. The fold: the Baroque invents the infinite work or process. The
problem is not how to finish a fold, but how to continue it, to have it go
through the ceiling, how to bring it to infinity. It is not only because the
fold affects all materials that it thus becomes expressive matter, with
different scales, speeds, and different vectors (mountains and waters,
papers, fabrics, living tissues, the brain), but especially because it
determines and materializes Form. It produces a form of expression, a
Gestaltung, the genetic element or infinite line of inflection, the curve with
a unique variable.
2. The inside and the outside: the infinite fold separates or moves
between matter and soul, the facade and the closed room, the outside and
the inside. Because it is a virtuality that never stops dividing itself, the line
of inflection is actualized in the soul but realized in matter, each one on
its own side. Such is the Baroque trait: an exterior always on the outside,
an interior always on the inside. An infinite 'receptivity,' an infinite
'spontaneity': the outer facade of reception and inner rooms of action. Up
to now Baroque architecture is forever confronting two principles, a
bearing principle and a covering principle (on the one hand, Gropius, and
on the other, Loos). 19 Conciliation of the two will never be direct, but
necessarily harmonic, inspiring a new harmony: it is the same expression,
the line, that is expressed in the elevation of the inner song of the soul,
through memory or by heart, and in the extrinsic fabrication of material
partitions, from cause to cause. But, justly, what is expressed does not
exist outside its expressions.
3. The high and the low: the perfect accord of severing, or the resolution
of tension, is achieved through the division into two levels, the two floors
being of one and the same world (the line of the universe). The facadematter goes down below, while the soul-room goes up above. The infinite
fold then moves between the two levels. But by being divided, it greatly
expands on either side: the fold is divided into folds, which are tucked
inside and which spill onto the outside, thus connected as are the high
39
THE FOLD
and the low. Pleats of matter in a condition of exteriority, folds in the soul
in a condition of closure. Pleats of the partition and folds of the song.
Baroque is abstract art par excellence: on the lower floor, flush with the
ground, within reach, the art comprehends the textures of matter (the
great modern Baroque painters, from Paul Klee to Fautrier, Dubuffet,
Bettencourt ). But abstraction is not a negation of form: it posits form
as folded, existing only as a 'mental landscape' in the soul or in the mind,
in upper altitudes; hence it also includes immaterial folds. Material matter
makes up the bottom, but folded forms are styles or manners. We go from
matter to manner; from earth and ground to habitats and salons, from the
Texturologie to the Logologie. These are the two orders, Dubuffet's two
levels, with the discovery of their harmony that must go as far as
indiscernibility. Is it a texture, or a fold of the soul, of thought? 2° Matter
that reveals its texture becomes raw material, just as form that reveals its
folds becomes force. In the Baroque the coupling of material-force is what
replaces matter and form (the primal forces being those of the soul).
4. The unfold: clearly this is not the contrary of the fold, nor its
effacement, but the continuation or the extension of its act, the condition
of its manifestation. When the fold ceases being represented in order to
become a 'method,' a process, an act, the unfold becomes the result of the
act that is expressed exactly in this fashion. Hantai begins by representing
the fold — tubular and swarming — but soon folds the canvas or paper.
Then, it resembles two axes, one of 'Studies' and another of 'Tables.'
Sometimes the surface is locally or irregularly folded. These are the outer
sides of the open fold that are painted, such that stretching, splaying, and
unfolding cause surfaces of color to alternate with zones of white that all
modulate over one another. Sometimes it is the solid that projects its
inner sides on a regularly folded plane surface in accord with the creases:
here the fold has a fulcrum, it is knotted and closed at each intersection,
and is unfolded to cause the inner white to circulate. 2 '
Sometimes light vibrates color in the pleats and crannies of matter,
sometimes light vibrates in the folds of an immaterial surface. However,
what is it that makes the Baroque line only a possibility for Hantal? He
never stops facing another possibility, which is that of the Oriental line.
Painted and nonpainted surfaces are not divided as are form and content,
but as the full and the void in a reciprocal becoming. That is how HantaI
hollows out the eye of the fold and paints only the sides (the Oriental
line); but sometimes he makes successive foldings in the same area that
leave no place for voids (a full Baroque line). It may be that the Baroque
40
WHAT IS BAROQUE?
will have to confront the Orient profoundly. This happened to be
Leibniz's adventure with his binary arithmetic: in one and zero Leibniz
acknowledges the full and the void in a Chinese fashion; but the Baroque
Leibniz does not believe in the void. For him it always seems to be filled
with a folded matter, because binary arithmetic superimposes folds that
both the decimal system — and Nature itself — conceal in apparent voids.
For Leibniz, and in the Baroque, folds are always full. 22
5. Textures: Leibnizian physics includes two principal chapters, the one
involving active or so-called derivative forces related to matter, and the
other involving passive forces, or the resistance of material or texture. 23
Perhaps only at the limit does texture become most evident, before
rupture or tearing, when stretching, no longer being opposed to the fold,
now expresses it in its pure state, according to a Baroque figure that
Bernard Cache has indicated (hysteresis more than stretching). 24 Not
belonging to the same pictorial vision, here the fold still pushes back the
opening or the hole. As a general rule the way a material is folded is what
constitutes its texture. It is defined less by its heterogenous and really
distinct parts than by the style by which they become inseparable by
virtue of particular folds. Whence the concept of Mannerism in its
working relation with the Baroque. That is what Leibniz stated when he
invoked the 'paper or the tunic.' Everything is folded in its own manner,
cord and rod, but also colors distributed according to the concavity and
convexity of the luminous rays, sounds, all the more strident where 'the
trembling parts are shorter and more taut.' Hence texture does not
depend on the parts themselves, but on strata that determine its
'cohesion.'
The new status of the object, the objectile, is inseparable from the
different layers that are dilating, like so many occasions for meanders and
detours. In relation to the many folds that it is capable of becoming,
matter becomes a matter of expression. In this respect, the fold of matter
or texture has to be related to several factors, first of all, light, chiaroscuro,
the way the fold catches illumination and itself varies according to the
hour and light of day (Tromeur's and Nicole Grenot's contemporary
41
THE FOLD
research). But then, depth: how does the fold itself determine a 'thin' and
superimposable depth, the paper fold defining a minimum of depth on
our scale of things, as we see in Baroque letter holders in trompe l'oeil,
where the representation of a pleated card casts a sense of depth in front
of the wall. And third, there is the soft and overlaid depth of fabric that
has never ceased to inspire painting, brought to new power in our time by
Helga Heinzen: her representation of striped and folded fabrics covers the
entire painting, the body disappears in the falls and rises, the waves and
sums, which follow a line now coming from Islam.
But still the theater of matter, to the extent a material can be grasped,
hardened in its distortion or its hysteresis, is apt to express within itself
the folds of another material, as in Renonciat's wooden sculpture, where
Lebanese cedar turns into a plastic drop cloth, or the Parana pine becomes
'cotton and feathers.' Finally, the way that all these textures of matter
tend toward a higher point, a spiritual point that envelops form, that
holds it enveloped, and that contains alone the secret of material folds
below. Where would these come from? They are not explained by
composite parts, since the 'swarming,' the perpetual displacement of
contour, originates in the projection of something spiritual into matter.
Are they a phantasmagoria of the order of thought, as Dubuffet would
say? In another manner, the sculptor Jeanclos finds an analogous way
when he goes from physical leaves of cabbage — infinitely folded, tied,
bloodied — or infinitely stretched sheets, to metaphysical peas, spiritual
crabs, heads of monads that concretize the meaning of the expression 'the
folds of sleep.' 25 Whether active or passive, derivative forces of matter
refer to primitive forces which are those of the soul. But always the two
levels, their harmony, and their harmonization.
6. The paradigm: the search for a model of the fold goes directly
through the choice of a material. Would it be the paper fold, as the Orient
implies, or the fold of fabric, that seems to dominate the Occident? But
the point is that the composite materials of the fold (texture) must not
conceal the formal element or form of expression. In this respect, the
Greek fold is not satisfactory, even if it has the correct ambition to be
worthy of the highest areas, in political force, and in the power of
thinking: the Platonic paradigm of weaving as interlacing is contained in
textures but does not extract the formal elements of the fold. It is because
the Greek fold, as the Politics and the Timaeus have shown, presupposes a
common measure of two terms that are mixed, and thus operates through
encirclements that correspond to the repetition of proportion. That is
42
WHAT IS BAROQUE?
why, for Plato, forms are folded. The formal element of the fold is not
attained. This formal element appears only with infinity, in what is
incommensurable and in excess, when the variable curve supersedes the
circle. 26 Such is the case for the Baroque fold, with its corresponding
status of a power of thinking and political force. The paradigm becomes
'mannerist,' and proceeds to a formal deduction of the fold.
In this way the psychiatrist Clerambaules taste for folds of Islamic origin,
and his extraordinary photographs of veiled women — true paintings that
resemble those of Helga Heinzen nowadays — amounts, despite what has
been said, to much more than a simple personal perversion. So does
Mallarme's shawl, or the poet's wish to edit a fashion journal. If
Clerambault manifests a delirium, it is because he discovers the tiny
hallucinatory perceptions of ether addicts in the folds of clothing. It falls
upon formal deduction to straddle many diverse materials and areas. It
will have to distinguish: simple and composite Folds; Hems (knots and
seams being corollaries of the fold); Drapes, with their proppings. 27 Only
then will ensue material Textures and, finally, Agglomerations or
Conglomerations (felt made by fulling and not by weaving). We will
see to what extent this deduction is properly Baroque or Leibnizian.
43
4
Sufficient reason
'Everything has a reason ...' This vulgar formulation already suffices to
suggest the exclamatory character of the principle, the identity of the
principle and of the cry, the cry of Reason par excellence. Everything is
everything that happens, no matter what happens. Everything that
happens has a reason!' It is understood that a cause is not the reason
being sought. A cause is of the order of what happens, either to change a
state of things, or to produce or destroy the thing. But the principle claims
that everything that happens to a thing — causations included — has a
reason. If an event is called what happens to the thing, whether it
undergoes the event or makes it happen, it can be said that sufficient
reason is what includes the event as one of its predicates: the concept of
the thing, or the notion.
'Predicates or events,' says Leibniz. 2 Whence the path that we have
just followed in the chapters above, from inflection to inclusion.
Inflection is the event that happens to the line or to the point. Inclusion
is the predication that places inflection in the concept of the line or the
point, that is, in this other point that will be called metaphysical. We go
from inflection to inclusion just as we move from the event of the thing to
the predicate of the notion, or from 'seeing' to 'reading.' What we see on
the thing we read in its concept or notion. The concept resembles a
signature or an enclosure. Sufficient reason is inclusion; in other words,
the identity of the event and the predicate. Sufficient reason proclaims,
'Everything has a concept!' Its metaphysical formulation goes as follows:
'All predication is grounded in the nature of things'; as a logical
formulation: 'Every predicate is in the subject,' the subject or nature of
things being the notion, the concept of the thing.
47
THE FOLD
The Baroque is widely known to be typified by the 'concetto,' but only
insofar as the Baroque concetto can be opposed to the classical concept. It is
also widely held that Leibniz brings a new conception to the concept,
with which he transforms philosophy. But we have to wonder about the
composition of this new, Leibnizian conception. That it is opposed to the
'classical' conception of the concept — in the way that Descartes had
invented it — is best shown in Leibniz's correspondence with De Voider, a
Cartesian. First of all, the concept is not a simple logical being, but a
metaphysical being; it is not a generality or a universality, but an
individual; it is not defined by an attribute, but by predicates-as-events.
But does this hold for every inclusion? In response to the question we
encounter the distinction of two great types of inclusion or analysis,
analysis being the operation that discovers a predicate in a notion taken
as a subject, or a subject for an event taken as a predicate. Leibniz seems
to be saying that in the case of necessary propositions or truths of essence
('2 plus 2 equal 4'), the predicate is expressly included in the notion, while,
for contingent existences ('Adam sins,' 'Caesar crosses the Rubicon'),
inclusion is only implicit or virtual. 3 Must we be led to understand, as
Leibniz sometimes suggests, that analysis is finite in one case and
indefinite in the other? Yet beyond the fact that in each case we cannot
be sure of what the concept or subject is made, we run the risk of a double
misreading if we associate 'expressed intention' with the finite, and the
'implicit or virtual' with the indefinite. It would be astonishing to find
that the analysis of essences is finite, since the latter are inseparable from
the infinity of God himself.
In turn, the analysis of existences cannot be separated from the
infinity of the world, which is no less existent than all other infinity: were
the indefinite existing in the world, God would not be submitted to it, and
would thus see the end of analysis, which is not the case. 4 In short, we
can no more identify the virtual that Leibniz invokes with an inexistent
indefinite than we can identify express intention with finitude.
Difficulties accrue if we consider crucial texts in which Leibniz presents
the implicit or the virtual, not as what has pertained to inclusions of
existence, but now as a type of inclusion of essence: these are necessary
propositions that are divided in case of an intentional inclusion ('2 plus 2
equal 4'), and in the case of stated inclusion ('every duodenary is a
sonary'). 5 We might even say that propositions of essence attend to all
analysis — intended or implicit — while propositions of existence ultimately
escape it.
48
SUFFICIENT REASON
The first task would entail defining essences. Yet we cannot do so
without knowing what a definition is, because we begin from already
definable essences without any inkling about what they presuppose. A
definition posits the identity of one term (the defined) with at least two
other terms (definers or reasons). The definition can possibly be
substituted for the defined, this substitution being the reciprocal inclusion:
for example, I define 3 by 2 and 1. Several remarks must follow. First, at
stake are real or genetic definitions that reveal the possibility of the
defined: we do not define 3 by 1, 1, plus 1, nor by 8 minus 5, but by the
first numbers that the defined includes and that include it. Second,
definitions of this kind never operate by genre and difference. They solicit
neither the comprehension, the extension of a concept, abstraction, nor
generality that would, moreover, go back to nominal definitions. Third,
the demonstration can be defined as a chain of definitions, that is, as a
concatenation of reciprocal inclusions: thus we demonstrate that '2 plus 2
equal 4.' 6 Finally, we predict that antecedence, what Aristotle previously
had called the before and the after — although no temporal order is in
question here — is a complicated notion: the definers or reasons must
precede the defined since they determine its possibility, but only by
following the 'power,' and not the 'act' that, on the contrary, would
suppose the antecedence of the defined. Whence, justly, reciprocal
inclusion and the absence of all temporal relations.
From then on it goes without saying that, from one definition to
another, if we go back along the nontemporal chain, we arrive at
undefinables; in other words, definers that are last reasons, and that can
no longer be defined. Why not proceed indefinitely? This question loses all
meaning as soon as we are placed in the midst of real definitions, for the
indefinite would furnish or have furnished only nominal definitions. Had
we known from the beginning what a real definition was, we would have
had to begin with undefinables. But we get there through this intermediary,
and we discover them as absolutely first in the order of the before and after:
they are called 'simple primitive notions.' From definition to definition
(demonstration), everything can only begin with undefinable terms that
enter into the initial definitions. These undefinables are obviously not
reciprocal inclusions, like definitions, but they are auto-inclusions: they are
Identicals in the pure state, each of which includes itself and includes only
itself, each only capable of being identical to itself. Leibniz draws identity
into infinity: the Identical is an auto-position of the infinite, without which
identity would remain hypothetical (if A is, then A is A ...).
49
THE FOLD
This mark of identity can allow us to demonstrate that Leibniz makes a
very special, indeed Baroque, conception from these principles. In this
respect Ortega y Gasset makes a set of subtle remarks: on the one hand,
Leibniz loves principles, and he is probably the only philosopher who
invents them endlessly. He invents them with pleasure and enthusiasm,
and he brandishes them like swords. But on the other hand, he plays with
principles, multiplies formulas, varies their relations, and incessantly
wants to 'prove' them as if, loving them too much, his respect for them
were lacking.' Leibniz's principles are not universal empty forms; nor are
they hypostases or emanations that might turn them into beings. But
they are the determination of classes of beings.
If the principles appear to us as cries, it is because each one signals the
presence of a class of beings that are themselves crying and draw
attention to themselves by these cries. In this way we could not be led to
believe that the principle of identity causes us to be aware of nothing,
even if it does not make us penetrate into this awareness. The principle of
identity or, rather, the principle of contradiction, as Leibniz says, makes
us become aware of a class of beings, that of the Identicals, which are
complete beings. The principle of identity - or rather, of contradiction - is
only the cry of the Identicals. It cannot be an abstraction. It is a signal.
Identicals are undefinables in themselves and exist perhaps beyond our
ken; they have, no less, a criterion that the principle makes us aware of or
able to hear.
Every form that can be thought of as infinite by itself would be
identical to itself, capable of being raised directly to infinity, by itself, and
not by means of a cause: 'nature susceptible to the last degree.' Such is
the criterion. For example, can we imagine a speed, a number, or a color
as infinite? In contrast, thought appears to be a form that can be raised to
infinity, or even extension, under the condition that these forms are not
wholes, and that they do not have parts: these are 'absolutes,' 'fundamental
qualities,' 'distinctly knowable qualities,' A, B, C ... 8 Each one, being
included in itself and including only itself, not being a whole and having
no parts, has strictly no relation with an other. These are pure
'disparities,' diverse absolutes that cannot be contradicted since no
element exists that one can affirm or the other can deny. They are, as
Blanchot would say, in a 'nonrelation.' And this is just what the principle
of contradiction states: it states that since two distinct Identicals cannot be
contradicted by each other, they surely form a category.
They might be called 'attributes' of God. There we find in fact the only
50
SUFFICIENT REASON
thesis that ties Spinoza to Leibniz, their common manner of requiring in
the ontological proof of the existence of God a detour that Descartes had
confidence enough to cut short: before concluding that an infinitely
perfect being necessarily exists, it had to be shown that it is possible (a
real definition), and that it does not imply contradiction. Now it is
precisely because all absolute forms are incapable of being contradicted
that they can belong to a same Being and, in being able to, they
effectively belong to it. Since they are forms, their real distinction is
formal and carries no ontological difference among beings to which each
might be attributed: they are all attributed to a single and same Being that
is both ontologically one and formally diverse. 9 There the real distinction
already does not involve separability. As Kant will state, the ontological
proof goes from totality of all possibilities to the individuality of a
necessary being:
Identicals are a class of beings but a class with one sole member. Here we find
the law of antecedence, since absolute forms precede God as do the first
elements of his possibility, although God precedes them 'in re' and 'in
actu.'
How do we go from Identicals to Definables? Identicals are absolutely
simple primitive notions, A, B, ..., that metaphysically 'compose' a
unique Being, AB ... But the metaphysical composition and the logical
derivation cannot be confused. Definables are derived notions: they can
be simple if they are first in their order, but they always presuppose at
least two primitives that define them in a relation, under a 'vinculum,' or
through the intermediary of a particle that itself can be simple or complex
(for example, A in B). That is the Combinatory that goes thus from
Identicals to Definables, from primary to derived beings, through a
distinction of levels: level I includes the primary or the indefinable
Identicals; level II is composed of the simple derived beings, defined by
two primary beings in a simple relation; level III is composed of composite
derived beings defined by three primaries, or by a simple primary and a
simple derived being in a relation that is itself composite ... 10
We can take an example that works by analogy: even if we cannot
begin from absolute primaries in order to deduce our thought, we can
always convene relative primaries in an area (they presuppose the area
51
SUFFICIENT REASON
THE FOLD
instead of engendering it); thus the first numbers are prime in arithmetic
because, being divisible only by itself or by unity, each is a phenomenon
of auto-inclusion. Or else the undefinable axioms in geometry (for
instance 'point,"space,"intermediary' ...) form a level I, from which
derives a level II through the combination each time of two primaries,
then a level III (line being the intermediary space between two points)." In
the absolute God probably assures the passage from Identicals to
Definables: he is composed of all absolute primary forms, but he is also
the first and last definable, from which all others will derive. But we are
thus not resolving the difficulty that weighs upon the whole combinatory. Couturat demonstrates it perfectly: How can an account be made of
the relations marked by articles, prepositions, verbs, and cases that surge
forth from level II on? We began from absolute forms taken in their
nonrelation. And all of a sudden relations or 'particles' spring up, not only
for our understanding, but in the understanding of God himself. How
could the relation jump out of the nonrelation?
Clearly many areas are found in the understanding of God. We can
state that the relations surge up in a region that no longer involves God
himself, but the possibility of creation. That is at least an indication, even
if the question does not entail knowing whence the relations spring forth,
but how they do. Baroque thinking has in fact ascribed a particular
importance to the distinction of several orders of infinity. And in the first
place, if absolute forms constitute God as an infinity by itself, which
excludes wholes and parts, the idea of creation goes back to a second
infinity, through cause. It is this infinity by way of cause that constitutes wholes
and parts, without there being either a largest or a smallest part. It is no
longer a whole, but a series that has neither a final term nor a limit. It is
not quite ruled by the principle of identity, but by a principle of similitude
or of homothesis that signals a new class of beings. Here is everything that
might be called extensions or extensities: not only extension strictly
speaking, but also time, number, infinitely divisible matter, everything
that is 'partes extra partes,' and, as such, submitted to the principle of
similitude. Thus each term of the series, which forms a whole for the
precedents and a part for everything that ensues, is defined by two or
several simple terms which assume an assignable relation in this new
function, and which no longer play the role of parts, but of requisites, of
reasons or constituent elements.
Thus, in a numerical set, each as whole and part is defined by the first
numbers that enter into the relation in this respect: 4, which is twice 2
52
and half of 8, is defined by 3 and 1. Or else, in the arithmetical triangle,
each line as a series of numbers is twice its precedent, but is defined by a
power of two that places the requisite in a relation of multiplication with
itself (and the requisites in relation to one another). We need only
understand that the whole and the parts (and similitude) are not already
related, but the original formula of a derived infinity, a sort of
intelligible matter for every possible relation: thus the primary terms,
without relations in themselves, acquire relations by becoming the
requisites or the definers of the derived, in other words, the shapers of
this material. As long as the primaries were without relation, as simple
auto-inclusions, they were attributes of God, predicates of an absolutely
infinite Being.
But as soon as we consider an infinity of a second order that derives
from this Being, predicates abandon being attributes in order to become
relations. They enter into relations that define wholes and parts to
infinity, and are themselves in reciprocal inclusion with the defined, in
accord with the double antecedence. Here we have entered into
'sufficient reason,' simply because the definers in their relation are in
each instance the reason of the defined. Were a relation to be defined, we
would say that it is the unity of the nonrelation with matters of wholesand-parts. If it has often been held that relations presented Leibniz with
an irreducible difficulty, it is because predicates and attributes were
lumped together, in a confusion that is legitimate only at the level of
absolutely simple notions specifically excluding all relation, but is not so
at the level of the derived forms, or Predicate = relation, in the reciprocal
inclusion of the predicate-relation with the defined subject (4 is 3R1).
And even when the subject will be the monad without parts, predicates
will continue to be 'affections and relations,' at least in the lexicon of the
Monadology.
But previously there exists a third order of infinity. The question
involves series that do not always possess a last term, but that are
convergent and tend toward a limit. 12 Extension no longer pertains, but
intensions or intensities do. No longer relations, but rather laws. No
longer Combinatory, but Characteristic. No longer matter, but something
'real' in matter that fills extension (to be sure, a 'possible' reality). It is the
real in matter, the thing, that has inner characters whose determination
enters each time into a series of magnitudes converging toward a limit,
the relation between these limits being that of a new type,
53
SUFFICIENT REASON
THE FOLD
dy
(—)
dx
and making up a law. Hermann Weyl will state that a law of Nature is
necessarily a differential equation. The notion of requisite, one of
Leibniz's most original notions, no longer designates definers but takes on
its most rigorous, autonomous meaning by designating conditions, limits,
and differential relations among these limits.
Parts or wholes do not exist any more; they are replaced by degrees for
each character. The inner characters of a sound include an actual
intensity, a pitch, a duration, a timbre; a color has a tint, a saturation, a
value; gold, in an example that Leibniz often uses, has a color, a weight, a
malleability, a resistance to melting and to dissolution in nitric acid. The
real in matter is not only extension; it possesses an 'impenetrability,
inertia, impetuosity and attachment.' It is what is called the texture of a
body, it is specifically the sum of its inner qualities, the latitude of their
variation and the relation of their limits: hence the texture of gold."
Insofar as the Requisites are thus distinguished from the Definables
(although they can furnish definitions), we discover that we are facing a
third type of inclusion, in this instance a nonreciprocal and unilateral one:
here sufficient reason becomes a principle. Everything real is a subject
whose predicate is a character put into a series, the sum of predicates
being the relation among the limits of these series (we shall avoid
confusing limit and subject).
We have to mark at once the irreducibility of this new area from the
point of view of an object of knowledge; but we also have to account for
its transitory role, in another sense, from the point of view of knowledge
itself. On the one hand, requisites are in fact neither presupposed,
intuitive essences of the first infinity, nor theorematic essences of the
second infinity in definitions and demonstrations. They are problematic
essences that correspond to the third infinity. Leibniz's mathematics are
forever forging an irreducible instance from problems; it is added to the
concatenations of definitions, but without it, perhaps, definitions would
not concatenate: if there are exchanges of mathematical letters, it is
because we are thrown into problems before being sent off to theorems.' 4
In this sense, axioms deal with problems, and surely escape demonstration. If the Characteristic is distinguished from the Combinatory, it is
because it is a veritable calculus of problems or of limits. Requisites and
54
axioms are conditions; not always conditions of experience in the Kantian
fashion that still turns them into universals, but the conditions of a
problem to which the thing responds in one case or another, the cases
referring to values of the variable in the series.
What appears is that we are linked – almost fixed – to requisites: even
the definers that we attain, in arithmetic or in geometry for example,
have value only through analogy, and are in fact the inner characters of a
presupposed domain (thus the first numbers whose converging series are
sought). The theorem, the demonstration as a concatenation of
definitions, can appeal to syllogistic form; but we go by 'enthymemes,'
which hold only for syllogisms, and which work by means of 'inner
suppressions,' ellipses, and problematic shortcuts. 15 In short, if the
Combinatory realizes something of its dream, it can do so only through
the Characteristic. Yet at this point we move over to the other aspect of
the question, which now involves knowledge itself and not its nearest
object.
The inner characters of the thing can in fact be understood from the
outside and through successive experiments. As happens with animals,
their relation remains in the state of simple empirical consecutiveness.
However, according to every given case, we can also attain the texture,
that is, the true connection of these characters, as in the intrinsic relations
between the limits of their respective series (reason): there, we have a
rational knowledge, and that is what explains how the inner characters
already hold for definitions, the calculus of limits, for demonstrations,
and how enthymemes work for complete syllogisms.' 6 Whence Leibniz's
worry over reintegrating axioms in the order of necessary truths and
demonstrations (if they escape demonstrations inasmuch as they are
requisites, it must all the more be shown that they involve the form of the
whole and of parts). Thus characters have to lead us at times downward,
toward knowledge of animals, and at others upward, toward rational,
definitive, and demonstrative knowledge.
We therefore have three types of inclusion: auto-inclusions, reciprocal
inclusions, and unilateral inclusions that can be localized at their limits.
Their corresponding term, the absolute-simples, Identicals or infinite forms
lacking any relation to each other; the relative-simples, the Definables, that
enter into infinite series of wholes and parts, while their definers enter
into relations; the limitative-simples, Requisites or converging series that
tend toward limits, with their relations among limits. It is the Alphabet,
the Combinatory, and the Characteristic.
55
THE FOLD
If we go back to the model of the Baroque fabric, it could be stated that
knowledge is known only where it is folded. Leibniz remarks that
concatenations of syllogisms or definitions are a 'fabric.' But 'there exists
an infinity of other, more composite fabrics,' folded like their enthymemes, that are always available for our use.' 7 Even the purest syllogistic
fabric has been folded according to different speeds of thinking. Ideas are
so folded in the soul that we can't always unfold or develop them, just as
things themselves are inextricably wrapped up in nature. Malebranche's
error is to have believed that in God we see completely unfolded Ideas.
But even for God notions have folds that adorn infinite understanding.
Absolute Forms, Identicals, are simple and separated folds; Definables are
already composite folds; Requisites with their limits resemble even more
complex hems (and take up textures). Monads, that necessarily imply a
point of view or a grounding, cannot fail to bear resemblance to draped
forms.
Now we come to the fourth category of notions: individual notions or
monads, that are no longer possible things, but now possible existants
(substances). The complete schema is therefore: identities, extensities,
intensities, individualities; forms, magnitudes, things, substances. Are the
latter still simple or individual-simple notions, and in what sense? In
every event it is clear that predicates of a given notion taken as a subject
form yet another infinite convergent series that tends toward a limit. That
is why the individual naturally has a presently infinite comprehension; it
'envelops the infinite.' 18 The individual notion, the monad, is exactly the
inverse of God to the degree that reciprocals are numbers that exchange
their numerator and their denominator: 2, or f, has as a reciprocal z. And
God, whose formula is has as its reciprocal the monad, Icc. Now the
question entails knowing if the infinite convergent series in the monad,
in the individual, is of the same type as that of the intentions [intentions],
or if indeed another case is involved, of another, fourth type of inclusion.
Clearly we can and must present individual substances as having
requisites and inner characters.
In fact that is how Leibniz salvages Aristotle, by making requisites of
substance from both form and matter and powers both active and passive.
Great differences are no less marked between the thing and substance, or
the thing and the existant. The first difference is that the thing has several
internal characters, x, y, ... and therefore figures in several series, each of
which tends toward its limit, the reason or connection of the series in the
thing being a differential relation of the order
56
SUFFICIENT REASON
It might be said that our perception of things is a 'pleonasm' or that, in
the instance of things, 'we have more than one notion of a same subject,'
for example, weight and malleability for gold. 19 Now the same does not
hold for individuals: we have seen that the world was a unique, infinitely
infinite, converging series, and that each monad expressed it in its
entirety, even though it clearly expressed only one portion of the series.
But, rightly, the clear region of a monad is extended in the clear portion of
another, and in a same monad the clear portion is prolonged infinitely
into the obscure zones, since each monad expresses the entire world. A
searing pain in me is only the prolongation of a series that led me into it,
even if I did not notice it, and now it is continued in the series of my pain.
There is a prolongation or continuation of convergent series, one into the other.
That is the very condition of 'compossibility,' in a manner of
reconstituting over and again one and the same, infinitely infinite,
converging series, the World, made of all series, its curvature having a
unique variable. The differential relation thus acquires a new meaning,
since it expresses the analytical extension of one series into another, and
no more the unity of converging series that would not diverge in the least
from each other. Now then, infinity also changes meaning. It acquires a
fourth and still current dimension: it is no longer defined either by itself
or by the 'limit' of a series, but by a law of order or continuity that
classifies limits or transforms series into a 'totality' (the presently infinite
totality of the world, or the transfinite). Just as each monad conveys the
entire world, so then a single notion can no longer pertain for one
subject, and subject-monads will now be distinguished only by their
inner manner of expressing the world: the principle of sufficient reason
will become a principle of indiscernibles. Since there never exist two
identical subjects, there can be no apparently identical individuals.
There is a second difference that does not seem to be to the monad's
liking. The thing in its texture surely contained the serial law that
determined the play of its characters and the differential relation between
limits. Whereas monads in their folds, including the same world in one
order or another, contain the infinite series, they do not contain the law
of this unique series. Differential relations, different orders refer to a
totality of all orders that exists outside of the monad. In this way the
world is in the monad, but the monad lives for the world: God himself
57
THE FOLD
conceives individual notions only as a function of the world that they
express, and chooses them only through a calculus of the world. With all
series being extended into each other, law or reason appears to be pushed
back into transfinite totality, into the whole of the infinitely infinite
series, the world, and the limits or relations among limits, in God who
conceives and chooses the world.
Whence the cosmological proof of God's existence, which goes from
the series to the whole, and from the whole to God. 2° The whole series is
clearly in the monad, but the reason of the series — from which the monad
receives only its particular effect or individual capacity to complete a part
of it — is not. The limit remains extrinsic and appears only in a harmony
preestablished among the monads. But perhaps the monad draws its force
from it instead of being impoverished by it: the exteriority of reason is
only the consequence of the positive possibility of prolonging the series
into each other; not only the finite series that correspond to the clear
expression of each monad, but the infinite series that correspond to the
order or to the point of view of each individual. It is because each monad
includes the entire world that it cannot include the serial reason common
to all monads. We thus face a fourth type of inclusion. Inclusion of the
world in the monad is surely unilateral, but cannot be localized. It cannot be
localized at the limit, since the limit is outside of the monad. There exist
four inclusions just as there are four infinities: the infinite sum of
primitive forms ( = God); infinite series without limits; infinite series with
intrinsic limits; infinite series with extrinsic limits that restore an infinite
whole ( = World).
From this point we can dissipate the ambiguities of the beginning. First
of all, why does Leibniz appear to present the truths of essences being
amenable to a finite analysis that leads them back to Identicals, while the
truths of existence would refer solely to an infinite analysis and would be
'irreducible to identical truths'? But the two hypotheses are false.
Whether intuitive, theorematic, or problematic, essences are always
understood in an infinity. Identicals themselves are intuitive essences, in
this way taken as infinite forms. In contrast, it is true that in the area of
essences we can always stop, and make use of a definition as if it were a
final Identical, or of a Requisite as if it were a definition, of a Limit, as if it
had been reached. In the area of existences, to the contrary, we cannot
stop, because series are liable to be extended and must be so because
inclusion cannot be localized.
In the second place, we are not any more exact when we state that the
58
SUFFICIENT REASON
analysis of existences is virtual, while that of essences would only be
actual. All analysis is infinite, and in analysis the present or actual exists
only in infinity. That inclusion is virtual in propositions of existence
signifies merely that nothing is included in an existent unless it may be
the entire world, and unless the world currently exists only in the
existents that include it: there still, 'virtual' designates the character of
current inclusion that cannot be localized. There is always a double
antecedence: the world is virtually first, but the monad is actually first.
Now we understand that the word 'virtual' also fits certain propositions of
essence. In respect to those concerning Requisites, the word designates
the unilateral character of inclusion. If we return to the text of De la
liberti, we see that the virtual inclusion is based on a non-reciprocal
proposition: 'Every bino-binary ternary is binary-ternary.' Inclusion is
virtual, Leibniz specifies, because it has to be extracted, and because the
predicate is included in the subject only 'under a certain power.' 21
Here it seems that the arithmetical example is clear and simple, but not
adequate. The adequate example, as the rest of the text affirms, is the
irrational number because it is a root that has to be extracted, or even the
differential relation because it involves quantities that are not of the same
power. This is how Leibniz regroups the two cases of nonreciprocal
inclusion: irrational and existent numbers. The analysis of things is
effectively a determination of predicates as requisites, which is accomplished through the extraction of the root or even by a depotentialization
of magnitudes, in line with the idea of intrinsic limits. The analysis of
existents is a determination of predicates as world, which is accomplished
through the prolongation of series of powers, in line with the idea of
extrinsic limits. Time and again we discover an incertitude that is
objective: On the one hand, does the fold pass between essences and
existents or, on the other, between essences of God and what follows? Or
between the essences of things and existents?
Predicates are never attributes except in the case of infinite forms or first
quiddities; and even there they are more like conditions of possibility for
the notion of God, nonrelations that would condition any possible
relation. Now in all other cases the predicate is only a relation or an
event. Relations themselves are types of events, and problems in
mathematics. In antiquity predicates were defined by events that happen
to figures. Events in their turn are types of relations; they are relations to
existence and to time. 22 Included in the notion as subject is forever an
59
THE FOLD
event marked by a verb, or a relation marked by a preposition: I am
writing, I am going to Germany, I cross the Rubicon ... (and, if things had
the gift of speech, they would say, as might, for example, gold: 'I will
resist melting and nitric acid'). How strange it was to think that the
unilateral inclusion carried with it the reduction of the proposition to a
judgment of attribution.
Attribution, to the contrary, is what Arnault opposes to Leibniz in order
to criticize inclusion and to salvage the Cartesian conception of substance
(I am a thinking being, I am a thing that thinks ...). The attribute
expresses a quality and designates an essence; now Leibniz refuses to
define the predicate by a quality, or by the existing subject, even 'sub
ratione possibilitatis,' as an essence. The subject is defined by its unity,
and the predicate as a verb expressing an action or a passion. Leibniz
knows well the scheme of the attribution of the subject-copula-attribute:
I am writing, I am traveling. ... But this scheme of a 'general grammar'
that is so dear to Arnauld implies a conception of affirmation and a theory
of distinction that hardly favors inclusion. 23 Leibnizian inclusion is based
upon a scheme of subject-verb-object that since antiquity resists the scheme of
attribution. Here we have a Baroque grammar in which the predicate is
above all a relation and an event, and not an attribute. When Leibniz uses
the attributive model, he does so from the point of view of a classical logic
of genres and species, which follows only nominal requirements. 24 He
does not use it in order to ground inclusion. Predication is not an
attribution. The predicate is the 'execution of travel,' an act, a movement,
a change, and not the state of trave1. 25 The predicate is the proposition itself
And I can no more reduce 'I travel' to 'I am a traveling being' than I can
reduce 'I think' to 'I am a thinking being.' Thought is not a constant
attribute, but a predicate passing endlessly from one thought to another.
That the predicate is a verb, and that the verb is irreducible to the
copula and to the attribute, mark the very basis of the Leibnizian
conception of the event. In the first place the event is deemed worthy of
being raised to the state of a concept: the Stoics accomplished this by
making the event neither an attribute nor a quality, but the incorporal
predicate of a subject of the proposition (not 'the tree is green,' but 'the
tree greens ...'). They conclude that the proposition stated a 'manner of
being' of the thing, an 'aspect' that exceeded the Aristotelian alternative,
essence-accident: for the verb 'to be' they substitute 'to follow,' and they
put manner in the place of essence. 26 Then Leibniz implemented the
second great logic of the event: the world itself is an event and, as an
60
SUFFICIENT REASON
incorporeal ( = virtual) predicate, the world must be included in every
subject as a basis from which each one extracts the manners that
correspond to its point of view (aspects). The world is predication itself,
manners being the particular predicates, and the subject, what goes from
one predicate to another as if from one aspect of the world to another.
The coupling basis-manners disenfranchises form or essence: Leibniz
makes it the mark of his philosophy. 27 The Stoics and Leibniz invent a
mannerism that is opposed to the essentialism first of Aristotle and then
of Descartes. Mannerism as a composite of the Baroque is inherited from
a Stoic mannerism that is now extended to the cosmos. A third great logic
of the event will come with Whitehead.
It is very curious to hear Russell state that Leibniz encounters great
difficulty in pondering relations. In a certain fashion all Leibniz does is
ponder relations, and Russell is aware of the fact. The only difficulties
originate in what cannot be easily extracted, beginning with sentences, in
which propositions of inherence show that the predicate is an internal
relation. Sometimes the predicate is not given in the sentence, while at
others the subject is missing, and at others both of them are lacking. When
I say, 'Here are three men,' the real subject is an extension 3, which is only
qualified as human, and quantified by three parts; but the predicate is 2
and 1 (men), the internal relation. If I say, 'Water boils at 100° C,' the
subject is clearly a thing, water, but the predicate is a vaporization curve
that enters into relation with the fusion curve and the sublimation curve
at a triple point. And if I say, 'Peter is smaller than Paul,' 'Paul is bigger
than Peter,' clearly this time the subjects are substances, but the relation in
each case is not between the two subjects: the true relation is the
predication of a 'representative of Paul' in the subject Peter, in the aspect
of length, or of a 'representative of Peter' in the subject Paul, this relation
or this predicate always being internal. And size itself refers to the
preceding cases, sometimes the extension-subject, sometimes the predicate of the thing (the body). In short, in Leibniz we have an entire
history of the concept that goes through the wholes-and-parts, things and
substances, by means of extensions, intensions, and individuals, and by
which the concept itself, in conformity with each level, becomes a subject.
A rupture is opened with the classical conception of the concept as a being
of reason: the concept is no longer the essence or the logical possibility of
its object, but the metaphysical reality of the corresponding subject. It can
be stated that all relations are internal, precisely because the predicates are
not attributes (as in the logical conception).
61
THE FOLD
The proof would come from Leibniz's theory of substance. This theory
appears to be made expressly for this proof. The two nominal characters
on which everyone agrees in principle, from Aristotle to Descartes, are:
on the one hand, substance, what is concrete, determined, individual, in
the sense that Aristotle speaks of this, and Descartes, of that stone; on the
other hand, substance is subject to inherence or inclusion, in the way that
Aristotle defines accident as 'what is present in substance,' and Descartes
states that substance is a 'thing in which what we conceive exists formally
or eminently.' 28 But no sooner than we search for a real definition of
substance, it appears that the two characters are removed for the sake of
an essential, necessary, and universal essence or attribute in the concept.
Thus, for Aristotle, the attribute is not in the subject as if by accident, but
is affirmed by the subject, such that it can be treated as a second
substance. And for Descartes the essential attribute is confused with
substance, to the point that individuals now tend only to be modes of the
attribute as it generally is. Far from proving individuality and inclusion,
attribution and the definition of substance call them into question.
According to Descartes, the initial criterion of substance is the simple,
simple notion: that from which elements can be distinguished only by
abstraction or distinction of reason (thus extension and the body, thought
and the mind). Substance is simple because it can be distinguished from
its attribute only by abstraction. Now Leibniz denounces simplicity as a
pseudo-logical criterion, for the reason that many simple notions — three
at least — are lacking in substance. Only later does he speak of the monad
as a simple notion, when he feels that all dangers are set aside, and when
he will bring forward two kinds of substance in the problem, of which
some are said to be simple only because the others are composite. Yet
from one end of his work to the other he invokes a unity of being as a
metaphysical criterion instead of a simplicity of concept. Arnauld notes
that it is an unusual procedure since one cannot then define substance by
an essential attribute that would oppose it to 'modality, or manner of
being,' that is, to movement or change. To which Leibniz responds
ironically that he has his own 'ordinary philosophers' who account for
degrees of unity, Aristotle contra Descartes.
Leibniz specifically claims for substance a unity that can be interior to
movement, or a unity of change that can be active, that excludes simple
extension at the level of substances. 29 As long as movement is defined as
'the successive existence of a moving body in different places,' we
apprehend only an accomplished movement, and not the inner unity to
62
SUFFICIENT REASON
which it refers when it is in the act of moving. Movement that moves
refers at once (1) to a unity in the instant, in the way that the following
state must issue 'from itself from the present through a natural force,' and
to (2) an inner unity for the totality of its duration (the physical criterion
of substance). And more profoundly, the qualitative change refers (3) to
an active unity that incites a state to move in a flash, but also assures the
totality of the movement (a psychological criterion, perception and
appetite). 3° Substance therefore represents the double spontaneity of
movement as event, and of change as predicate. If the true logical
criterion of substance is inclusion, it is because predication is not an
attribution, because substance is not the subject of an attribute, but the
inner unity of an event, the active unity of a change.
Beyond the Simple, Descartes proposed another criterion, the
Complete, that refers to the real distinction. But the latter, no less than
the distinction of reason, entails only the concept: the complete is not
what is entire (what includes the sum of what belongs to the thing), but
what is really distinct, in other words, what can be 'thought' by itself by
denying what belongs to other things. It is in this way, according to
Descartes, that the thinking thing and the extended thing are in
themselves, or really distinct, and thus separables. But there still, Leibniz
shows that Descartes does not push the concept far enough: two things
can be thought as being really distinct without being separable, no matter
how little they may have requisites in common. Descartes does not see
that even simple beings and even individual substances have requisites,
even if it were in the common world that they express, or in the inner
characters toward which they converge (form-matter, act-force, active
unity-limitation). We have already seen that the really distinct is neither
necessarily separate nor separable, and the inseparable can be really
distinct. 31 At the limit, and as the Stoics stated, nothing is either separable
or separated, but everything conspires, including substance, by virtue of
requisites. It is false to state that a substance possesses only one attribute
since it has an infinity of modes, but false too that several substances do
not have a common attribute since they have requisites that still
constitute one of their criteria (an epistemological criterion). 32 Thus there
are five criteria of substance: (1) metaphysical, unity of being; (2) logical,
inclusion of the predicate in the subject; (3) physical, inner unity in
movement; (4) psychological, active unity of change; ( 5) epistemological,
the requisites of inseparability. None permits substance to be defined by
an essential attribute, or predication to be confused with an attribution.
63
THE FOLD
Essentialism makes a classic of Descartes, while Leibniz's thought appears
to be a profound Mannerism. Classicism needs a solid and constant
attribute for substance, but Mannerism is fluid, and the spontaneity of
manners replaces the essentiality of the attribute. Can we say that a pain
is spontaneous in the soul of a dog that is flogged while it eats its meal, or
in that of Caesar the baby when stung by a wasp while sucking at his
mother's breast? But the soul is not flogged or stung. Instead of sticking to
abstractions, we have to restore the series. The movement of the rod does
not begin with the blow: carrying his stick, a man has tiptoed up to the
dog from behind, then he has raised the instrument in order then to strike
it upon the dog's body.
Just as this complex movement has an inner unity, so also, in the soul
of the dog, the complex change has an active unity: pain has not abruptly
followed pleasure, but has been prepared by a thousand minute
perceptions — the pitter-patter of feet, the hostile man's odor, the
impression of the stick being raised up, in short, an entire, imperceptible
'anxiousness' from which pain will issue 'sua sponte,' as if through a
natural force integrating the preceding modifications. 33 If Leibniz attaches
so much importance to the question of the souls of animals, it is because
he knows how to diagnose the universal anxiety of the animals watching
out for danger, that seeks to grasp the imperceptible signs of what can
turn its pleasure into pain, that will cause its quarry to flee, or turn its
repose into movement. The soul assigns itself a pain that delivers to its
consciousness a series of minute perceptions that it had almost failed to
remark because they were first buried in its depths. Leibniz is haunted by
depth of the soul, the dark depth, the 'fuscum subnigrum.' Substances or
souls 'draw everything from their own depths.' That is the second aspect
of Mannerism, without which the first would remain empty. The first is
the spontaneity of manners that is opposed to the essentiality of the
attribute. The second is the omnipresence of the dark depths which is
opposed to the clarity of form, and without which manners would have
no place to surge forth from. The entire formula of the Mannerism of
substances is: 'All is born to them out of their own depths, through a
perfect spontaneity.' 34
What founds Ortega y Gasset's impression, that of a play of principles
within principles? It is because most of these terms are slippery. Or rather,
they have been pigeonholed into boxes and columns, in places where
they formerly unfolded themselves: they reign by unfolding themselves
in a zone. But they already or still exist folded in what precedes, or they
64
SUFFICIENT REASON
Class of
beings
Predicate
Subject
Inclusion
Infinity
Infinity by
itself
Identical&
(absolutely
simple)
Forms or
attributes
God
Autoinclusion
Definable'
(relatively
simple)
Relations
among definers
Extensions
or Sizes
(wholes and
parts)
Reciprocal Infinity by
Inclusion the cause
Principle
Principle of
contradiction
Principle of
similitude
Conditionables Requisites (their Intentions or Inclusion Infinite Series Principle of
Things (what unilateral with internal sufficient
relations or
(limitatively
reason
has degrees localizable limit
laws)
simple)
& tends
toward
limits)
Individuals
(wholly
simple)
Events or Modes Existents or
Substances
(relations with
existence)
Inclusion
unilateral
cannot be
localized
Infinite series Principle of
indiscernibles
with outer
limit
are folded into what follows. Thus sufficient Reason: it appears for itself in
things, where inner characters begin to connect in order to provide the
reason for the thing. But then, the principle of indiscernibles is only the
explication of Reason at the level of individuals, at the point of appearing
to be a simple dependency of sufficient reason.
And formerly, sufficient reason resided in the definables, like the
relation among definers, such that it previously played in the frame or in
the zone of the principle of similitude. And further, the principle of
contradiction itself already expresses the very reason of the identicals,
and is not limited to forming an alternative with the principle of sufficient
reason. To the contrary, it rules in the zone where noncontradiction
suffices as reason. In this sense the principle of contradiction is a case of
sufficient reason. 35 But is not sufficient reason in its turn a case of
noncontradiction? The same goes for substances and things, for
conditionables and definables. And yet still we have considered only a
small number of principles. There is a whole play of passages and
transformations of principles: sufficient reason is the reciprocal of
noncontradiction, as Couturat has observed. 36 But the principle of
indiscernibles is also the inverse of the principle of sufficient reason
inasmuch as the following can be stated: 'a concept through a thing,' and
65
THE FOLD
then: 'a thing, and only one thing, through a concept' (in which case
thing = individual).
There we have a unique trait that is found only in Leibniz's
philosophy: the extreme taste for principles, far from favoring division
into compartments, presides over the passage of beings, of things, and of
concepts under all kinds of mobile partitions. In the midst of this
extraordinary philosophical activity, which consists of the creation of
principles, we might state that it is the least of principles that there are
two poles, one toward which all principles are folding themselves
together, the other toward which they are all unfolding, in the opposite
way, in distinguishing their zones. These two poles are: Everything is
always the same thing, there is only one and the same Basis; and:
Everything is distinguished by degree, everything differs by manner ...
These are the two principles of principles. No philosophy has ever pushed
to such an extreme the affirmation of a one and same world, and of an
infinite difference or variety in this world.
66
5
Incompossibility, individuality, liberty
Adam sinned, but his opposite, Adam the nonsinner, is neither impossible
nor inherently contradictory (as would be '2 plus 2 do not equal 4'). Such
is the tenor of propositions of existence. But we have to know where the
problem is: between the two contraries, Adam the sinner and Adam the
nonsinner, is a relation of contradiction. In contrast, an entirely different
kind of relation must be added if we are to explain that Adam the
nonsinner is not contradictory in itself. This other relation is not between
the two Adams, but between the Adam nonsinner and the world in
which Adam sinned. Surely, insofar as the world in which Adam sinned is
included in Adam, we would fall back into a contradiction. But he is also
included in an infinity of other monads. In this way there must be a
relation of original exclusion between Adam the nonsinner and the world
in which Adam sinned. Adam the nonsinner would include another
world.
Between the two worlds there exists a relation other than one of
contradiction (although there may be a local contradiction between the
subjects that compose them, when taken two by two). It is a vice-diction,
not a contradiction. That God chooses among an infinity of possible
worlds is a rather conventional idea (found, for instance, in Malebranche). Leibniz innovates when he invokes a profoundly original
relation among all possible worlds. By stating that it is a great mystery
buried in God's understanding, Leibniz gives the new relation the name
of incompossibility. 1 We discover that we are in a dilemma of seeking the
solution to a Leibnizian problem under the conditions that Leibniz has
established: we cannot know what God's reasons are, nor how he applies
67
THE FOLD
them in each case, but we can demonstrate that he possesses some of
them, and what their principle may be.
We have seen that the world was an infinity of converging series, capable
of being extended into each other, around unique points. Thus every
individual, every individual monad expresses the same world in its
totality although it only clearly expresses a part of this world, a series or
even a finite sequence. The result is that another world appears when the
obtained series diverge in the neighborhood of singularities. Compossibles can
be called (1 ) the totality of converging and extensive series that constitute
the world, (2) the totality of monads that convey the same world (Adam
the sinner, Caesar the emperor, Christ the savior ...). Incompossibles can
be called (1) the series that diverge, and that from then on belong to two
possible worlds, and (2) monads of which each expresses a world different
from the other (Caesar the emperor and Adam the nonsinner). The
eventual divergence of series is what allows for the definition of
incompossibility or the relation of vice-diction.
By thus positing an infinity of possible worlds, Leibniz in no way
reintroduces a duality that would turn our relative world into the
reflection of a more profound, absolute world: to the contrary, he turns
our relative world into the only existing world, a world that rejects all
other possible worlds because it is relatively 'the best.' God chooses
between an infinity of possible worlds, incompossible with each other,
and chooses the best, or the one that has the most possible reality. While
the Good was the criterion of the two worlds, the Best is the criterion of
the unique and relative world. The principle of the best renews the issue
of principles because it is the first time sufficient reason is applied to the
world.
There is an antecedence to monads, although a world does not exist
outside of the monads that express it. But God does not first of all create
Adam, although he is free to have him sin or to be aware that he is
sinning. He creates the world in which Adam sins, and also includes it in
every individual that conveys it (Sextus raping Lucretia, Caesar crossing
the Rubicon ...). We begin with the world as if with a series of inflections
or events: it is a pure emission of singularities. Here, for example, are three
singularities: to be the first man, to live in a garden of paradise, to have a
wife created from one's own rib. And then a fourth: sinning. Singularityevents of this kind hold a relation with 'ordinaries' or 'regulars' (the
difference here being minimal). A singularity is surrounded by a cloud of
68
INCOMPOSSIBILITY, INDIVIDUALITY, LIBERTY
ordinaries or regulars. And we can state that whatever is remarkable or
singular is so to the degree that an inflection that erects a singular point
can be made to move anywhere. But we can also state that everything is
ordinary because a singular point is only the coincidence of two ordinary
points from different vectors (point B of a square is the coincidence of a,
the last point of the line AB, and of c, the first of the line BC). 2 When we
follow the two poles of Leibniz's philosophy, we discover that Everything
is regular! Everything, too, is singular! On a given scale, it remains for us
to distinguish the singulars from the ordinaries or regulars in their
relation with one another.
We can now return to our four singularities. We suppose that, every
time, one of them can be extended into the neighboring area of the
others, along regular lines that have common values in both directions.
But then a fifth singularity appears: resistance to temptation. It is not
simply that it contradicts the fourth, 'sinning,' such that a choice has to be
made between the two. It is that the lines of prolongation that go from
this fifth to the three others are not convergent, in other words, they do
not pass through common values. It is neither the same garden, nor the same
primeval world, nor even the same gynegenesis. A bifurcation takes place
that we at least take for granted, since reason escapes us. We are satisfied
to know that one exists. It always suffices to be able to say: that is what
makes Adam the nonsinner to be supposed incompossible with this
world, since it implies a singularity that diverges from those of this world.
That a calculus and even a divine play may exist at the origin of the
world is a topic pondered among the greatest philosophers. But
everything depends on the nature of the game, on its eventual rules
and of the too human model that we are able to reconstitute from it. With
Leibniz, it seems to us that in the first place there is a calculus of infinite
series ruled by convergences and divergences.
Leibniz furnishes its great Baroque staging at the end of the Theodicee. The
text responds marvelously to the general criteria of Baroque narrative:
stories enclosed one in the other, and the variation of the relation of
narrator-and-narration. 3 It is in fact a philosophical dialogue, in which a
divinatory consultation of Apollo by Sextus Tarquin is inserted, followed
by a direct meeting of Sextus and Jupiter in the presence of Theodorus,
that gives way to Theodorus's conversation with Jupiter who sends him
back to Pallas, until Theodorus's sublime dream precedes this new
meeting. It is an architectural dream: an immense pyramid that has a
69
THE FOLD
summit but no base, and that is built from an infinity of apartments, of
which each one makes up a world. It has a summit because there is a
world that is the best of all worlds, and it lacks a base because the others
are lost in the fog, and finally there remains no final one that can be
called the worst. In every apartment a Sextus bears a number on his
forehead. He mimes a sequence of his life or even his whole life, 'as if in a
theatrical staging,' right next to a thick book.
The number appears to refer to the page that tells the story of the life
of this Sextus in greater detail, on a smaller scale, while the other pages
probably tell of the other events of the world to which he belongs. Here is
the Baroque combination of what we read and what we see. And, in the
other apartments, we discover other Sextuses and other books. Leaving
Jupiter's abode, one Sextus will go to Corinth and become a famous man,
while another Sextus will go to Thrace and become king, instead of
returning to Rome and raping Lucretia, as he does in the first apartment.
All these singularities diverge from each other, and each converges with
the first (the exit from the temple), only with values that differ from the
others. All these Sextuses are possible, but they are part of incompossible
worlds.
A bifurcation, like the exit from the temple, is called a point in the
neighborhood of series' divergence. Borges, one of Leibniz's disciples,
invoked the Chinese philosopher-architect Ts'ui Pen, the inventor of the
'garden with bifurcating paths,' a baroque labyrinth whose infinite series
converge or diverge, forming a webbing of time embracing all
possibilities. 'Fang, for example, keeps a secret; a stranger knocks at his
door; Fang decides to kill him. Naturally, several outcomes are possible:
Fang can kill the intruder; the intruder can kill Fang; both of them can
escape from their peril; both can die, etc. In Ts'ui Pen's work, all
outcomes are produced, each being the point of departure for other
bifurcations.'' Another of Leibniz's disciples, the great popular novelist
Maurice Leblanc, told the story of Balthazar's life. He was a 'professor of
everyday philosophy,' for whom everything was ordinary, everything
was always regular. ... But, an orphan, he launched himself in a quest to
find his father, with three singularities: his own fingerprints, the letters
MTP tattooed on his chest, and the revelation of a clairvoyant who had
told him that his father was headless. Then Count Coucy-VendOme, who
died with his throat cut, made Balthazar his inheritor in a document that
bears the fingerprints and describes the tattoo. But Balthazar is
intercepted by the Mastropieds gang (MTP) whose former head, a victim
70
INCOMPOSSIBILITY, INDIVIDUALITY, LIBERTY
of the guillotine, claimed him as his son. He is taken away by an
Englishman who hands him over to a pasha, who is soon decapitated,
whose missing son, Mustapha (MTP) bore the same fingerprints. He is
saved by a poet whose device is Mane Thecel Phares, who claims him in
turn, but who loses his head in a fit of madness and assassinates a tramp.
The final explanation is that the tramp had formerly organized a boarding
school for rich children, four plus his own child. But, after a flood, he
could not tell which of the five children remained. Having become an
alcoholic, having also lost his head, he had sent to the four fathers the
impression of the survivor's fingerprints and the sign of the tattoo, in
order to persuade each of them that the child was his son. 5 Whence the
entanglement of bifurcating stories that are developed simultaneously in
divergent series in incompossible worlds. Balthazar cannot be the son of
all these fathers in the same world. It is a multiple fraud.
It is clear why Borges invokes the Chinese philosopher rather than
Leibniz. He wanted, just as did Maurice Leblanc, to have God pass into
existence all incompossible worlds at once instead of choosing one of
them, the best. And probably it would be globally possible, since
incompossibility is an original relation, distinct from impossibility or
contradiction. There would nonetheless be local contradictions, like that
of Adam the sinner and Adam the nonsinner. But what especially
impedes God from making all possibles — even incompossibles — exist is
that this would then be a mendacious God, a trickster God, a deceiving
God, such as Maurice Leblanc's tramp. Leibniz, who strongly distrusts the
Cartesian argument of the nonmalevolent God, gives him a new basis at
the level of incompossibility: God plays tricks, but he also furnishes the
rules of the game (contrary to Borges's and Leblanc's game without
rules). The rule is that possible worlds cannot pass into existence if they
are incompossible with what God chooses. According to Leibniz, only
novels of the order of D'Urfee's L' A stra give us the idea of these
incompossibles. 6
Here we can deduce a definition of the individual and of the individual
notion. We had seen that every monad conveyed the world (an inclusion
that cannot be localized), but clearly conveyed only one partial zone or
subdivision by virtue of its point of view (a localized borough). And this
enlightened region probably passed through the body of every individual.
But since we did not know what constituted the region of or relation to
the body, only a nominal definition of the individual was offered. Now
71
THE FOLD
we can say that an individual is established first of all around a certain
number of local singularities, which are its 'primary predicates': thus for
Adam the four predicates previously considered.' That is the real
definition of the individual: concentration, accumulation, coincidence of a
certain number of converging preindividual singularities (it being said that
singular points can coincide in a same point, as the different summits of
separate triangles coincide at the common summit of a pyramid). It
resembles the nucleus of a monad. At the kernel of every monad,
according to Gueroult's hypothesis, there exists no 'simple notion.'
Contrary to Leibniz's method, we would have to be satisfied with two
extremes in a chain of notions. 8 At the core of every monad there exist
singularities that in every case are the requisites of the individual notion.
That each individual clearly expresses only a part of the world derives
from the real definition: it clearly expresses the region determined by its
constituent singularities. That every individual expresses the entire world
also derives from the real definition: the constitutive singularities of each
one are effectively extended in all directions up to the singularities of
others, under the condition that the corresponding series converge, such
that each individual includes the sum of a compossible world, and
excludes only the other worlds incompossible with that world (where the
series would diverge).
Whence Leibniz's stress when he states that God does not create a
'vague' or vagabond Adam who straddles several incompossible worlds,
but creates, 'sub ratione possibilitatis,' as many divergent Adams as there
are worlds, each Adam containing the entire world to which he belongs
(and to which, also by including it, belong all other compossible monads
of such a world). In short, every possible monad is defined by a certain
number of preindividual singularities, and is thus compossible with all the
monads whose singularities converge with its own, and incompossible
with those whose singularities imply divergence or nonprolongation.
But why is Adam's proper name given to all these divergent
individuals in incompossible worlds? It is because a singularity can
always be isolated, excised, or cut from its prolongations. Then it no
longer matters if the garden in which Adam sins is not the same one in
which Adam cannot sin. The singularity becomes indefinite, it is no more
than a garden, and the primary predicate is no longer grasped in one
world or another, but only considered 'sub ratione generalitatis,' at the
same time its subject becomes an Adam in general, a Sextus. ... From this
we shall not conclude that individuation begins from these general
72
INCOMPOSSIBILITY, INDIVIDUALITY, LIBERTY
predicates. They can be studied more closely later. Individuation does not
go from a genre to smaller and smaller species, in accord with a law of
differentiation, but goes from singularity to singularity, under the law of
convergence or of prolongation that ties the individual to one world or
another.
Individual difference is not specific, and the individual is not a last or
final species. 9 However, Leibniz happens to say that the individual is like
a 'species infima' [lower species]; but that is merely a nominal definition
of the individual, and Leibniz appeals to it for a specific end, that of
breaking with everyone who opposes the individual to the concept. For
some, the Nominalists, individuals would be the only existants, concepts
being only carefully ordered words; for others, the Universalists, the
concept has the power of being infinitely determinable, the individual
referring only to accidental or extraconceptual determinations. But for
Leibniz, at the same time only the individual exists, and it is by virtue of
the power of the concept: monad or soul. Thus this power of the concept
(to become a subject) does not consist in determining a genre to infinity,
but in condensing and in prolonging singularities. The latter are not
generalities but events, or droplets of an event. They are not in the least
preindividual, insofar as the world is virtually first in respect to
individuals that express it (God has created, not Adam the sinner, but
the world in which Adam has sinned ...). In this sense the individual is the
actualization of preindividual singularities, and implies no previous determination. The contrary must be noted by observing that determination itself
supposes individuation.
It is true for the two cases that Leibniz distinguishes: mathematical
species and physical species. In the first case, 'the least difference that
causes two things not to resemble one another totally is enough to make
them differ in species.' All individual difference between two mathematical beings is necessarily specific, since it can be stated mathematically
only in the form of a relation between definers (thus, for the ellipse, the
relation of axes). It is even in this sense that the metaphysical individual
can be assimilated to a 'species infima.' The comparison only works
mathematically. In mathematics, specific difference is individuating, but
because individual difference is already specific: there are as many species
as individuals, and the differing material of two figures, whether iron or
plaster, does not constitute them as two potential mathematical
individuals. In mathematics, individuation is what constitutes a determination; now the same does not hold for physical things or organic
73
THE FOLD
bodies. 1° There, as we have observed, different characters make up series
according to which the species never stops varying or dividing, at the
same time that the thing or the body never stops changing. Series impose
no evolutionism, but they do mark the relation of determination with the
alteration of bodies. This multidetermination, which is confused with the
diverse characters of classification, assumes that the individuality of the body
or the thing comes from elsewhere. And in effect, what is individual and what
individuates the alterable body is only the soul that is inseparable from
it." And even for the thing all substantial forms are everywhere within. It
thus appears that determination assumes an individuation coming from
without, and first of all in relation to species and genres.
We look in vain for the least opposition between the principle of
indiscernibles and the law of continuity. The latter is a law of
determination that rules in three principal areas: the mathematical
domain of wholes and parts, the physical domain of species or corporeal
characters, the cosmological domain of singularities (inasmuch as a
singularity is extended as far as the neighborhood of another in a
determined order. The principle of indiscernibles is a principle of
individuation, according to which no two similar individuals could be
distinguished solely from the outside by number, space, or time: in the
first place, the soul is what is individual because it circumscribes a certain
number of singularities that are distinguished from those of an other,
although they all may be extensible. In the second place, the soul or souls
individuate physical bodies taken in the continuity of their species. In the
third place, if properly mathematical species are themselves individuating, it is because two figures of the same species are mathematically one
and the same individual, referring to a same 'soul or entelechia,' even if
they are physically different.
The principle of indiscernibles establishes divisions; but the divisions
are not lacunae or ruptures of continuity; on the contrary, they divide
continuity in such a fashion that there can be no holes, that is, in the
'best' way (thus the irrational number). In order to oppose indiscernibles
and continuity, we must hold to an overly rapid formulation of the two
principles: thus it is said that the difference between two individuals must
be internal and irreducible (= 1), while it must vanish and tend toward 0
by virtue of continuity. But never in any of its three meanings does
continuity make difference vanish: what vanishes is merely all value that
can be assigned to the terms of a relation for the gain of its inner reason,
which precisely constitutes difference. 12 Difference no longer exists
74
INCOMPOSSIBILITY, INDIVIDUALITY, LIBERTY
between the polygon and the circle, but in the pure variability of the sides
of the polygon; difference is no longer between movement and inertia,
but in pure variability of speed. Difference ceases being extrinsic and
palpable (in this sense it vanishes) in order to become intrinsic,
intelligible or conceptual, in conformity with the principle of indiscernibles.
And should we desire the most general formulation of the law of
continuity, we might perhaps locate it in the concept, which is unknown
and which cannot be known, where the sensible ends and the intelligible
begins: this is a new way of saying that two worlds do not exist. 13 In the
accord of the two instances, there is even a reflux of continuity on the
souls. For if every individual is distinguished from all others by its primary
singularities, the latter fall short of extending themselves as far as the
primary singularities of other individuals, according to a spatiotemporal
order that makes the 'subdivision' of an individual be continued into the
nearest subdivision and then into the subdivision following that, all the
way up to infinity. The comparative extension and intensity of these
subdivisions — favored zones that belong to each monad — even allow
species of monads or souls to be divided into vegetal, animal, human, or
angelic traits, 'an infinity of degrees in the monads' in continuity."
The play of the world has several aspects: it emits singularities; it puts
forward infinite series that go from one singularity to another; it invents
rules of convergence and divergence according to which these series of
possibles are organized in infinite totalities, each totality being compossible, but two totalities together being incompossible with each other; it
allots the singularities of each world in one way or another in the nucleus
of monads or individuals that express this world. Thus God does not
merely choose the best of all worlds — that is, the richest compossible
totality in possible reality — but he also chooses the best allotment of
singularities in possible individuals (other allotments of singularities and
other demarcations of individuals could be conceived for the same
world). Hence we have rules of the world's composition in a compossible
architectonic totality, but also rules of the world's actualization in the
individuals of this totality at the upper level and, finally, as we shall
observe, rules for the realization of the world at the lower level, in a
materiality proper to this totality.
Leibniz suggests in this regard that three intervening criteria come into
play. One involves the building's tastefulness; the second, the 'number
75
THE FOLD
and elegance of the rooms' on the inside; and the third, the convenience,
the 'rightness' of the grounds, of the materials, and even of the outer
facade of a single adjacent part) 5 It is a vast play of architecture or of
paved grounds: How can a space be filled with the fewest possible voids,
and with the greatest possible number of figures? With this reservation
excepted, space-time is not a grid or a preexisting receptacle that would
be filled (for the best) by the chosen world: on the contrary, a space-time,
as an order of indivisible distances from one singularity to another or
from one individual to another, and even an extension, as a continuous
prolongation in respect to distances, belong to each world. It is space,
time, and extension that are in the world on each occasion and not the
inverse. The play interiorizes not only the players who serve as pieces, but
the board on which the game is played, and the material of that board.
Nietzsche and Mallarme have rewarded us with the revelation of a
Thought-world that throws dice. But for them the world lacks principle,
has lost its principles. That is why the roll of the dice is the power of
affirming Chance, of thinking of chance in sum, which is above all not a
principle, but the absence of all principle. Thus Mallarme gives to absence
or nothingness what issues from chance, what claims to escape it all the
while limiting it by principle: 'The world is the anonymous domain of
absence, from which things appear or into which they will then
disappear. ... The apparition is the mask behind which no one exists,
behind which nothing really exists other than nothing,' Nothing rather
than something.' 6 To think without principles, in the absence of God and
in the absence of man himself, has become the perilous task of a childplayer who topples the old Master of play, and who makes incompossibles
enter into the same world, shattered (the board is broken to bits ...).
But what happened in this long history of 'nihilism,' before the world
lost its principles? At a point close to us human Reason had to collapse,
like the Kantian refuge, the last refuge of principles. It falls victim to
'neurosis.' But still, before, a psychotic episode was necessary. A crisis and
collapse of all theological Reason had to take place. That is where the
Baroque assumes its position: Is there some way of saving the theological
ideal at a moment when it is being contested on all sides, and when the
world cannot stop accumulating its 'proofs' against it, ravages and
miseries, at a time when the earth will soon shake and tremble ...? The
Baroque solution is the following: we shall multiply principles — we can
always slip a new one out from under our cuffs — and in this way we will
change their use. We will not have to ask what available object
76
INCOMPOSSIBILITY, INDIVIDUALITY, LIBERTY
corresponds to a given luminous principle, but what hidden principle
responds to whatever object is given, that is to say, to this or that
'perplexing case.' Principles as such will be put to a reflective use. A case
being given, we shall invent its principle. It is a transformation from Law
to universal Jurisprudence."
We witness the honeymoon of singularity and the concept. Such is the
Leibnizian revolution, and Leibniz is very close to Prospero, the
Mannerist hero par excellence, 'the mysterious Prospero, magician and
rationalist, who knows the secrets of life, a mountebank, a dispenser of
good fortune, but who is himself lost in his splendid isolation.' I8
It surely does not suffice to say that for Leibniz the game falls under
the principle of the Best, with God being given to choose the best of all
possible worlds. For the best is only a consequence and, as a consequence,
it is immediately derived from the defeat of the Good (to save from the
Good whatever can be saved ...). The true character of the Leibnizian
game — and what opposes it to the roll of the dice — is first of all a
proliferation of principles: play is executed through excess and not a lack
of principles; the game is that of principles themselves, of inventing
principles. It is thus a game of reflection, of chess or checkers, where skill
(not chance) replaces old gifts of wisdom or prudence. In the third place,
it is a game of filling holes, in which emptiness is imagined and where
players refuse to give way to absence: it is an inverted solitaire, the player
'filling a square on which he lands' instead of jumping onto an empty
spot, and removing the checker he lands on until the board is empty.
Finally, it is a nonbattle closer to guerrilla warfare than a war of
extermination, more like go than chess or checkers: You don't catch your
adversary in order to reduce him to absence, you encircle his presence to
neutralize him, to make him incompossible, to impose divergence upon
him. 19 The Baroque is just that, at a time just before the world loses its
principles. It is the splendid moment when Some Thing is kept rather
than nothing, and where response to the world's misery is made through
an excess of principles, a hubris of principles, and a hubris inherent to
principles.
Leibniz's optimism is really strange. 2° Yet again, miseries are not what
was missing; the best of all possibilities only blossoms amid the ruins of
Platonic Good. If this world exists, it is not because it is the best, but
because it is rather the inverse; it is the best because it is, because it is the
one that is. The philosopher is still not the Inquisitor he will soon become
77
THE FOLD
with empiricism, and he is even less the Judge he will become with Kant
(the tribunal of Reason). He is a Lawyer, or God's attorney. He defends
God's Cause, following the word that Leibniz invents, 'theodicy.' 21 Surely
the justification of God in the face of evil has always been a philosophical
commonplace. But the Baroque is a long moment of crisis, in which
ordinary consolation no longer has much value. There results a collapse
of the world; the lawyer has to rebuild it, exactly the same world, but on
another stage and in respect to new principles capable of justifying it
(whence jurisprudence). An aggravated justification has to correspond to
the enormity of the crisis: the world must be the best, not only in its
totality, but in its detail or in all of its instances. 22
We clearly witness a schizophrenic reconstruction: God's attorney
convenes characters who reconstitute the world with their inner, so-called
autoplastic modifications. Such are the monads, or Leibniz's Selves,
automata, each of which draws from its depths the entire world and
handles its relations with the outside or with others as an uncoiling of the
mechanism of its own spring, of its own prearranged spontaneity.
Monads have to be conceived as dancing. But the dance is the Baroque
dance, in which the dancers are automata: there we have an entire
'pathos of distance,' like the indivisible distance between two monads
(space); the meeting between the two of them becomes a parade, or
development, of their respective spontaneities insofar as their distance is
upheld; actions and reactions give way to a concatenation of postures
allotted now and again through distance (Mannerism). 23
The principle of optimism, or of the Best, saves the freedom of God: it is
the game of the world and God that guarantees this liberty. In other
possible worlds an Adam does not sin, and a Sextus does not rape Lucretia.
That Caesar does not cross the Rubicon is not impossible, but only
incompossible with the chosen, best world. That Caesar crosses the river is
therefore not absolutely necessary, but relatively certain, at least in respect
to our world. However, human liberty is not itself safeguarded inasmuch as
it has to be practised in this existing world. In human eyes it does not
suffice that Adam may not sin in another world, if he is certainly sinning in
this world. Leibniz leaves the impression that he is condemning us even
more strongly than Spinoza, for whom there at least existed a process of
possible liberation, whereas for Leibniz everything is sealed off from the
beginning and remains in a condition of closure.
Most of the writings in which Leibniz promises us human liberty
bifurcate at the simple liberty of God. To be sure, incompossibility allows
78
INCOMPOSSIBILITY, INDIVIDUALITY, LIBERTY
Leibniz to resolve the ancient problem of future contingent events (Will a
naval battle take place tomorrow?), without falling into the Stoics'
aporias. 24 But it in no way guarantees the character of so-called voluntary
events, or the freedom of whoever wants to engage a naval battle, or of
whoever does not want to. How could there be free will, a will whose
'individual notion encloses once and for all those who will never come to
it?' How to conjoin liberty with a schizophrenic automaton's inner,
complete, and preestablished determination?
We are thrown back to the inclusion of the predicate in the subject. And
doubtless, if the predicate were an attribute, it would be hard to see what
might salvage the liberty of the subject. But the predicate is an event, and
appears in the subject as a change of perception: the event is voluntary
when a motive can be assigned, such as reason or change of perception.
In at least two writings — one short and the other extensive — Leibniz
inaugurates the first great phenomenology of motives. 25 There he
denounces two illusions: one consists in objectifying motives, as if they
were weights placed on the pans of a scale, and as if deliberation were
seeking to know in what direction, all conditions being equal, the scale
would tip. The other illusion consists in dividing motives, since an infinity
of subjective motives are needed so that a choice of objectified motives
can be made, as if one might be able 'to desire to desire.' But in truth the
soul is what invents its own motives, and these are always subjective. We
have to begin from all of the smallest inclinations that ply our soul in
every direction, in the flash of an instant, under the stress of a thousand
'little springs': disquiet. That is the model of the pendulum or balance
wheel, the Unruhe, that replaces the scale. The action is voluntary when
the soul — instead of undergoing the total effect into which these little
appeals enter — gives itself a certain amplitude, such that it bends entirely
in one direction or toward one side.
For example, I hesitate between staying home and working or going
out to a nightclub: these are not two separable 'objects,' but two
orientations, each of which carries a sum of possible or even
hallucinatory perceptions (not only of drinking, but the noise and smoke
of the bar; not only of working, but the hum of the word processor and
the surrounding silence ...). And if we return to motives in order to study
them for a second time, they have not stayed the same. Like the weight
on a scale, they have gone up or down. The scale has changed according
to the amplitude of the pendulum. The voluntary act is free because the
79
THE FOLD
free act is what expresses the entire soul at a given moment of its
duration. That act is what expresses the self. Does Adam sin freely? In
other words, at that instant his soul has taken an amplitude that is found
to be easily filled by the aroma and taste of the apple, and by Eve's
solicitations. Another amplitude — one having retained God's defense — is
possible. The whole question turns on 'laziness.'
Going from inflection to inclusion, we have seen how inflections were
naturally included in souls. Inclination is the fold in the soul, inflection
the way the fold is included. Whence Leibniz's formula: the soul is
inclined without being necessitated. 26 The motive is not even an internal
determination, but an inclination. It is not the effect of the past, but the
expression of the present. It must be observed to what degree Leibniz's
inclusion is always coded in the present: I write, I travel.... If inclusion is
extended to infinity in the past and the future, it is because it concerns
first of all the living present that in each instance presides over their
division. Because it includes what I am doing right now — what I am in
the act of doing — my individual notion also includes everything that has
driven me to do what I am doing, and everything that will result from it,
all the way to infinity. 27 This privilege accorded to the present clearly
refers to the function of inherence in the monad: the function does not
include a predicate without giving it verbal value — that is, the unity of a
movement in the act of being made. Inherence is the condition of liberty
and not of impediment.
When Leibniz appeals to the perfect or completed act (entelechia), he
is not dealing with an act that inclusion would require us to consider as
past, and that would return to an essence. The condition of closure, of
being shut off, has an entirely different meaning: the perfect, completed act is
that which receives from the soul that includes it the unity proper to a movement
that is being made. In this respect Bergson is very close to Leibniz, but in
Leibniz the formula is expressed time and again: the present portends the
future and is burdened with the past. 28 It is not a determinism — even an
internal one — but an interiority that constitutes liberty itself. It is because
the living present is essentially variable in both extension and intensity.
At every moment, it is confused with the favored area or subdivision of
the monad, the zone that it expresses clearly. Hence this is what
constitutes the amplitude of the soul at a given instant. Extended more or
less, more or less intense, the living present neither motivates the same
action nor confers the same movement with a unity of its own. Adam
might have been capable enough not to sin, but only if, at this moment,
80
INCOMPOSSIBILITY, INDIVIDUALITY, LIBERTY
his soul could have taken another amplitude that might constitute the
unity of another movement. The act is free because it expresses the
wholeness of the soul in the present.
Nothing demonstrates the point better than the dark and wondrous
theory of damnation. Even in this case the damned, Judas or Beelzebub,
does not pay retribution for a past action, but for the hate of God that
constitutes the present amplitude of his soul and fills it in the present. He
is not damned for a past action, but by a present action that he renews at
every moment. This hate of God in which he finds a horrible pleasure is
rebegun endlessly so that 'crime will pile upon crime.' Judas is not
damned because he betrayed God, but because, having betrayed God, he
hates God all the more, and he dies of that hate. For a soul that is the
absolute minimum of amplitude: to include in its clear region only a
single predicate, that of 'hating God.' The only glimmer that remains for
him — a uniquely pallid glimmer — is a 'rage of Reason.'
Were it to regain a little of its amplitude, and were it to refrain from
hating in the present, the soul would immediately cease being damned —
but it would be another soul causing the unity of another movement. As
Leibniz states, a damned soul is not eternally damned, he is merely
'forever damnable,' and damns himself at every moment. 29 Thus the
damned are free — and free in the present — as are the happy souls. What
damns them is their current narrow-mindedness, their lack of amplitude.
These are vengeful or resentful people, like those whom Nietzsche later
describes. It is not as if they were undergoing the effects of their past, but
as if they could not be done with the current and present wound they
cannot keep themselves from scratching over and over again. Perhaps this
vision of damnation is so deeply rooted in the Baroque as a function of a
much broader context. The Baroque has conceived of death in the
present, as a movement that is in the act of being completed, and that is
unexpected, but that is 'accompanied.' 3°
If Adam were capable of not sinning, the damned could free
themselves: it would suffice to have the soul take another amplitude,
another fold, or another inclination. It can be stated that the soul cannot
do so, except in another world, one that is incomposssible with ours. Yet
clearly, that it cannot do so signifies that the soul would be other by doing
so: what it does, it does entirely, that being what comprises its liberty. The
soul is not determined to do it. It can be stated further that the soul is at
least determined to be what it is, and that its degree of amplitude at every
81
THE FOLD
moment is inscribed in it and foreseen by God. What does all that
change? That God foresees Adam's laziness and the narrow-mindedness
of the damned does not impede the one or the other from being the
motive of a free act, and not the effect of a determination. That God
preordains the degrees of a soul's amplitude does not impede each one
from being the entire soul at a given moment. That another degree
implies another soul and another world does not hinder this degree from
actualizing the liberty of a given soul in this world. The automaton is free
not because it is determined from within, but because every time it
constitutes the motive of the event that it produces. The automaton is
programmed, but the 'spiritual automaton' is programmed by motivation
for voluntary acts, just as the 'material automaton' is programmed by
determination for mechanical actions: if things are enveloped in God's
understanding, it is such as they are, 'the free as free, and the blind and
mechanical still as mechanical.' 3 1
A reader is immediately struck by the similarity of Leibniz's themes to
Bergson's thesis: the same critique of illusion on motives, the same
conception of the inflections of the soul, the same requirement of
inherence or inclusion as a condition of the free act, the same description
of the free act as what expresses the self ('it is from the entire soul that
free decision emanates, and the act will be all the freer since the dynamic
series to which it is attached will tend to be identified further with the
fundamental self'). 32 And how can we not fail to recall Leibniz again
when Bergson appeals to a second problem, that does not take up the act
as it is being done, but 'future or past action': can a superior intelligence,
apt enough to know 'all antecedents,' predict the act with an absolute
necessity? With Leibniz that is the situation of God the reader, who reads
in everyone 'what is being done everywhere and even what has been
done or will be,' who reads the future in the past because he can 'unfold
all the pleats that are only sensorially developed over time.' 33 Here the
present seems to be losing its privilege, since determinism is being
reintroduced as predestination.
But in what way? Is it because God knows everything in advance? Is it
not rather because he exists forever and everywhere? The first
hypothesis, in effect, is quite ambiguous: either God only knows
everything about antecedents, or we are sent back to the question 'Can
God predict or foresee the act?' Either God knows absolutely everything,
or we have to return to the second hypothesis. Now, to say that God is
82
INCOMPOSSIBILITY, INDIVIDUALITY, LIBERTY
forever and everywhere is to strictly state that God passes through all the
conditions of the monad, no matter how minute they are, and in such a
way that God coincides with it at the instant of action 'without any
postponement.' 34 Reading does not consist in concluding from the idea of
a preceding condition the idea of the following condition, but in grasping
the effort or tendency by which the following condition itself ensues from
the preceding 'by means of a natural force.'
Divine reading is God's apparent passage into the monad (somewhat
in the way Whitehead speaks of a 'passage of Nature' into a place).
Further, each monad is none other than a passage of God: each monad
has a point of view, but this point of view is the 'result' of God's reading
or viewing, which goes through the monad and coincides with it. 35 The
monad is free because its action is the result of what passes through it and
is happening within it. To state that God has already passed through, by
virtue of his prescience, means nothing since eternity consists, much less
in forging ahead or in going backwards, than in coinciding each time with
all the passages that follow in the order of time, with all the present living
beings that make up the world.
Liberty is not what is threatened in the system of inclusion. Rather, it is
morality. For if the free act is what expresses the entire soul at the
moment it conveys its expression, what happens to the tendency to the
best that has to animate every part of the world or monad inasmuch as it
animates God's choice for the totality of the world or of monads? And yet
no one has pondered morality — a very concrete morality — more than
Leibniz himself. The amplitude of a reasonable soul is the region that it
clearly expresses, that is, its living present. This amplitude is rather
statistical, and subject to broad variation: the same soul does not have the
same amplitude as a child, an adult, or an aging being, in good or bad
health, and so on. Amplitude even has variable limits at any given
moment. Morality consists in this for each individual: to attempt each
time to extend its region of clear expression, to try to augment its
amplitude, so as to produce a free act that expresses the most possible in
one given condition or another.
That is what progress is called, and all Leibniz's morality is a morality
of progress. For example, when I go to the nightclub, have I chosen the
side where amplitude is maximal, the side where my region goes the
furthest, even if I were unable to wait a second, with time enough to
discover another means or direction that would have inclined me
83
THE FOLD
otherwise? Does Adam's sin not correspond to a soul, too pressed or too
lazy, that has not explored everything in its subdivision or its garden?
Extending its clear region, prolonging God's passage to the maximum,
actualizing all the singularities that are concentrated on, and even won
over to, new singularities would amount to a soul's progress. In this way
we might say that it imitates God. Of course it is not only a conquest or
extension that matters, but an amplification, an intensification of an
elevation of power, a growth in dimensions, and a gain in distinction.
However, this possibility for progress or expansion of the soul seems to
run up against the total quantity of progress in the world, this quantity
being defined by the convergence of all regions that correspond to
compossible monads. 36 And this would be true if time did not pertain,
that is, if all existing monads were simultaneously summoned to the
altitude that makes them reasonable. But things do not work that way:
souls fated to become reasonable wait for their time in the world, and are
first of all only sensitive souls who sleep in Adam's seed, bearing only an
'official act' that marks the hour of their future elevation as on to a birth
certificate. This birth certificate or act is a flame lit within the dark monad.
And inversely, when we die, we fold infinitely upon ourselves; we return
to the state of an animal until the bodily resurrection brings us to a
second and final elevation. But further, the soul, which has for some time
become sensitive again, will bring with it a new and official act, now akin
to an act or certification of death, which is its last reasonable thought
prior to death. More precisely, the damned are those whose last thought
is a scorn of God because, when their soul vomits all and can no longer
enclose clearly anything other than this hate or this rage, it is the
maximum of all possible hate or the smallest amplitude of reason.
Resurrection still brings them to this thought from which they forge their
new present. 37 This order of time must be considered in all questions of
progress: a whole dramaturgy of souls, which makes them rise, descend,
and rise again.
In all cases it is true that the world only exists folded in the monads
that express it, and is only unfolded virtually as the common horizon of
all monads, or as the outer law of the series they include. But in a more
restricted sense, in an intrinsic way, it can be said that when a monad is
summoned to 'live' — yet more when it is called to reason — it unfolds in
itself this region of the world that corresponds to its enclosed enlightened
zone: it is called upon to 'develop all its perceptions,' and therein its task
resides. Then, at the same time, an infinity of monads has not yet been
84
INCOMPOSSIBILITY, INDIVIDUALITY, LIBERTY
called and remains folded; another infinity of them has fallen or falls in
the night, folded onto themselves; while another infinity has been
damned, hardened in a single fold that it will not unfurl. It is due to these
three involutions that a soul-monad can amplify and deepen the region
that it unfolds during the course of its reasonable life; it can bring it to the
region of the highest degree of evolution, of development, of distinction,
and reflection: an infinite progress of the conscience that exceeds the
statistical variations of which we were speaking not long ago. It has often
been said that this progress of a soul could only be accomplished to the
detriment of others. But this is not true. Except for the damned others
can do just as much. It is only to the detriment of the damned, who are
freely cut away. Their worst punishment may be that of serving the
progress of others, not by the negative example that they offer, but
through the quantity of positive progress that they involuntarily leave to
the world when they renounce their own clarity. In this sense, despite
themselves, the damned could be attached in no better way to the best of
all possible worlds.
Leibniz's optimism is based on the infinity of the damned as the
foundation of the best of all worlds: they liberate an infinite quantity of
possible progress. That is what multiplies their rage, and thus they make
possible a world of progress. We could never think of the best of all worlds
without hearing the scornful shrieks of Beelzebub make the lower level
tremble. The Baroque house divides its two floors between the world of
the damned and that of the saved, in the fashion of Tintoretto's Last
Judgment. There again God does not determine the total quantity of
progress either beforehand or afterwards, but eternally, in the calculus of
the infinite series that moves through all increased magnitudes of
consciousness and all the subtractions of the damned. 38
85
WHAT IS AN EVENT?
6
What is an event?
Whitehead is the successor, or diadoche, as the Platonic philosophers used
to say, of the school's leader.' The school is somewhat like a secret
society. With Whitehead's name there comes for the third time an echo of
the question, W hat is an event? 2 He takes up the radical critique of the
attributive scheme, the great play of principles, the multiplications of
categories, the conciliation of the universal and the individual example,
and the transformation of the concept into a subject: an entire hubris. He
stands provisionally as the last great Anglo-American philosopher before
Wittgenstein's disciples spread their misty confusion, sufficiency, and
tenor. An event does not just mean that 'a man has been run over.' The
Great pyramid is an event, and its duration for a period of one hour, thirty
minutes, five minutes ..., a passage of Nature, of God, or a view of God.
What are the conditions that make an event possible? Events are
produced in a chaos, in a chaotic multiplicity, but only under the
condition that a sort of screen intervenes.
Chaos does not exist; it is an abstraction because it is inseparable from
a screen that makes something — something rather than nothing — emerge
from it. Chaos would be a pure Many, a purely disjunctive diversity, while
the something is a One, not a pregiven unity, but instead the indefinite
article that designates a certain singularity. How can the Many become
the One? A great screen has to be placed in between them. Like a formless
elastic membrane, an electromagnetic field, or the receptacle of the
Timaeus, the screen makes something issue from chaos, and even if this
something differs only slightly. In this way Leibniz had long been able to
ascribe several approximations to chaos. According to a cosmological
86
approximation, chaos would be the sum of all possibles, that is, all
individual essences insofar as each tends to existence on its own account;
but the screen only allows compossibles — and only the best combination
of compossibles — to be sifted through.
Following a physical approximation, chaos would amount to depthless
shadows, but the screen disengages its dark backdrop, the 'fuscum
subnigrum' that, however little it differs from black, nonetheless contains
all colors: the screen is like the infinitely refined machine that is the basis
of Nature. From a psychic point of view, chaos would be a universal
giddiness, the sum of all possible perceptions being infinitesimal or
infinitely minute; but the screen would extract differentials that could be
integrated in ordered perceptions. 3 If chaos does not exist, it is because it
is merely the bottom side of the great screen, and because the latter
composes infinite series of wholes and parts, which appear chaotic to us
(as aleatory developments) only because we are incapable of following
them, or because of the insufficiency of our own screens.' Even the
cavern is not a chaos, but a series whose elements remain caverns filled
with an increasingly rarefied matter, each of which is extended over the
following ones.
That is clearly the first component or condition of both Whitehead's and
Leibniz's definition of the event: extension. Extension exists when one
element is stretched over the following ones, such that it is a whole and
the following elements are its parts. Such a connection of whole-parts
forms an infinite series that contains neither a final term nor a limit (the
limits of our senses being excepted). The event is a vibration with an
infinity of harmonics or submultiples, such as an audible wave, a
luminous wave, or even an increasingly smaller part of space over the
course of an increasingly shorter duration. For space and time are not
limits but abstract coordinates of all series, that are themselves in
extension: the minute, the second, the tenth of a second. ... Then we can
consider a second component of the event: extensive series have intrinsic
properties (for example, height, intensity, timbre of a sound, a tint, a
value, a saturation of color), which enter on their own account in new
infinite series, now converging toward limits, with the relation among
limits establishing a conjunction. Matter, or what fills space and time,
offers characters that always determine its texture as a function of
different materials that are part of it. No longer are these extensions but,
as we have seen, intensions, intensities, or degrees. It is something rather
87
THE FOLD
than nothing, but also this rather than that: no longer the indefinite
article, but the demonstrative pronoun. How remarkable that Whitehead's analysis, based on mathematics and physics, appears to be
completely independent of Leibniz's work even though it coincides with
it!
Then comes the third component, which is the individual. There the
confrontation with Leibniz is the most direct. For Whitehead the
individual is creativity, the formation of a New. No longer is it the
indefinite or the demonstrative mood, but a personal mood. If we call an
element everything that has parts and is a part, but also what has intrinsic
features, we say that the individual is a 'concrescence' of elements. This is
something other than a connection or a conjunction. It is, rather, a
prehension: an element is the given, the 'datum' of another element that
prehends it. Prehension is individual unity. Everything prehends its
antecedents and its concomitants and, by degrees, prehends a world. The
eye is a prehension of light. Living beings prehend water, soil, carbon,
and salts. At a given moment the pyramid prehends Napoleon's soldiers
(forty centuries are contemplating us), and inversely. We can say that
'echoes, reflections, traces, prismatic deformations, perspective, thresholds, folds' are prehensions that somehow anticipate psychic life. 5 The
vector of prehension moves from the world to the subject, from the
prehended datum to the prehending one (a 'superject'); thus the data of a
prehension are public elements, while the subject is the intimate or private
element that expresses immediacy, individuality, and novelty. 6 But the
prehended, the datum, is itself a preexisting or coexisting prehension,
such that all prehension is a prehension of prehension, and the event
thus a 'nexus of prehensions.' Each new prehension becomes a datum. It
becomes public, but for other prehensions that objectify it; the event is
inseparably the objectification of one prehension and the subjectification
of another; it is at once public and private, potential and real,
participating in the becoming of another event and the subject of its
own becoming.
Beyond the prehending and the prehended, prehension offers three other
characteristics. First, the subjective form is the way by which the datum is
expressed in the subject, or by which the subject actively prehends the
datum (emotion, evaluation, project, conscience ...). It is the form in
which the datum is folded in the subject, a 'feeling' or manner, at least
when prehension is positive. For there are negative prehensions that exist
88
WHAT IS AN EVENT?
as long as the subject excludes certain data from its concrescence, and is
thus only filled by the subjective form of this exclusion. Second, the
subjective aim assures the passage from one datum to another in a
prehension, or from one prehension to another in a becoming, and places
the past in a present portending the future. Finally, satisfaction as a final
phase, as self-enjoyment, marks the way by which the subject is filled with
itself and attains a richer and richer private life, when prehension is filled
with its own data. This is a biblical — and, too, a neo-Platonic — notion that
English empiricism carried to its highest degree (notably with Samuel
Butler). The plant sings of the glory of God, and while being filled all the
more with itself it contemplates and intensely contracts the elements
whence it proceeds. It feels in this prehension the self-enjoyment of its own
becoming.
These traits of prehension also belong to Leibniz's monad. And,
initially, perception is the datum of the prehending subject, not in the
sense that the latter would undergo a passive effect, but, on the contrary,
to the degree it fulfills a potential or objectifies it by virtue of its
spontaneity: thus perception is the active expression of the monad, as a
function of its own point of view.' But the monad has several forms of
active expression that make up its ways or manners, according to the
ways in which its perceptions are sensitive, active, or conceptual. 8 In this
sense appetite designates the movement from one perception to another
as being constitutive of a becoming Finally, this becoming is not
completed without the sum of perceptions tending to be integrated in a
great pleasure, a Satisfaction with which the monad fills itself when it
expresses the world, a musical Joy of contracting its vibrations, of
calculating them without knowing their harmonics or of drawing force
enough to go further and further ahead in order to produce something
new. 9 For with Leibniz the question surges forth in philosophy that will
continue to haunt Whitehead and Bergson: not how to attain eternity,
but in what conditions does the objective world allow for a subjective
production of novelty, that is, of creation? The best of all worlds had no
other meaning: it was neither the least abominable nor the least ugly, but
the one whose All granted a production of novelty, a liberation of true
quanta of 'private' subjectivity, even at the cost of the removal of the
damned. The best of all worlds is not the one that reproduces the eternal,
but the one in which new creations are produced, the one endowed with
a capacity for innovation or creativity: a teleological conversion of
philosophy. 1°
89
THE FOLD
There are no fewer eternal Objects. It is even the fourth and last
component of Whitehead's definition of the event: extensions, intensities, individuals or prehensions, and, finally, eternal objects or 'ingressions.' Extensions effectively are forever moving, gaining and losing parts
carried away in movement; things are endlessly being altered; even
prehensions are ceaselessly entering and leaving variable components.
Events are fluvia. From then on what allows us to ask, 'Is it the same
flow, the same thing or the same occasion? It's the Great pyramid ...' A
permanence has to be born in flux, and must be grasped in prehension.
The Great Pyramid signifies two things: a passage of Nature or a flux
constantly gaining and losing molecules, but also an eternal object that
remains the same over the succession of moments." While prehensions
are always current forms (a prehension is a potential only in respect to
another current prehension), eternal objects are pure Possibilities that are
realized in fluvia, but also pure Virtualities that are actualized in
prehensions. That is why a prehension does not grasp other prehensions
without apprehending eternal objects (properly, conceptual feeling).
Eternal objects produce ingression in the event. Sometimes these can
be Qualities, such as a color or a sound that qualifies a combination of
prehensions; sometimes Figures, like the pyramid, that determine an
extension; sometimes they are Things, like gold or marble, that cut
through a matter. Their eternity is not opposed to creativity. Inseparable
from the process of actualization or realization into which they enter,
they gain permanence only in the limits of the flux that creates them, or
of the prehensions that actualize them. An eternal object can thus cease
becoming incarnate, just as new things — a new shade of color, or a new
figure — can finally find their conditions.
With Leibniz the situation hardly differs. For if monads or simple
substances are always current forms, they not only arch back to
virtualities that they actualize in themselves, as innate ideas demonstrate,
but yet again to possibilities that are realized in composite substances
(thus perceived qualities), or in aggregate materials (things), or in
extended phenomena (figures). Everything flows down below, 'in a
perpetual flux, with bits and pieces continually entering and exiting: 1 '
From that moment permanency is not reduced to monads that actualize
the virtual, but is extended to the possibilities that they seize in their acts
of reflection, and that are born in the extended composite materials.
Reflexive objects are correlative to reasonable monads, just as in
Whitehead, where eternal objects are correlative to thinking prehensions.
90
WHAT IS AN EVENT?
Figures, things, and qualities are schema of permanence that are reflected
or actualized in monads, but that are realized in flux; even composite
substances, as we shall observe, need an ultimate quality that marks
every one of them.
A concert is being performed tonight. It is the event. Vibrations of sound
disperse, periodic movements go through space with their harmonics or
submultiples. The sounds have inner qualities of height, intensity, and
timbre. The sources of the sounds, instrumental or vocal, are not content
only to send the sounds out: each one perceives its own, and perceives
the others while perceiving its own. These are active perceptions that are
expressed among each other, or else prehensions that are prehending one
another: 'First the solitary piano grieved, like a bird abandoned by its
mate; the violin heard its wail and responded to it like a neighboring tree.
It was like the beginning of the world. ...'
The origins of the sounds are monads or prehensions that are filled
with joy in themselves, with an intense satisfaction, as they fill up with
their perceptions and move from one perception to another. And the
notes of the scale are eternal objects, pure Virtualities that are actualized
in the origins, but also pure Possibilities that are attained in vibrations or
flux. 'As if the instrumentalists played the little phrase far less than they
were performing the rites it required in order to appear ...' But then, in
the midst of this totality, Leibniz adds the conditions of a Baroque
concert. If we suppose that the concert is divided into two sources of
sound, we are positing that each hears only its own perceptions but is
harmonized with those of the other even better than if it had perceived
them, because of the vertical rules of harmony that happen to be
enveloped in their respective spontaneity. These are the harmonies that
replace horizontal connections.' 3
There is a great difference that depends on Leibniz's Baroque
condition. For Whitehead it involves prehensions being directly connected to each other, either because they draw on others for data and
form a world with them, or because they exclude others (negative
prehensions), but always in the same universe in process. For Leibniz, to
the contrary, monads exclude only universes that are incompossible with
their world, and all those that exist express the same world without
exclusion. As this world does not exist outside of the monads that express
it, the latter are not in contact and have no horizontal relations among
them, no intraworldly connections, but only an indirect harmonic
91
THE FOLD
contact to the extent they share the same expression: they 'express one
another' without harnessing each other. We might say that in the two
instances monadic or prehensive units have neither doors nor windows.
But for Leibniz, it is because the monads' being-for the world is submitted
to a condition of closure, all compossible monads including a single and
same world. Now for Whitehead, to the contrary, a condition of opening
causes all prehension to be already the prehension of another prehension,
either to control it or to exclude it. Prehension is naturally open, open
onto the world, without having to pass through a window." A difference
of this kind must surely have a reason.
For Leibniz, as we have seen, bifurcations and divergences of series are
genuine borders between incompossible worlds, such that the monads
that exist wholly include the compossible world that moves into
existence. For Whitehead (and for many modern philosophers), on the
contrary, bifurcations, divergences, incompossibilities, and discord belong
to the same motley world that can no longer be included in expressive units,
but only made or undone according to prehensive units and variable
configurations or changing captures. In a same chaotic world divergent
series are endlessly tracing bifurcating paths. It is a 'chaosmos' of the type
found in Joyce, but also in Maurice Leblanc, Borges, or Gombrowicz. 15
Even God desists from being a Being who compares worlds and chooses
the richest compossible. He becomes Process, a process that at once
affirms incompossibilities and passes through them. The play of the world
has changed in a unique way, because now it has become the play that
diverges. Beings are pushed apart, kept open through divergent series and
incompossible totalities that pull them outside, instead of being closed
upon the compossible and convergent world that they express from
within. Modern mathematics has been able to develop a fibered
conception according to which 'monads' test the paths in the universe
and enter in syntheses associated with each path. 16 It is a world of
captures instead of closures.
WHAT IS AN EVENT?
dissonances are between different worlds. In short, the Baroque universe
witnesses the blurring of its melodic lines, but what it appears to lose it
also regains in and through harmony. Confronted by the power of
dissonance, it discovers a florescence of extraordinary accords, at a
distance, that are resolved in a chosen world, even at the cost of
damnation.
This reconstitution could only be temporary. With the neo-Baroque,
with its unfurling of divergent series in the same world, comes the
irruption of incompossibilities on the same stage, where Sextus will rape
and not rape Lucretia, where Caesar crosses and does not cross the
Rubicon, where Fang kills, is killed, and neither kills nor is killed. In its
turn harmony goes through a crisis that leads to a broadened chromatic
scale, to an emancipation of dissonance or of unresolved accords, accords
not brought back to a tonality. The musical model is the most apt to make
clear the rise of harmony in the Baroque, and then the dissipation of
tonality in the neo-Baroque: from harmonic closure to an opening onto a
polytonality or, as Boulez will say, a 'polyphony of polyphonies.'
We can better understand in what way the Baroque is a transition.
Classical reason toppled under the force of divergences, incompossibilities, discords, dissonances. But the Baroque represents the ultimate
attempt to reconstitute a classical reason by dividing divergences into as
many worlds as possible, and by making from incompossibilities as many
possible borders between worlds. Discords that spring up in a same world
can be violent. They are resolved in accords because the only irreducible
92
93
Part III
HAVING A BODY
7
Perception in the folds
I must have a body, it's a moral necessity, a 'requirement.' And in the first
place, I must have a body because an obscure object lives in me. But, right
from this first argument, Leibniz's originality is tremendous. He is not
saying that only the body explains what is obscure in the mind. To the
contrary, the mind is obscure, the depths of the mind are dark, and this
dark nature is what explains and requires a body. We can call 'primary
matter' our passive power or the limitation of our activity: we say that our
primary matter requires extension, but also resistance or antitype, and yet
an individuated requirement to possess a body that belongs to us.' It is
because there is an infinity of individual monads that each one requires
an individuated body, this body resembling the shadow of other monads
cast upon it. Nothing obscure lives in us because we have a body, but we
must have a body because there is an obscure object in us. In the place of
Cartesian physical induction Leibniz substitutes a moral deduction of the
body.
But this first argument gives way to another, which seems to contradict
it, and which is even more original. This time, we must have a body
because our mind possesses a favored - clear and distinct - zone of
expression. Now it is the clear zone that is the requirement for having a
body. Leibniz will go as far as stating that what I express clearly is what
'relates to my body.' 2 And in effect, if the monad Caesar clearly expresses
the crossing of the Rubicon, is it not because the river maintains a relation
of proximity with his body? The same holds for all other monads whose
zone of clear expression coincides with the body's immediate environment.
There we nonetheless find an inversion of causality - justifiable in
97
THE FOLD
certain respects — that must not impede our putting together the real
order of deduction: (1) each monad condenses a certain number of
unique, incorporeal, ideal events that do not yet put bodies in play,
although they can only be stated in the form, 'Caesar crosses the Rubicon,
he is assassinated by Brutus ...'; (2) these unique events included in the
monad as primary predicates constitute its zone of clear expression, or its
'subdivision'; (3) they necessarily relate to a body that belongs to this
monad, and are incarnated in bodies that act immediately upon it. In
brief, it is because every monad possesses a clear zone that it must have a
body, this zone constituting a relation with the body, not a given relation,
but a genetic relation that engenders its own 'relatum.' It is because we
have a clear zone that we must have a body charged with traveling
through it or exploring it, from birth to death.
Here we confront two difficulties. Why is the requirement of having a
body sometimes based on a principle of passivity, in obscurity and
confusion, but at others on our activity, on clarity and distinction? And
more particularly, how does the existence of the body derive from the
clear and distinct? As Arnauld states, how can what I express clearly and
distinctly have anything to do with my body, the sum of whose
movements are known only in obscurity? 3
Singularities proper to each monad are extended as far as the
singularities of others and in all senses. Every monad thus expresses
the entire world, but obscurely and dimly because it is finite and the
world is infinite. That is why the lower depths of the monad are so dark.
Since it does not exist outside of the monads that convey it, the world is
included in each one in the form of perceptions or 'representatives,'
present and infinitely minute elements. 4 Still again, since the monad does not
exist outside of other monads, these are minute perceptions lacking an
object, that is, hallucinatory microperceptions. The world exists only in its
representatives as long as they are included in each monad. It is a lapping
of waves, a rumor, a fog, or a mass of dancing particles of dust. It is a state
of death or catalepsy, of sleep, drowsiness, or of numbness. It is as if the
depths of every monad were made from an infinity of tiny folds
(inflections) endlessly furling and unfurling in every direction, so that the
monad's spontaneity resembles that of agitated sleepers who twist and
turn on their mattresses. 3
PERCEPTION IN THE FOLDS
one of Hantars paintings, or one of Clerambault's toxic hallucinations. 6
And these are minute, obscure, confused perceptions that make up our
macroperceptions, our conscious, clear, and distinct apperceptions. Had it
failed to bring together an infinite sum of minute perceptions that
destabilize the preceding macroperception while preparing the following
one, a conscious perception would never happen. How could a pain
follow a pleasure if a thousand tiny pains or, rather, half-pains were not
already dispersed in pleasure, which will then be united in conscious
pain? However abruptly I may flog my dog who eats his meal, the animal
will have experienced the minute perceptions of my stealthy arrival on
tiptoes, my hostile odor, and my lifting of the rod that subtend the
conversion of pleasure into pain. How could a feeling of hunger follow
one of satisfaction if a thousand tiny, elementary forms of hunger (for
salts, for sugar, butter, etc.) were not released at diverse and indiscernible
rhythms? And inversely, if satisfaction follows hunger, it is through the
sating of all these particular and imperceptible hungers.
Tiny perceptions are as much the passage from one perception to
another as they are components of each perception. They constitute the
animal or animated state par excellence: disquiet. These are 'pricklings,'
or little foldings that are no less present in pleasure than in pain. The
pricklings are the representative of the world in the closed monad. The
animal that anxiously looks about, or the soul that watches out, signifies
that there exist minute perceptions that are not integrated into present
perception, but also minute perceptions that are not integrated into the
preceding one and that nourish the one that comes along ('so it was
that!').
The macroscopic distinguishes perceptions, and appetites that are the
passage from one perception to another. Such is the condition of great
composite folds, or draped forms. But the microscopic level no longer
distinguishes minute perceptions and minute inclinations: pricklings of
anxiety render all perception unstable.' The theory of minute perceptions
is based thus on two causes: a metaphysical cause, according to which
every perceptive monad conveys an infinite world that it contains; a
psychological cause, according to which every conscious perception
implies this infinity of minute perceptions that prepare, compose, or
follow it. From the cosmological to the microscopic. but also from the microscopic
to the macroscopic.
Microperceptions or representatives of the world are these little folds that
unravel in every direction, folds in folds, over folds, following folds, like
98
The task of perception entails pulverizing the world, but also one of
spiritualizing its dust. 8 The point is one of knowing how we move from
99
PERCEPTION IN THE FOLDS
THE FOLD
minute perceptions to conscious perceptions, or from molecular perceptions to molar perceptions. Is it through a process of totalization, when for
instance I grasp a whole whose parts are imperceptible to me? Thus I
apprehend the sound of the sea, or of an assembly of people, but not the
murmur of each wave or person who nonetheless is part of each whole.
But, although Leibniz states the point in terms of totality, the question
involves something other than a sum of homogenous parts. 9 We are not
dealing with a relation of parts-and-wholes because the totality can be as
imperceptible as the parts, as also when I do not sense the grinding noise
of the water mill to which I am overly accustomed. And a buzzing or a
deadening effect are wholes without necessarily being perceptions.
In truth, Leibniz never fails to specify that the relation of the
inconspicuous perceptions to conscious perception does not go from part
to whole, but from the ordinary to what is notable or remarkable. 'There are
countless inconspicuous perceptions, which do not stand out enough for
one to be aware of or to remember them.' I° We have to understand
literally - that is, mathematically - that a conscious perception is
produced when at least two heterogenous parts enter into a differential
relation that determines a singularity. It works thus in the equation of
circumferences in general:
ydy + xdx = 0, or dy
a=
x
y
- -
expresses a determinable magnitude. For example, the color green:
yellow and blue can surely be perceived, but if their perception vanishes
by dint of progressive diminution, they enter into a differential relation
db
(—)
dy
that determines green. And nothing impedes either yellow or blue, each
on its own account, from being already determined by the differential
relation of two colors that we cannot detect, or of two degrees of
chiaroscuro:
dy
dx
100
y
Such is the case of hunger, where a lack of sugar, butter, etc., engages
differential relations that determine hunger as something notable or
remarkable. For example, the sound of the sea: at least two waves must
be minutely perceived as nascent and heterogenous enough to become
part of a relation that can allow the perception of a third, one that 'excels'
over the others and comes to consciousness (implying that we are near
the shoreline). For example, the position of the sleeper: all the little bends
and tiny creases engage relations that produce an attitude, a habitus, and
a great sinuous fold as a good position that can bring all of them together.
'Good' macroscopic form always depends on microscopic processes.
All consciousness is a matter of threshold. In each case we would
probably have to state why the threshold is marked where it is. Yet if we
take thresholds to be so many minimal units of consciousness, tiny
perceptions are in each instance smaller than the virtual minimum and,
in this sense, are infinitely small. The ones selected in each order are those
engaged in differential relations, and hence they produce the quality that
issues forth at the given threshold of consciousness (for example, the
color green). Inconspicuous perceptions are thus not parts of conscious
perception, but requisites or genetic elements, 'differentials of consciousness.' Even more than Fichte, Salomon Maimon - the first post-Kantian
who returns to Leibniz - draws all the consequences from this kind of
psychic automatism of perception. Far from having perception presuppose an object capable of affecting us, and conditions in which we would
be apt to be affected, the reciprocal determination of the differentials
(
dy
)
dx
brings about the complete determination of the object as a perception,
and the determinability of space-time as a condition. Beyond the Kantian
method of conditioning, Maimon restores an internal subjective method
of genesis: between red and green there is given an empirically outer
difference, but also an inner concept of difference such that 'the mode of
the differential makes up the particular object, and the relations of
differentials the relations among different objects."' The physical object
and mathematical space both refer to a transcendental (differential and
genetic) psychology of perception. Space-time ceases to be a pure given in
order to become the totality or the nexus of differential relations in the
101
THE FOLD
subject, and the object itself ceases to be an empirical given in order to
become the product of these relations in conscious perception. Thus there
exist Ideas of understanding, the color green as a quality being as much
the actualization of an eternal Object or Idea in the subject as a given
figure is a determination of space.
If, with Kant, it is objected that such a conception reintroduces infinite
understanding, we might be impelled to remark that the infinite is taken
here only as the presence of an unconscious in finite understanding, of
something that cannot be thought in finite thought, of a nonself in the
finite self, the presence that Kant will himself be forced to discover when
he will hollow out the difference between a determinant and a
determinable self. For Malmon, as for Leibniz, reciprocal determination
of differentials does not refer to a divine understanding, but to tiny
perceptions as representatives of the world in the finite self (the relation
with infinite understanding devolves from it, and not the inverse). The
infinite present in the finite self is exactly the position of Baroque
equilibrium or disequilibrium.
Now we can understand how the same argument can appeal to both
obscurity and clarity. It is because for Leibniz clarity comes of obscurity
and endlessly is plunging back into it. Thus the Cartesian map of
darkness-clarity-confusion-distinction is redrawn with an entirely new
meaning and new set of relations. Inconspicuous perceptions constitute
the obscure dust of the world, the dark depths every monad contains.
There are differential relations among these presently infinitely small
ones that are drawn into clarity; that is to say, that establish a clear
perception (the color green) with certain tiny, dark, evanescent
perceptions (the colors yellow and blue). And no doubt yellow and blue
can themselves be clear and conscious perceptions, but only if they too
are drawn into clarity, each from its own position, by differential relations
among other minute perceptions, or differentials of other orders.
Differential relations always select minute perceptions that play a role in each
case, and bring to light or clarify the conscious perception that comes
forth. Thus differential calculus is the psychic mechanism of perception,
the automatism that at once and inseparably plunges into obscurity and
determines clarity: a selection of minute, obscure perceptions and a
perception that moves into clarity.
An automatism of this kind has to be taken in two ways, universally
and individually. On the one hand, insofar as the same world is included
102
I
PERCEPTION IN THE FOLDS
in all existing monads, the latter offer the same infinity of minute
perceptions, and the same differential relations that yield in them
strangely similar conscious perceptions. All monads thus perceive the
same green color, the same note, the same river, and in every case a
single and same eternal object is actualized in them. Yet, on the other
hand, actualization is different for each monad. Never do two monads
perceive the same green in the same degree of chiaroscuro. It could be
said that every monad favors certain differential relations that hereafter
confer on it exclusive perceptions; that the monad leaves other relations
below the necessary degree; or, further, that it lets an infinity of minute
perceptions subsist in it without at all assuming relations. At the limit,
then, all monads possess an infinity of compossible minute perceptions,
but have differential relations that will select certain ones in order to yield
clear perceptions proper to each. In this way every monad, as we have
seen, expresses the same world as the others, but nonetheless owns an
exclusive zone of clear expression that is distinguished from every other
monad: its subdivision.
These subdivisions appear even if we adhere to orders of clarity and
distinction in Leibniz's classification of ideas. Contrary to Descartes,
Leibniz begins in darkness. Clarity emerges from obscurity by way of a
genetic process, and so too clarity plunges into darkness, and continues to
plunge deeper and deeper: it is natural chiaroscuro, a development out of
obscurity, and it is more or less clear to the degree that sensibility reveals it
as such.' 2 Thus the preceding paradox is resolved: even if we grant that
the same differential relations are established in all monads, not all of
them will attain the same level of clarity, required by conscious
perception in conformity with its threshold.
And, above all, we can clear up the two difficulties encountered at the
beginning, that is, that the same requirement appeals now and again to
obscurity and to clarity, and that clarity itself depends on what is only
fathomed obscurely. For clarity has to emerge out of darkness, as if
through a first filter that would be followed by many other filters, for
what is distinct, what is confused, and so on.' 3 In effect, differential
relations indeed fill the role of a filter — and already of an infinity of filters
— since they let through only minute perceptions that in each instance
can furnish a relatively clear perception. But, because filters change their
nature at each level, we must admit that clarity is relatively obscure and
absolutely confused, just as what is distinct remains relatively confused
and absolutely inadequate. What then is the implication of the Cartesian
103
THE FOLD
PERCEPTION IN THE FOLDS
expression 'clear and distinct,' which Leibniz nonetheless retains? How
can he say that the privileged zone of every monad is not only clear but
also distinct, all the while it consists of a confused event? It is because
clear perception as such is never distinct.
Rather, it is 'distinguished,' in the sense of being remarkable or
notable. It is decisive in respect to other perceptions, and the first filter is
obviously applied to ordinary perceptions in order to extract from them
whatever is remarkable (clear and distinguished). 14 But, strictly speaking,
the distinct presupposes another filter that assumes the remarkable to be
regular, and from it extracts singularities. These are the inner singularities
of the idea or of the distinct perception. Must a third filter be imagined, of
the adequate or even of the complete, that draws the ordinary out of the
singular, in a manner that the organization of filters would constitute a
circular system, although this last filter exceeds our power of imagination? The totality would allow us to utter in the same breath, like
Balthazar, 'Everything is ordinary!' and 'Everything is unique!'
The development of the theory of the idea pertains less here than the
different meanings of the singular. We have encountered three of its
meanings: singularity is above all (1) inflection, the point of inflection
that is extended up to the neighborhood of other singularities, thus
tracing the lines of the universe mapped according to relations of
distance; and then (2) it is the axis of the curve from the concave side
insofar as the monad's point of view is defined according to relations of
perspective; finally, (3) it is what is remarkable, according to differential
relations that in the monad are constituting perception. We shall observe
that a fourth kind of singularity can be added, one that makes up
maximal and minimal 'extrema' in matter or extension. Already, in the
deepest Baroque regions, and in the deepest Baroque knowledge of the
world, this subordination of the true to what is singular and remarkable is
being made manifest.
Now we can return to perception. All monads express the whole world
darkly, even if not in the same order. Each one encloses in itself the
infinity of minute perceptions. They cannot be distinguished by weakness
or strength. What distinguishes them is their zone of clear, remarkable, or
privileged expression. Ultimately, 'totally naked monads' (lacking this
zone of light) might be conceived. They would live in darkness or neardarkness, in the vertigo and giddiness of minute and dark perceptions. No
differential mechanism of reciprocal determination would come to select
a few of these tiny perceptions in order to extract a clear perception. They
would have nothing remarkable about them.
A limit-condition of this kind is present only in death; everywhere else
it is merely an abstraction." The tiniest of all animals has glimmers that
cause it to recognize its food, its enemies, and sometimes its partner. If life
implies a soul, it is because proteins already attest to an activity of
perception, discrimination, and distinction — in short, a 'primary force'
that physical impulsions and chemical affinities cannot explain ('derivative forces'). Thus there can be no reactions ensuing from excitations, but
from outer organic actions that in the soul are proof of an inner
perceptive activity. If life has a soul, it is because it perceives,
distinguishes, or discriminates, and because a whole world of animal
psychology is first of all a psychology of perception. In most cases, the soul
gets along quite well with very few clear or distinguished perceptions: the
soul of the tick has three, including a perception of light, an olfactory
perception of its prey, and a tactile perception of the best place to burrow,
while everything else in the great expanse of Nature, which the tick
nevertheless conveys, is only a numbness, a dust of tiny, dark, and
scattered perceptions."
But if an animal scale exists, or an 'evolution' in the animal series, it is
insofar as increasingly numerous differential relations of a deepening
order are determining a zone of clear expression that is both more
extensive and increasingly hermetic. Each of the conscious perceptions
that comprise the zone is associated with others in the infinite process of
reciprocal determination. These are remembering monads. And furthermore, certain monads are endowed with the power of extending
themselves and intensifying their zones, of attaining a real connection
of their conscious perceptions (and not a simple associative consecution),
and of surpassing clarity with what is distinctive and even with what is
adequate: reasonable or reflexive monads, to be sure, find their condition of
self-development in the sacrifice of certain ones among them — the
Damned — that regress to the state of almost naked monads, their only
single and clear perception being their hatred of God.
Whence the possibility for an admittedly summary classification of
monads as functions of their perceptive qualities: there are almost naked
monads, remembering monads, and reflexive or reasonable monads. 17
Fechner, another of the great disciples of Leibniz, and the founder of a
psychophysics inseparable from the spiritual mechanisms of the monadic
104
105
PERCEPTION IN THE FOLDS
THE FOLD
soul, does not hesitate to develop classifications endlessly, from vertigo or
dizziness to luminous life. In them he envisions the three ages of man,
with all their possibilities of regression and damnation, through which
Fechner himself passes as a monad, reduced to his dark room or his
somber depths, turned over to the digestive swarm of tiny perceptions,
but also to the force of a resurrection, to an ascendant surge of intense
and expansive light. I8 Few monads fail to believe themselves damned at
certain moments of their existence. When their clear perceptions are now
and again extinguished, when they recede into the night — in relation to
this the tick's life appears to be singularly rich. But with freedom there
also comes the moment when a soul is won over to itself and can whisper
with a convalescent's astonishment, 'My God, what did I do in all of these
years?'
If the differential mechanisms of our clear perceptions are checked,
then the minute perceptions force selection and invade consciousness, as
in drowsiness or in giddiness. A dust of colored perceptions falls on a
black backdrop; yet, if we look closely, these are not atoms, but
minuscule folds that are endlessly unfurling and bending on the edges
of juxtaposed areas, like a mist or fog that makes their surface sparkle, at
speeds that no one of our thresholds of consciousness could sustain in a
normal state. But when our clear perceptions are reformed, they draw yet
another fold that now separates the conscious from the unconscious, that
joins the tiny edges of surface to a great area, that moderates the different
speeds, and rejects all kinds of minute perceptions in order to make from
all the others the solid fabric of apperception: dust falls, and I see the great
fold of figures just as the background is unfurling its tiny folds.
Fold over folds: such is the status of the two modes of perception, or of
microscopic and macroscopic processes. That is why the unfolded surface
is never the opposite of the fold, but rather the movement that goes from
some to the others. Unfolding sometimes means that I am developing —
that I am undoing — infinite tiny folds that are forever agitating the
background, with the goal of drawing a great fold on the side whence
forms appear; it is the operation of a vigil: I project the world 'on the
surface of a folding 19 At other times, on the contrary, I undo the folds
of consciousness that pass through every one of my thresholds, the
'twenty-two folds' that surround me and separate me from the deep, in
order to unveil in a single movement this unfathomable depth of tiny and
moving folds that waft me along at excessive speeds in the operation of
vertigo, like the 'enraged charioteer's whiplash ...' 20 I am forever
unfolding between two folds, and if to perceive means to unfold, then I
am forever perceiving within the folds.
Every perception is hallucinatory because perception has no object. Conscious
perception has no object and does not even refer to a physical mechanism
of excitation that could explain it from without: it refers only to the
exclusively physical mechanism of differential relations among unconscious perceptions that are comprising it within the monad. 21 And
unconscious perceptions have no object and do not refer to physical
things. They are only related to the cosmological and metaphysical
mechanism according to which the world does not exist outside of the
monads that are conveying it. The mechanism is thus inevitably folded in
the monads, with unconscious perceptions comprising these minute folds
as the representatives of the world (and not representations of objects).
The idea of hallucinatory perception has clearly undergone a slow
degradation in psychology; but because it overlooked the properly
Leibnizian conditions: that is, the double — microscopic and macroscopic
— circuit, the being-for the world of unconscious or minute perceptions,
and the differential relations that hold for conscious perceptions.
Hallucination is always duplicitous, somewhat like what Clerambault
distinguishes in the chloralic state as hallucinations of 'a small area' and
others of 'a large area.' That we were always perceiving in folds means
that we have been grasping figures without objects, but through the haze
of dust without objects that the figures themselves raise up from the
depths, and that falls back again, but with time enough to be seen for an
instant. I see the fold of things through the dust they stir up, and whose
folds I cast aside. I do not see into God, but I do see into the folds. The
situation of perception is not what Gestalt theory describes when it erects
the laws of the 'proper form' against the idea of hallucinatory perception,
but what Leibniz and de Quincey describe: W hen a herd or an army
approaches, under our hallucinated gaze ... — the event:
Through the next hour, during which the gentle morning breeze
had a little freshened, the dusty vapour had developed itself far and
wide into the appearance of huge aerial draperies, hanging in
mighty volumes from the sky to the earth; and at particular points,
where the eddies of the breeze acted upon the pendulous skirts of
these aerial curtains, rents were perceived, sometimes taking the
form of regular arches, portals, and windows, through which began
107
THE FOLD
dimly to gleam the heads of camels 'indorsed' with human beings —
and at intervals the moving of men and horses in tumultuous array
— and then through other openings or vistas at far distant points the
flashing of polished arms. But sometimes, as the wind slackened or
died away, all those openings, of whatever form, in the cloudy pall
would slowly close, and for a time the whole pageant was shut up
from view; although the growing din, the clamours, shrieks, and
groans, ascending from infuriated myriads, reported, in a language
not to be misunderstood, what was going on behind the cloudy
screen. 22
The first stage of the deduction goes from the monad to what is
perceived. But everything seems to stop right there, in a sort of suspense
in the mode of Berkeley, and nothing authorizes us to conclude in favor
of the presence of a body that might be ours, or the existence of the body
that would have happened to affect it. There exists only what is
perceived, interior to the monad, while the phenomenon is what is
perceived. 23 However, a first great difference is marked in respect to
Berkeley: the perceived as a 'being of imagination' is not a given, but
possesses a double structure that allows for its genesis. Macroperception is
the product of differential relations that are established among microperceptions; it is thus an unconscious psychic mechanism that engenders
the perceived in consciousness. 24 Thus the variable and relative unity of
any given phenomenon or another can be explained: all phenomena are
collective, like a herd, an army, or a rainbow.
The collection of unconscious perceptions surely has no unity
(dizziness), but nonetheless it receives a mental unity from the
differential relations that are being exerted, and from a degree of
reciprocal determination of these relations. A collection will have as
much more unity as there are 'relations among the ingredients,' relations
carried out necessarily through thought. The whole question is of
knowing if, in ascribing to itself the force to engender the perceived and
the unity of the perceived in the monad, Leibniz does not also ascribe to
himself the force to engender bodies outside of monads and outside of
their perceptions.
Why can't we get along without bodies? What leads us to go beyond the
phenomenon or the perceived? Leibniz often says that if bodies did not
exist outside of perception, the only perceiving substances would be
108
PERCEPTION IN THE FOLDS
either human or angelic, to the detriment of the variety and of the
animality of the universe. If bodies did not exist outside of the perceived,
there would be less variety in perceivers themselves (that 'must' rightly
be united with bodies). 25 But the likely argument is even more bizarre
and complex: it is that the perceived resembles something that it forces us
to reflect upon. I have a white perception; I perceive white: this perceived
element looks like froth, that is, an infinity of tiny mirrors that would be
reflecting a ray of light beneath our eyes. I feel a tremor of pain: this pain
resembles the movement of something pointed that would dig into my
flesh in concentric circles. 26
The argument appears so difficult to understand that precautions have
to be multiplied. In the first place, Leibniz is not stating that perception
resembles an object, but that it evokes a vibration gathered by a receptive
organ: pain does not represent the needle, nor its movement from one
level to another, 'such as that of a wagon's wheel,' but the thousands of
minute movements or throbs that irradiate in the flesh: 'It is true that
pain does not resemble the movement of a pin; but it might thoroughly
resemble the motions that the pain causes in our body, and might
represent them in the soul.' White does 'not resemble a convex spherical
mirror,' but an infinity of 'little convex mirrors such as there are seen in
foam when we look at it closely.' Here the relation of resemblance is like a
'projection': pain or color are projected on the vibratory plan of matter,
somewhat in the way that a circle can be projected onto a plane as a
parabola or a hyperbola. Projection is the basis for a 'relation of order,' or
analogy, which can be formulated in the following way:
minute perceptions _ vibrations of matter
conscious perceptions the organ
In the second place, that the perceived resembles something does not
immediately mean that perception represents an object. Cartesians had
testified to a geometrism of perception, but through which clear and
distinct perceptions were apt to represent extension. As for obscure or
confused perceptions, they were operating only as conventional signs
stripped of their representativity, hence of resemblance. Leibniz's point of
view is entirely different, since neither the geometry nor the status of
resemblance is the same. These are affective qualities, confused or even
obscure perceptions that resemble something by virtue of a projective
geometry. From then on they are 'natural signs.' And what they resemble
109
THE FOLD
is neither extension nor even movement, but matter in extension,
vibrations, elasticities, 'tendencies or efforts' in motion. Pain does not
represent the pin in extension, but resembles molecular movements that
it produces in matter. Along with perception, geometry plunges into
obscurity. Above all, it is the meaning of resemblance that entirely
changes. Resemblance is equated with what resembles, not with what is
resembled. That the perceived resembles matter means that matter is
necessarily produced in conformity with this relation, and not that this
relation conforms to a preexisting model. Or rather, it is the relation of
resemblance, it is the likeness that is itself the model, that makes matter
be that which it resembles.
In the third place, if we follow the preceding analogy, how then does
the resembled come forward? How does the material side of the analogy
get presented? Appeal cannot be made to a material physical mechanism
that would remain identical to the psychical mechanism in the soul, since
the latter, because it is inherent to the monad, excludes all external
causality. It often happens that Leibniz puts the status of differential
calculus in question. For him it is merely a convenient and well-founded
fiction. 27 In this respect the question is not that of existing infinity or of
the infinitesimal, which pertain as much to matter as to obscure
perceptions (they are 'alike').
The question is rather: Is differential calculus adequate for infinitesimal
things? And the answer is negative insofar as the existing infinite
comprehends neither a great whole nor the smallest parts; nor does it
tend toward limits. Differential relations intervene only in order to
extract a clear perception from minute, obscure perceptions. Thus the
calculus is precisely a psychic mechanism, and if it is fictive, it is in the
sense that this mechanism belongs to a hallucinatory perception. Calculus
surely has a psychological reality, but here it is deprived of physical
reality. There can be no question of assuming it in what perception
resembles, that is, by turning it into a physical mechanism, except
through convention and by increasing the fiction. Physical mechanisms
are infinitely tiny fluvia that form displacements, crisscrossings, and
accumulations of waves, or 'conspiracies' of molecular movements.
When defining the essential characters of bodies, Leibniz assigns two
of them, the power of diminishing infinitely (by virtue of their infinitely
tiny parts), and the power of being in constant flux (to have parts that
never stop coming and going). 28 Physical mechanisms do not work by
PERCEPTION IN THE FOLDS
differentials, which are always differentials of consciousness, but by
communication and propagation of movement, 'like ripples that a stone
creates when it is thrown into water.' It is even in this sense that matter is
full of organs, or that organs fully belong to matter because they are
merely the contraction of several waves or rays: the nature of a receptive
organ is to contract the vibrations that it receives. 29 It is at the origin of a
principle of physical causality, because it gathers together the effect of an
infinity of causes ('equality of the full cause and of the entire effect').
Thus there exists a great difference between an always extrinsic
physical causality, which goes from one body, to all those from which it
receives the effect, to infinity in the universe (the regime of influx or of
universal interaction), and an always intrinsic psychic causality, which
goes from each monad on its account to effects of perception of the
universe that it produces spontaneously, independently of all influx from
one monad to another. To these two causalities correspond two
calculations — or two aspects of the calculus that, even if they are
inseparable, must be distinguished: one relates to the psycho-metaphysical
mechanism of perception, and the other to the physico-organic
mechanism of excitation or impulsion. And these are like two halves of
each other. This does not prevent conscious perception from resembling
vibrations contracted by the body, or the threshold of consciousness from
corresponding to the conditions of the organ, as Fechner's psychophysics
is developed on the basis of the preceding analogy. A quality perceived by
consciousness resembles the vibrations contracted through the organism. 3° Differential mechanisms on the inside of the monad resemble
mechanisms of communication and propagation of extrinsic movement,
although they are not the same and must not be confused.
The relation of vibrations at the receiver introduces limits into matter that
make possible the application of differential calculus, but this relation is
not in itself differential. The application of differential calculation to
matter (through resemblance) is based on the presence of receptive
organs everywhere in this matter. From it we might be able to draw
conclusions that pertain to the respective interpretations of calculus for
Leibniz and for Newton. It is commonly known that they did not
conceive it in the same way. Now, by determining magnitudes according
to the speed of movements or intensities that form them ('fluxions'),
Newton invents a calculus adequate to the movement of a fluid matter,
and even to its effects upon an organ. But, while considering that these
THE FOLD
fluxions disappear in the growing magnitude of which they are a part,
Newton leaves aside the problem of knowing where the different parts
remain. To the contrary, Leibniz's calculus, based on the reciprocal
determination of 'differentials,' is strictly inseparable from a Soul, insofar
as the soul alone conserves and distinguishes the small components. 31
Leibniz's calculus is adequate to psychic mechanics where Newton's is
operative for physical mechanics. The difference between the two is as
much metaphysical as it is mathematical. We would not be wrong to state
that Leibniz's calculus resembles Newton's. In effect, it applies to nature
only by means of resemblance, but we must recall that it is the likeness
that is the model, and that it determines whatever it resembles.
The deduction has two stages, the one positing the monad's
requirement of having a body (primary matter or limitation-matter),
the other showing how the requirement is filled (secondary matter or
flux-matter). To sum up the second stage, which moves from the
perceived to the body: (1) clear-obscure perception manifests a relation of
resemblance with a material receptor that receives vibrations; (2) such
receptors are called organs or organic bodies, and as bodies they
constitute the vibrations that they receive to infinity; (3) the physical
mechanism of bodies (fluxion) is not identical to the psychic mechanism
of perception (differentials), but the latter resembles the former; (4) using
resemblance as a model, God necessarily creates a matter in conformity
with what resembles him, a presently infinite vibratory matter (of
infinitely tiny parts) in which receptive organs are distributed everywhere, swarming; (5) thus we move from one aspect of perception to
another, which is no longer solely the representative of the world but
becomes the representation of an object in conformity with organs.
PERCEPTION IN THE FOLDS
I possess a clear and distinguished zone of expression because I have
primitive singularities, ideal virtual events to which I am destined. From
this moment deduction unwinds: I have a body because I have a clear and
distinguished zone of expression. In fact, that which I express clearly, the
moment having come, will concern my body, and will act most directly on
my body, surroundings, circumstances, and environment. Caesar is the
spiritual monad who clearly expresses the crossing of the Rubicon. He
thus has a body that the flowing waters, a given flow of water, will
eventually be soaking. But up to this point, when perception has become
the perception of an object, everything can be easily inverted. I can
recover ordinary language, or the habitual and empirical order of
resemblance: I have a clear or privileged zone of expression because I
have a body. What I clearly express is what happens to my body.
The monad expresses the world 'according to' its body, according to
the organs of its body, according to the action of other bodies upon itself:
'What happens in the soul represents what happens in bodily organs.' 32
Hereafter the monad can be said to 'suffer.' While in truth the monad
draws all perceptive traces from itself, I act as if the bodies that are acting
upon itself were acting upon it and were causing its perceptions. Is this a
simple manner of speaking, or a deeper problem that can be resolved only
through analysis of causalities?
In short, God endows the monad with organs or the organic body
corresponding to its perceptions. Thus we are prepared to understand the
sum of the theory of the fold. The implementation of perception
establishes the folds in the soul, the folds whose monad is decorated on
the inside; but these are like a matter that must hereafter be organized in
outer pleats. We even find ourselves in a quadripartite system of folding,
to which the preceding analogy attests, because perception straddles the
micro-folds of tiny perceptions and the great fold of consciousness, and
matter, the tiny vibratory folds and their amplification on a receiving
organ. The folds in the soul resemble the pleats of matter, and in that
fashion they are directing them.
112
113
THE TWO FLOORS
8
The two floors
Already in a writing of his youth Leibniz reproaches nominalists for
conceiving totalities only as collective and, by doing so, spoiling the
concept. Comprehension of the concept is distributive and not collective.
Collectively, sheep are members of a flock, but people are reasonable only
on an individual basis.' Therefore Leibniz notices that, insofar as they are
reasonable, monads stand in the same respect to the world as to the
comprehension of their concept: each one on its own basis comprises the
entirety of the world. Monads are each or every one for itself, while bodies
are one, some, or any. 2 William James and Russell used this difference to
their advantage. Monads are distributive units that follow a relation of
part and whole, while bodies are collectives — flocks or aggregates — that
follow a relation of the-ones-to-the-others. Division into two floors thus
appears strict since, in the upper area, we have reasonable monads or the
Each, like private apartments that are not connected to one another, that
do not act upon each other, and that are variants of the same interior
decoration.
On the floor below we find the material universe of bodies, like that of
Commoners who are forever expressing movement, propagating waves,
and acting upon one another. Surely there is a convergence, because each
monad expresses the sum of the world, and because a body receives the
impression of 'all' the others up to infinity. 3 But this convergence moves
along two diverging paths or according to two entirely different regimes, a
regime of expression and a regime of impression, a vertical immanent
causality and a transitive horizontal causality. They can be summarily
opposed: in one case, concepts of liberty or grace are at stake; 'free
114
decrees,' final causes and 'moral necessity' (the best) are involved. In the
other case, we are dealing with concepts of nature, with efficient causes,
'subaltern maxims' such as physical laws, in which necessity is
hypothetical (if one is ..., so then the other ...).
We not only have convergence, but here and there broad encroachments. Subaltern maxims are a part of free decrees, and among them a
certain number concern monads directly, inasmuch as the latter already
form a first 'nature'; with moral necessity and hypothetical necessity
lumped together, efficient causes would never exert influence if final
causes did not happen to fulfill the conditions. 4
And yet two halves are in question, as we have just seen in the case of
infinitesimal calculus. In fact, if we assimilate the object (that is, the
world) to the primary equation of an infinite curvature of inflection, we
obtain the position or the respective point of view of monads as primitive
or primal forces, by means of a simple rule of tangents (vectors of
concavity), and from the equation we extract differential relations that
are present in every monad between minute perceptions, in a way that
every one of them conveys the entire curvature of its point of view. Thus
we have a first part, a first moment of the object, the object as perceived
or the world as expression. But there persists the question of knowing
what the other part may be which now corresponds to the initial
equation: pure relations are no longer at stake, but differential equations
and integrations that determine the efficient causes of perception, that is,
which have to do with a matter and the bodies that perception resembles.
Such is the second moment of the object, no longer expression, but
contents These are no longer decrees, but maxims or empirical laws of
second Nature.
These are no longer singularities of inflection, but singularities of extremum,
because the curve is now related — but only now — to coordinates that
allow us to determine minima or maxima. These are no longer vectors of
concavity that define the position of monads in relation to inflection, but
vectors of weight that define the position of a body's equilibrium and the
lowest center of gravity (the catenary curve). It is no longer a reciprocal
determination through differential relations, but a complete determination of the object through a maximum or minimum: finding the form of a
closed line of a given length that limits the greatest possible planar
surface, finding the minimal area of surface limited by a given contour.
115
THE FOLD
Everywhere in matter the calculus of 'minimis and maximis' will allow
the modification of movement to be determined in respect to action, the
course of light in respect to reflection or refraction, the propagation of
vibrations in respect to harmonic frequencies, but also the organization of
receivers, and the general diffusion or balanced distribution of all kinds of
derivative forces, elastic and plastic alike. 6
It is as if the equation of the world had to be inscribed twice, once in
the minds that conceive it more or less distinctly, and a second time in a
Nature that makes it possible in the form of two calculi. And these two
calculi probably are concatenated or are continuous, and they are
probably complementary and have to be homogenized. That is why
Leibniz can put forward the choice of the world or of monads as if they
already operate through a calculus of minimum and maximum; the
difference of the two halves nonetheless remains, since in one case the
differential relations determine a maximum of quantity of being, while in
the other the maximum (or minimum) determines the relations in the
equation. We have seen the diversity of singulars in Leibniz's work:
properties of extremum rule over the constitution of the world chosen in
Nature, but the very choice goes back first of all to other properties — of
inflection — that put the form of the whole into play at an upper level, as if
it were the property of being the limit of a convergent series.' The great
equation, the world thus has two levels, two moments, or two halves,
one by which it is enveloped or folded in the monads, and the other, set
or creased in matter. If the two are confused, the whole system falls apart,
and no less mathematically than metaphysically.
On the upper level we have a line of variable curvature, without
coordinates, a curve with infinite inflection, where inner vectors of
concavity mark for each ramification the position of individual monads in
suspension. But only on the lower level have we coordinates that
determine extrema, extrema that define the stability of figures, figures
that organize masses, masses that follow an extrinsic vector of gravity or
of the greatest incline: it is already the ogive, the Gothic arch, as a
symmetrical mapping of inflection, which represents the figure that meets
with a minimum of resistance from a fluid. 8 This is the organization of the
Baroque house with its division into two floors, one in individual
weightlessness, the other in a gravity of mass. Between them a tension is
manifested when the first rises up or drops down, in spiritual elevation
and physical gravity.
Raymond Ruyer (the latest of Leibniz's great disciples) opposes 'true
116
THE TWO FLOORS
forms' to figures and structures. 9 Figures are functions that refer to the
axes of coordinates, and structures are functionings that refer to relative
positions ordered from one to the next, according to states of equilibrium
and horizontal linkages, even when there exists a relation of dominance.
But the so-called substantial or individual forms are absolute vertical
positions, surfaces or absolute volumes, unified areas or 'overviews,'
unlike figures, which do not imply a supplementary dimension in order
to be themselves understood, and are not dependent as are preexisting
and localizable linkages. These are souls, monads,'self-surveiling' superj ects.
Self-present in the vertical dimension, overseeing themselves without
taking any distance, these are neither objects that can explain perception,
nor subjects capable of grasping a perceived object; rather, they are
absolute interiorities that take hold of themselves and everything that fills
them, in a process of 'self-enjoyment,' by withdrawing from themselves
all perceptions with which they are co-present on this one-sided inner
surface, independently of receptive organs and physical excitations that
do not intervene at this level. My eyes would refer to a third eye, which
would in turn refer to a fourth eye, if an absolute form were incapable of
seeing itself and, in that way, of seeing all the details from its domain in
all the areas from which it is located at the same time: nonlocalizable
linkages. Every time that we have attributable individual beings that are
not content with merely functioning, but that are endlessly 'being
formed,' these true forms do not only apply to living organisms, but to
physical and chemical particles, to molecules, atoms, and photons.
Although the inner variety of forms accounts for differences between the
organic and the inorganic, the question does not thus concern a matter of
vitalism. No matter what, genuine or absolute forms are primary forces,
essentially individual and active primary unities, that actualize a
virtuality or a potential, and that are in harmony with each other
without anyone being determined by the other.
Gestalttheorie believed that it attained these forms by appealing — as
much for perceived figures as for physical structures — to a total action and
to extreme dynamic equilibriums, a kind of 'soap bubble' that would be
capable of exceeding simple actions of contact, successive mechanisms,
and preexisting illusions (for example, a law of minimal tension would
explain foveal fixation without assuming special conductors). But
perhaps Gestalt thus revives the great Newtonian attempts when people
began to elaborate notions of force and field in order to get beyond
117
THE FOLD
classical mechanics. And in this respect the opposition of Leibniz to
Newton is not explained merely by the critique of vacuum, but because
phenomena of 'attraction,' in which Leibniz clearly recognizes a
specificity (magnetism, electricity, volatility), do not seem to him to be
of a nature that would exceed the order of mechanisms of contact or
succession ('thrusts' or 'impulsions'). m A journey created from one
instant to the next through an infinitesimal diminution of tension
operates no less successively than a preformed road, a set of rails, or a
pipeline; a progressive filling of all possible space by a sum of waves
implies just as much the actions of contact in a fluid.
The laws of extremum, to which D'Arcy Thomson recently appealed in
order to account for organic phenomena, still imply paths in extension
that can be compared only by assuming the form that one claims to
explain. In short, we are not moving thus toward active primary unities;
on the contrary, we remain in an extension without any overview, and in
linkages without sufficient reason. What Leibniz calls for, against Newton
(as does Ruyer against Gestaltists), is the establishment of a true form that
cannot be reduced to an apparent whole or to a phenomenal field,
because it must retain the distinction of its details and its own
individuality in the hierarchy in which it enters. To be sure, the semiwholes have as much importance as the parts, as do attractions as much
as thrusts, dynamic and mechanical equilibriums, laws of extremum and
laws of contact, ways and channels, bindings and adhesions. They are
indispensable but, once they are formed, only make up secondary horizontal
linkages and follow subaltern maxims according to which structures
function and figures are ordered or linked. If there is a finality here, it is
only what the mechanism is producing.
All these laws are like statistics because they pertain to collections,
masses, organisms, and no longer to individual beings. Thus they do not
convey primary forces or individual beings, but they distribute derivative
forces in masses, elastic forces, forces of attraction, and plastic forces that
in each case are determining the material linkages. A great line of
difference does not separate the organic from the inorganic, but crosses
the one and the other by distinguishing what is individual from what is a
collective or mass phenomenon, what is an absolute form and what are
massive, molar figures or structures." These are the two levels or two
aspects of the calculus.
Above, individual beings and true forms or primal forces; below,
118
THE TWO FLOORS
masses and derivative forces, figures and structures. Individual beings are
probably the last and sufficient reasons: their forms and primal forces are
hierarchy, accord, and variety and, in the last instance, they make up
collections and different types of collection. But the lower floor is no less
irreducible, because it implies a loss of individuality among its
components, and relates to different kinds of composite collections
material or secondary forces of linkage. Clearly, one level is folded over
the other, but above all each one conveys a very different kind of fold. A
chain of mountains, a genetic chain, or even a gastrula will not be creased
in the same way. The same example can even be applied to the organic
and inorganic. What must be radically distinguished are the bends of
matter, which always consist in hiding something from the relative
surface that they are affecting, and the folds of form, which on the
contrary reveal to itself the detail of an absolute surface that is copresent
with all its modifications.
Why the lower level, which is not a simple appearance? It is because
the world or the hazy line of the world resembles a virtuality that is
actualized in the monads. The world has actuality only in the monads,
which each convey it from each monad's own point of view and on its
own surface. But the coupling of the virtual-actual does not resolve the
problem. There exists a second, very different coupling of the possiblereal. For example, God chooses one world among an infinity of possible
worlds: the other worlds also have their actuality in monads that are
conveying them, Adam who does not sin or Sextus who does not rape
Lucretia. Therefore there exists an actual that remains possible, and that
is not forcibly real. The actual does not constitute the real; it must itself be
realized, and the problem of the world's realization is added to that of its
actualization. God is 'existentifying,' but the Existentifying is, on the one
hand, Actualizing and, on the other, Realizing.
The world is a virtuality that is actualized monads or souls, but also a
possibility that must be realized in matter or in bodies. It is curious, we
might argue, that the question of reality is posited in respect to bodies
that, even if they are not appearances, are simple phenomena. Yet what
happens to be a phenomenon in the strict sense is what is perceived in the
monad. When, by virtue of the resemblance of the perceived to
something = x, we ask if bodies might not be acting upon each other in
ways such that our inner perceptions correspond to them, we are thus
asking the question of a realization of the phenomenon or, better, of a
'realizing' of the perceived, that is, of the transformation of the currently
119
THE FOLD
THE TWO FLOORS
actualisation
realization
perceived world into an objectively real world, into an objective Nature. 12
It is not the body that realizes, but it is in the body that something is
realized, through which the body itself becomes real or substantial.
The process of actualization operates through distribution, while the
process of realization operates by resemblance. This raises an especially
delicate point. For if the world is taken as a double process — of
actualization in monads and of realization in bodies — then in what does it
itself consist? How can we define it as what is actualized and is realized?
We find ourselves before events: Adam's soul is now sinning (following
final causes), and thus his body is really absorbing the apple (according to
efficient causes). My soul feels a current pain, my body receives a real
blow. But what is it? What is this secret part of the event that is at once
distinguished from its own realization, from its own actualization, even
though realization does not exist on the outside? This death, for example,
is neither exterior reality nor its intimacy in the soul. We have seen that it
is pure inflection as ideality, a neutral singularity, incorporeal as much as
impassible or, if we use Blanchot's words, 'the part of the event as much
as its accomplishment' can neither actualize nor realize its carrying out.' 3
It is what can be conveyed by all expression, or what can be realized by all
realizations, the Eventum tantum to which the body and soul attempt to be
equal, but that never stops happening and that never ceases to await us: a
pure virtuality and possibility, the world in the fashion of a Stoic
Incorporeal, the pure predicate.
As the Chinese (or Japanese) philosopher would say, the world is the
Circle, the pure 'reserve' of events that are actualized in every self and
realized in things one by one. Leibniz's philosophy, as shown in the
letters written to Arnauld, as much in respect to spiritual monads as in
120
respect to the material universe, requires this ideal preexistence of the
world, this silent and shaded part of the event. We can speak of the event
only as already engaged in the soul that expresses it and in the body that
carries it out, but we would be completely at a loss about how to speak of
it without this withdrawn part. However difficult it may be, we must
think of the naval battle beginning with a potential that exceeds the souls
that direct it and the bodies that execute it.
It is in its relation both to the world and to the souls that the material
universe can be said to be expressive. Some souls express it through
actualization, others through realization. To be sure, these are two very
different regimes of expression. They are really distinct; one is distributive
where the other is collective. On its own account each monad conveys
the entire world independently of others and without influx, while every
body receives the impression or influx of others, and that is the totality of
bodies; that is the material universe that expresses the world.
Preestablished harmony is thus presented first of all as an accord between
the two regimes. But in turn these have a second difference: the
expression of the soul goes from the whole to the part, that is, from the
entire world to a designated zone, while the expression of the universe
goes from part to part, from the near to the far, to the degree that a body
corresponds to the designated zone of the soul and successively submits to
the impression of all the others. From this point of view there always
exists a body that expresses from its side, with its surroundings, what a
soul expresses in its own region, and preestablished harmony is located
between the soul and 'its' body.
But what allows us to speak of 'the body of a monad' or 'its body,'
since the monad is always an Each, an Every, while the body, always a
body, is a One? What founds the appurtenance of one body to each
monad, despite the real distinction and the difference of level or of
regime? A One — without ceasing to be a One — must belong to each Every.
In brief, preestablished harmony is distinguished not only in itself from
Malebranche's occasionalism or from Spinoza's parallelism, but also by its
consequences: far from replacing the problem of the union of the soul
and the body, of the incarnation or of 'immediate presence,' it makes it all
the more necessary, even if only to move from the first to the second
aspect." In fact, harmony explains the correspondence between each
soul and the material universe, but when it appeals to the correspondence between the soul and its body, it cannot explain it through any
relation in the body simply because a relation of this kind is based on a
121
THE FOLD
pregiven appurtenance. It is only at the level of a theory of appurtenance
that the problem will find its solution: What does it mean to belong, and
in what way does one body belong to each soul?
In the last of his Cartesian Meditations Husserl goes back to Leibniz for good
reason. He effectively develops an entire theory of appurtenance that
takes up three great moments that Leibniz had brought to light: the
monad is the Ego in its concrete plenitude, the Self is related to a 'sphere
of appurtenance,' to the sphere of its possessions; but myself, a monad, I
find in the sphere of what belongs to me the mark of something that I do
not possess, something foreign to me; thus I can constitute an objective
Nature to which the other in me belongs. To the first question, 'What
belongs to me?' Leibniz responds just as will Husserl much later: it is first
of all the thought of the self, the cogito, but also the fact that I have
diverse thoughts, all my changing perceptions, all my predicates included,
the entire world as perceived; and yet still, this is the zone of the world
that I convey clearly, it is my special possession; and then, primary matter
is what I own as the requirement of having a body. And finally, the body,
a body, is what I own, a body that happens to fill the requirement, as we
have seen just previously: an organic body with which I am immediately
'present,' that I can use in an immediate fashion and with which I
coordinate what is perceived (I perceive with organs, with my hands,
with my eyes ...). There is the whole list of my belongings; the last is
distinguished from all the others because it is extrinsic, a body not being
in my monad.
Now we can specify the great gap that will open between Leibniz and
Husserl: at the level of the body Husserl discovers the other as being the
other-self, the other monad, 'through aperceptive transposition that
begins with my own body.' The same does not hold for Leibniz, for whom
the plurality of monads was discovered at an earlier stage: indeed,
everything that exceeds my clear zone or my subdivision and that
nevertheless I include, everything that remains dark or obscure in me,
resembles the negative image of other monads, because other monads use
it to form their own clear zone. It happens then that a community of
monads is already in place, and a first Nature, constituted by all their
respective zones of clarity, does not need bodies in order to appear. To be
sure, no monad contains others, but my intrinsic possessions sufficiently
bear the mark of those foreign ones whose shadow I discover within me,
since there is nothing obscure in me that might not be pulled into clarity
122
THE TWO FLOORS
from another monad. Thus for Leibniz, if a meeting with the other is
produced at the level of the body, it will not be with the other-self, but
with an even more unexpected element that makes up a second Nature.
I have a body, a body belongs to me: How can my monad have an
extrinsic possession, outside of itself, on the lower level? One of Leibniz's
essential theses consists in positing at once the real distinction and the
inseparability: it is not because two things are really distinct that they are
separable. In the very same way Harmony and Union discover the
principle of their division: preestablished harmony of the soul and of the
body rules their real distinction, while the union determines their
inseparability.' 5 Even when I die, my monad is not separated from a body
whose parts are happy to become involuted. As we have observed, my
monad does not perceive in itself without having a body in 'resemblance'
with what it is perceiving. By virtue of the generality of the order of
resemblance, it is a generic, specific, organic body: a body of a man, or
even of a horse, a dog ... The requirement of having a body is quite
individual, but not the body that happens to fill it, at least not
immediately.
Leibniz often insists on this point: God does not endow the soul with a
body without furnishing the given body with organs. Now what makes an
organic, specific, or generic body? It is probably made of infinities of
present material parts, in conformity with infinite division, in conformity
with the nature of masses or collections. But these infinities in turn
would not comprise organs if they were not inseparable from crowds of
little monads, monads of heart, liver, knee, of eyes, hands (according to
their special zone that corresponds to one infinity or another): animal
monads that themselves belong to material parts of 'my' body, and that
are not confused with the monad to which my body belongs. These are
merely the requisites of my organic, specific, or generic body; and there is
no cause to ask if matter thinks or perceives, but only whether it is
separable from these little souls capable of perception. 16
Thus we see that Leibniz's theory of appurtenance leads to a
fundamental inversion that will forever begin over and again. Monads
that have a body must be distinguished, and monads that are the specific
requisites of this body, or that belong to parts of this body. And these
second monads, these monads of bodies, themselves possess a body that
belongs to them, a body specifically other than that whose requisites they
are, and whose parts in their turn possess crowds of tertiary monads. And
these tertiary monads
The soul and the body can always be truly
..."
123
THE FOLD
distinguished, but inseparability traces a coming and going between one
level and the other. My unique monad has a body; the parts of this body
have crowds of monads; each one of these monads has a body...
If my body, the body that belongs to me, is a body according to the law of
collections, it is because its parts not only grow and shorten, involve and
evolve, but also never cease to move about and go away (fluxion). And,
when they leave, the monads that are inseparable from either follow
them or evade me. Requisites of my body, these were merely 'pro
tempore' requisites. 18 The theory of appurtenance thus distinguishes
nonsymmetrical and inverted appurtenances (a body belongs to my
monad, some monads belong to parts of my body), but also constant or
temporary appurtenances (a body belongs constantly to my monad, some
monads belong temporarily to my body). That is where, in the theory of
appurtenance, the revelation of a half-other occurs: the animal in me as a
concrete being. The great difference with Husserl is that the latter does
not face any special problem in organic composition: my body does not
pose any problems in my sphere of appurtenance, and the other springs
up only with the other body, through which I aim at an Alter Ego that
does not belong to me; as for the animal, it is only an 'anomaly' of this
Other.
For Leibniz, on the contrary, the alter ego has already sprung up at an
earlier stage of phenomenological deduction, and is sufficiently explained
through preestablished harmony. With the union of the soul and the
body, the other who now springs forth amid my effects — in order to
throw them topsy-turvy — is the animal, and first of all the little animals
inseparable from the fluid parts of my body, insofar as they become as
foreign to me as they had formerly been. 'If Caesar's soul, for example,
had to be solitary in nature, the author of things would have been
perfectly able to get along without furnishing him with any organs; but
this same author wished to make yet an infinity of other beings that are
enveloped in the organs of one another; our body is a type of world full of
an infinity of creatures that are also worthy of life: 19
The animals that I meet outdoors are nothing but an enlargement of
the latter. This is not only an animal psychology, but also an animal
monadology. The two are essential to Leibniz's system: because my
sphere of appurtenance essentially discovers me, these are inverted,
temporary, or provisional appurtenances (although a body always
belongs to me). In fact, it is very difficult for every one of us to make a
124
THE TWO FLOORS
list of our own belongings. It is not easy to know what we own, and for
what length of time. Phenomenology does not suffice. The great
inventory of Beckett's Malone is consummate proof. Malone is a naked
monad, or almost naked, scatterbrained, degenerate, whose zone of
clarity is always shrinking, and whose body folds upon itself, its requisites
always escaping him. It's hard for him to tell what remains in his
possession, that is, 'according to his definition,' what belongs to him only
partially, and for what duration of time. Is he a thing or an animalcule? If
he does not have belongings, then to whom does he belong? That is a
metaphysical question. He needs a special hook, a sort of vinculum on
which he can hang and sort through his different things, but he has even
lost this hook.
These reincarnations of appurtenance or possession carry a great
philosophical importance. It is as if philosophy were penetrating into a
new element and were putting the element of Having in place of that of
Being. Clearly, there is nothing new about the formula of 'having a body,'
but what is new is that analysis bears upon species, degrees, relations, and
variables of possession in order to use it to fashion the content or the
development of the notion of Being . Much more than Husserl, Gabriel
Tarde fully discerned the importance of this mutation, and he called in
question the unjustifiable primacy of the verb 'to be.' 'The true opposite
of the self is not the non-self, it is the mine; the true opposite of being, that
is, the having, is not the non-being, but the had.'2°
Already Leibniz had been erecting, on the inside of the monad, 'I have
diverse thoughts' in correlation with 'I am thinking.' Perceptions as
included predicates, that is, as inner properties, were replacing attributes.
Predication was of the domain of having, and was resolving the aporias of
being or of attribution. This was all the more reason for the body, as an
extrinsic property, to introduce into possessions factors of inversion,
turnaround, precariousness, and temporalization. In fact, this new
domain of having does not put us into an element of calm, which would
be a relation of the proprietor and property that could be easily
established once and for all. What rules in the domain of having are
moving and perpetually reshuffled relations among the monads, as much
from the standpoint of harmony, where they can be considered 'each and
every one for each other,' as from the point of view of union, where they
are considered 'the one and the other.' There again we have a casuistry.
Finally, a monad has as its property not an abstract attribute — movement,
elasticity, plasticity — but other monads, such as a cell, other cells, or an
125
THE FOLD
atom, and other atoms. These are phenomena of subjugation, of
domination, of appropriation that are filling up the domain of having,
and this latter area is always located under a certain power (this being
why Nietzsche felt himself so close to Leibniz). To have or to possess is to
fold, in other words, to convey what one contains 'with a certain power.'
If the Baroque has often been associated with capitalism, it is because the
Baroque is linked to a crisis of property, a crisis that appears at once with
the growth of new machines in the social field and the discovery of new
living beings in the organism.
Appurtenance and possession hark back to domination. A specific body
belongs to my monad, but as long as my monad dominates the monads that
belong to the parts of my body. As a code of correspondences, expression
exceeds itself, moving toward domination as a cipher of appurtenances;
each monad conveys the entire world, and therefore all other monads, but
from a point of view that links each one more strictly to certain others,
which they dominate or which dominate them. If a body always belongs to
me, it is because the parts that go away are replaced by others whose
monads in turn come to replace them under the domination of my own
(there exists a periodicity of the renewal of parts, never all leaving at the
same time). The body is analogous to Theseus's ship 'which the Athenians
were always repairing: 21 But, as no monad contains any others,
domination would remain a vague notion, having only a nominal
definition, if Leibniz had not succeeded in defining it exactly by means of
a 'substantial vinculum.' It is a strange linkage, a bracket, a yoke, a knot, a
complex relation that comprises variable terms and one constant term.
Because the vincular relation belongs to it or is 'fixed' upon it, the
constant term will be the dominant monad. Apparently we can be all the
more astonished, because this relation, having other monads for its
variable terms (hereafter dominated), cannot be a predicate contained in
its subject. That is why the relation, not being a predicate, will be called
'substantial.' Because every relation has a subject, the dominant monad is
surely the subject of the vinculum, but a 'subject of adhesion,' not of
inherence or of inhesion. 22 As many readers have shown, this is an
almost insufferable paradox in Leibnizianism. That relations are predicates is in no way paradoxical, but only if we understand what a
predicate is, what makes it differ from an attribute; and the preestablished
harmony implies no outer relation among the monads, but only ties
regulated on the inside.
126
THE TWO FLOORS
In contrast, the paradox appears insurmountable as soon as appeal is
made to an extrinsic possession: that is, a relation that clearly has a
subject, but that is not in its subject, and that is not a predicate. There
Leibniz discovers that the monad as absolute interiority, as an inner
surface with only one side, nonetheless has another side, or a minimum
of outside, a strictly complementary form of outside. Can topology resolve
the apparent contradiction? The latter effectively disappears if we recall
that the 'unilaterality' of the monad implies as its condition of closure a
torsion of the world, an infinite fold, that can be unwrapped in
conformity with the condition only by recovering the other side, not as
exterior to the monad, but as the exterior or outside of its own interiority:
a partition, a supple and adherent membrane coextensive with everything inside. 23 Such is the vinculum, the unlocalizable primary link that
borders the absolute interior.
'allrn
_
fluxion
dominated
As far as variable terms are concerned, monads are what enter in the
relation as 'objects,' even if for brief moments. They can exist without the
relation, and the relation can exist without them. The relation is exterior
to variables, as it is the outside of the constant. 24 It is especially complex
since it acquires an infinity of variables. The latter are said to be
dominated, specifically insofar as they enter into the relation attached to
the dominant or constant. When they cease being submitted to this
relation, they enter under another, into another vinculum attached to
another dominant (unless they are not freed from every vinculum). In
order to evaluate the action of the vinculum, we have to distinguish the
two aspects very clearly. First, it is what acquires its variables en masse,
and by masses. Not that the monads that enter under its rule in themselves
lose their own individuality (which would imply a miracle). It even
presupposes this individuality, and the modifications or inner perceptions
of the monads, but it changes nothing and does not depend on them.
127
THE FOLD
From them it merely extracts a 'common modification,' in other words,
an Echo that they all have together when they are reflected on the
surface of a wal1. 25
As Yvon Belaval and Christiane Fremont have shown, the vinculum
itself is a 'reflecting wall,' and it is so because it comprises this form of the
outside that depends on the dominant or constant; variable monads,
then, are 'emitters,' while the echo is the modification of the whole. 26 In
this way the vinculum takes up its variables in a massive effect and not in
their individuality: whence the passage from optics to acoustics, or from
the individual mirror to the collective echo, the effects of whisper or
swarming that now refer to this new acoustical register. Then, if the
vinculum acquires monads en masse, it thus causes an inversion of
appurtenance. As long as monads are understood in their individuality, a
body belongs to each monad and is inseparable from it. It is true for the
dominant monad, but equally true for every dominated monad that,
taken individually, is in turn dominant and thus possesses a body. But the
inverse is produced when the dominated monads are taken en masse
under a vinculum. Then they are the ones belonging to infinities of
material parts that are inseparable from them. They make up the
specificity of these parts in general, in the double meaning of
homogeneity for the parts that are endlessly being replaced and
heterogeneity for the parts that are being coordinated.
In short, as a membrane, wall, or partition, the vinculum works as a
sort of grid filtering the monads that it receives as terms. These are sifted
masses that in each case make up the specificity of the organic parts,
hence the specific or generic unity of the body to which these parts refer.
And this body is surely not that of a variable monad, since the latter has a
body in its turn only as an individual and only when it serves as a
constant. Composed of material parts, the organic body is precisely that
which possesses the dominant, a body that here finds the determination
of its specific unity.
But the other aspect springs up when the vinculum is sent back, not to
dominated variable monads, but directly to this dominant or constant.
Fixed or attached to an individual dominant, the vinculum in fact
determines an individual unity of the body that belongs to it: this body
that I have is not only the body of a man, a horse, or of a dog, it is my own
body. Further, there would be no specific unity if individual unity were
not already presupposed in this first function of the vinculum. If so many
material parts can at all times disperse in order to be replaced by others, it
128
THE TWO FLOORS
is not only because they can be specifically replaced, it is because the body
to which they belong in passing remains individually one, a unified body,
by virtue of the monad of which it does not cease being a part. Here is an
entire cycle of the body and the soul that goes through Every and One, and
returns to Every by way of the intermediary of appurtenances or of the
'possessive': ( 1 ) each individual monad possesses a body that cannot be
separated from it; (2) each one possesses a body insofar as it is the
constant subject of the vinculum that is fixed to it (its vinculum); ( 3 ) for
variables this vinculum has monads taken en masse; (4) these masses of
monads are inseparable from infinities of material parts to which they
belong; ( 5) these material parts make up the organic composition of a
body, whose vinculum, envisioned in respect to the variables, assures its
specific unity; (6) this body is the one that belongs to the individual
monad, it is its body to the extent that it already avails itself of an
individual unity (thanks to the vinculum now envisioned in relation to
the constant).
It is even more complicated if we consider the necessary classification of
monads. Taken individually, without exception all monads convey the
entire world, and are distinguished only by their subdivisions, by the
clear zones of their expression. Reasonable monads have a zone so wide
and so intense that they lend themselves to operations of reflection or
deepening that makes them tend toward God. But every animal monad
also has its clear zone - no matter how reduced - including ticks, even a
monad of blood, of liver ... Taken thus in its individuality, every monad
is a simple substance, a primary active force, an inner unity of action or of change.
Clearly, it has a body, it is inseparable from a body corresponding to its
clear zone, but it does not contain it, and is really distinguished from it.
The monad merely requires it because of the limitation of its force that
constitutes its passive power or its initial matter ('moles'). It is a dominant
monad to the degree that it has requirements. All reasonable monads are
dominant and cannot be otherwise. But even in death, when it 'appears'
to have lost its body, when it becomes animal again, the formerly
reasonable monad does not cease to be dominant. All animal monads, all
monads, no matter how dark they may be, are dominant to a certain
degree - if they are considered individually, and if they have a body, even
if it is infinitely involuted, crushed, or mutilated. They are immediately
present in the body, but only through projection: active primary force is
projected as dominant at a point in the body. 27
129
THE FOLD
Dominated monads form a second species (although they are
dominant, or of the first species, from the preceding point of view).
Reasonable monads are never dominated, whereas animal monads can
always be dominated. They are so when taken en masse, and not in their
individuality. When they are taken in clusters, it is not in respect to the
bodies they possess, each on its own account, because they are dominant
under this relation. They are taken in clusters in respect to infinite
aggregates of material parts that own them, on the contrary, and that
remain inseparable from them. From then on these parts clearly compose
a body, but it is not the body of dominated monads, but rather the body of
the dominant one, the body that their dominant monad possesses. In
effect, what acquires an infinity of monads en masse is a knot, a vinculum
that is fixed to an individual monad that can be determined as dominant,
and that relates to the body of the latter the material aggregates
corresponding to the mass in question.
In the paragraphs above we have used 'clusters,' 'crowds,' and masses
or aggregates synonymously. Now we observe that they are (really)
distinguished, aggregates being material, and clusters being monads; with
the aggregates from which they are inseparable, under the vinculum
masses make organic parts from the body of the monad that dominates
them. They make an organism from masses; they organize aggregates. In
that way, they are active, but collective and derivative ('plastic' forces): no
longer as units of inner change, but as apparent units of generation and
corruption that account for organic composition through envelopment,
development, and fluxion of material parts.
And, instead of being projected in a body that belongs to them, they
are collectively related to the material parts to which they belong, and
they are themselves said to be materia1. 28 It can be concluded that the
monads of the second species, the monads in clusters, constitute, in the
most narrow sense of the term, corporal or composite substances. substantials:
'a multiplicity of substances of which the mass (massa) is that of the total
body,' and that are 'the parts of a second matter.' 29 But since monads are
taken in clusters only under a vinculum, corporal or composite
substances require a broader definition that includes the dominant
monad, of the first species, insofar as its requirement of having a body is
effectively filled by the monads that it dominates. 'Composite substance
exists only where a dominant monad is found with a living organic body.'
The same holds for what is called secondary matter. If primary or
'naked' matter (moles) is the requirement for having a body, secondary or
130
THE TWO FLOORS
'clothed' matter (massa) is, in a broad sense, what fills the requirement,
that is, the organism inseparable from a crowd of monads. Yet as there is
nonetheless a real distinction, secondary matter has a narrower meaning
according to which it designates only the inorganic aggregate that the
mass of monads organizes. 30 We can also remark that derivative forces are
exerted on secondary matter, or that they belong to it. It is because
material aggregates themselves possess structures and figures that
conform to statistical laws of equilibrium, of contact or of field, of thrust
or of traction, as we have seen for the extrema. But such laws or
secondary linkages imply that forces en masse are exerted upon the
aggregates, and may be collective without being, for that, statistical. These
derivative forces are effectively those of dominated monads that,
however, conserve their individuality, each in respect to another body
where it is projected as a primary force or a dominant monad. And
further, all clusters of dominated monads, along with their derivative
forces, exist only in the pure individuality of their dominant as a primary
force of surveillance.
Derivative forces thus trace an entire area that can be called mixed, or
rather, intermediary, between statistical collections and individual
distributions, and which is made manifest in the phenomena of crowds. 31
It is still more interindividual and interactive than it is collective. It is in
this aspect that derivative forces belong, as organic matter, to secondary
or clothed matter. They are exerted upon the aggregates but belong to the
organisms. Then matter has not only structures and figures but also
textures, insofar as it comprises these masses of monads from which it
cannot be detached. A Baroque conception of matter, in philosophy as in
science or in art, has to go up to that point, to a texturology that attests to
a generalized organicism, or to a ubiquitous presence of organisms (such
as Caravaggio's paintings?). 32 Secondary matter is clothed, with 'clothed'
signifying two things: that matter is a buoyant surface, a structure
endowed with an organic fabric, or that it is the very fabric or clothing,
the texture enveloping the abstract structure.
This area of interindividual, interactive clustering is quite agitated,
because it is an area of temporary appurtenances or of provisional
possessions. At all times aggregates of parts (never all at once) are leaving
my body, and thus crowds of monads that my monad was dominating
enter under another vinculum, under a new domination. It will no longer
be the same cluster, since the vinculum has changed, but neither will
131
THE FOLD
these be the same specific parts, since the new vinculum implements
another selection that breaks down and recomposes specified aggregates.
To be sure, for Leibniz there exists no place for a transformation of
species, but everywhere there are places available for mutations,
explosions, abrupt associations and dissociations, or reconcatenations.
What Leibniz calls metamorphosis or metaschematism not only involves
the initial property of bodies — in other words, their capacity to envelop
infinitely and, up to a certain point, develop their specific parts — but also
the second property, the fluxion that causes parts endlessly to leave their
specified aggregate in order to enter into entirely different aggregates that
are differently specified.
However, does it not also happen that material aggregates leave an
organic body without entering into another? Or that their monads escape
the domination where they were, without for all that entering under
another vinculum? They remain in the state of unlinked monads,
without a vinculum. Material aggregates seem to have nothing more than
secondary linkages. No longer are they fabrics, but a felt that is obtained
by simple pressing. Surely these inorganic, disorganized aggregates of felt
continue to have organisms in their subaggregates. Every body has
organisms in its folds; organisms are everywhere ... It remains the case
that not everything is organic. We might say that these inorganic bodies
are less composite or corporal substances than substantial components,
semisubstances, or sorts of substantiats. 33 In the style in which the question
is put forward, we clearly see that any response is impossible, just as we
might have wished in order to move ahead more quickly: these bodies are
purely mechanical (even with laws of extrema taken into account), these
bodies do not or no longer have any monads. For they would not be
bodies. They would only be 'phenomena,' and yet in this fashion they
would be 'perceived' by a monad. But, insofar as they are bodies, or
actualized phenomena, they 'have' monads. They follow secondary
mechanical linkages, but organisms were already doing that. Every
material particle has monads and derivative forces (although these are no
longer plastic forces), without which it would not heed any maxim or
law.
And Leibniz will never hesitate to remind us of it: organic or no, no
body can follow a law if it does not have an inner nature that enables it to
do so. It would be stupid to believe that the law acts on one occasion or
another: as if the law of gravitation 'were acting' in order to make things
fall. That is the fundamental point that opposes preestablished harmony
132
THE TWO FLOORS
to occasionalism. Leibniz reproaches Malebranche for having submitted
bodies (and souls) to general laws that — in order to be general — remain
not in the least miraculous, since no force in the individual nature of
things fails to enable it to follow them. 34 In short, inorganic bodies have
forces, monads, and a third species of monad.
These are neither dominant nor dominated monads. They might be
called defective monads, in the way that one speaks of defective conic
sections. Every monad is an inner unity, but what it is a unit of is not
forcibly inside the monad. Monads of the first species are unities of inner
change. Monads of the second species are units of organic generation and
corruption (composition). Degenerated or defective monads are themselves units of outer movement. The extrinsic character of movement is
mixed up in the very condition of bodies or of material parts, as a relation
with a surrounding, a successive determination, a mechanical linkage.
But all movement that goes, according to the law, to infinity under the
force of exterior bodies nonetheless possesses an inner unity without
which it could not be ascribed as movement, discerned as inertia.
As we have seen, the same holds for Leibniz as for Bergson: there is a
determination inevitably extrinsic to the course, but which supposes an
inner unity of the trajectory, in relation to which the extrinsic
determination is now only an obstacle or a means, or an obstacle and a
means together. Elasticity is what is determined from without, but not
the inner force exerted upon it. This force becomes only 'living' or 'dead'
in a proportion that conforms to the extrinsic state. There exists an active
elastic force, not only for the sum of movement in the universe, but for
each discernible movement in a determined aggregate, and that, in this
last case, can only be impeded or released by other aggregates. 35 These
forces or inner units of movement belong to aggregates as such, and are
defective monads that lack a vinculum. They are 'tendencies.' In effect,
Leibniz proposes to surpass all duality of force and of action, but
according to several levels.
Monads of the first species are actions, powers in action, since they are
inseparable from an actualization that they are implementing. But
monads of the second species are not 'bare' powers either; they are as
much dispositions, or habitus, inasmuch as they are arranged beneath a
vinculum. And those of the third species are tendencies to the degree that
what they await on the outside is not a movement toward action, but the
'sole suppression of impediment.' 36 It is true that the tendency is
extinguished in a flash. This seems to contradict the eternity of the monad
133
THE FOLD
and the unity of the trajectory. But the instantaneity of the tendency only
means that the instant itself is a tendency, not an atom, and that it does
not disappear without passing into the other instant: that is why it is up to
the tendency, or the inner unity of movement, to be recreated or
reconstituted at each and every instant, in accord with a particular mode
of eternity. Tendency is not instantaneous unless the instant is a tendency
to the future. Tendency dies ceaselessly, but it is only dead in the time
during which it dies, that is, instantaneously, in order to be recreated in
the following instant. 37 Monads of the third species are flashing,
twinkling in a way, through the difference of the illuminators and the
illuminated.
Would it not be a misreading to identify derivative forces — whether
elastic or plastic — with species of monads? Every monad is an individual,
a soul, a substance, a primal force, endowed with a solely inner action,
while derivative forces are said to be material, accidental, modal, 'states of
a substance' that are exerted on bodies. 38 But the issue involves knowing
what is meant by state, and if it is reducible to a predicate. If derivative
forces cannot be substances by virtue of their recognizable characters, it is
impossible to see how they could ever be predicates contained in a
substance. We believe that the terms 'state' or 'modification' must be
understood in the sense of predicate, but as a status or a (public) aspect.
Derivative forces are none other than primary forces, but they differ from them
in status or in aspect. Primary forces are monads or substances in
themselves or of themselves. Derivative forces are the same, but under a
vinculum or in the flash of an instant. In one case, they are taken in
multitudes and become plastic, while in the other they are taken in a
mass and become elastic, because masses are what change at every
instant (they do not go from one instant to another without being
reconstituted). Derivative force is neither a substance nor a predicate, but
several substances, because it exists only in a crowd or in a mass. 39 They
might be called mechanical or material forces, but in the sense in which
Leibniz also speaks of 'material souls,' because in the two cases they
belong to a body, they are present to a body, an organism or an aggregate.
They are no less really distinct from this body, and they do not act
upon it any more than they act upon one another. If they are present to
the body, it is by requisition, in the name of requisites. And this body to
which they belong is not their own, but a body that on its account
belongs to a monad removed from its status, from a multitude, and from a
134
THE TWO FLOORS
mass, in and by itself, as a primary force. The latter is also present to its
body, and without acting upon it, but in a different way. It is present by
projection. Now, in their turn, derivative forces have a body that belongs to
them, but insofar as they abandon their status in order to return in and of
themselves, each one becomes the primal force that it never ceased to be.
We have seen how Whitehead, by way of Leibniz, had developed the
public and the private as phenomenological categories.
For Leibniz the public means the status of monads, their requisition, their
in-multitude or in-mass, their derivative state. But the private means
their in-themselves of-themselves, their points of view, their primitive
condition and their projections. In the first aspect they belong to a body
that cannot be dissociated from them. In the other aspect, a body belongs
to them from which they are indissociable. It is not the same body, but
these are the same monads — except for the reasonable ones, whose basis
is only private, that have no public status, and that cannot be derived. Or
at least, reasonable monads own a 'public' status only by private means,
as distributive members of a society of spirits for whom God is the
mona rch
Leibniz often happens to distinguish three classes of monads: bare
entelechies or substantial forms that only have perceptions; animal souls
that have memory, feeling, and attention; and, finally, reasonable minds.
We have seen the direction that this classification follows. But what
relation exists among these 'degrees' in the monads given the fact that
'some more or less dominate over the others'? 41 It is that the reasonable
monads are always dominant and that the animal monads are sometimes
dominated and sometimes dominant: dominant insofar as they individually own a body, and dominated to the extent that they are related
massively to another body that a dominant, or a reasonable, monad may
or may not possess. Now entelechies are still souls, but are degenerate; that
is, they are no longer either dominant or dominated since they are tied to
a body, in a heap, and at all times. That is why, in the distinction of classes
of monads, another must be joined that is coinciding only partially, a
distinction of aspects such that a same class (animal souls) can take on
several states, sometimes by acceding to the role of dominants and
sometimes degenerating.
A real distinction holds between souls and matter and between the
body and the soul. One never acts upon the other, but each operates
according to its own laws, one by inner spontaneity or action, the other
135
THE FOLD
by outer determination or action. In other words, there exists no
influence, action, or even infrequent interaction between the two. 42
There is, however, an 'ideal action,' as when I assign something bodily to
be the cause of what happens in a soul (a suffering), or when I assign to a
soul the cause of what happens to a body (a movement taken as
voluntary). But this ideal action merely implies this: that the soul and the
body, each in its fashion or following its own laws, expresses a single and
same thing, the World. Therefore we have two really distinct expressions,
expressants of the world. One actualizes the world, the other realizes it. In
respect to a singular event of the world, in each case an 'ideal cause' will
be called the best expressant (if we can determine what 'the best' means).
Yet we realize that two worlds do not exist especially because there are
not three: there exists only one and the same world, conveyed on the one
hand by the souls that actualize it and, on the other, by the bodies that
realize it; this world does not itself exist outside of its expressants. We are
dealing with two cities, a celestial Jerusalem and an earthly one, but with
the rooftops and foundations of a same city, and the two floors of a same
house. Thus the allotment of the two worlds, the in-itself and the forourselves, gives way to an entirely different division of the rooms of the
house: private apartments are on top (individual ones) and the common
rooms below (the collectives or the totalities). Kant will derive a great
deal from Leibniz, most notably the respective autonomy of the two
floors; but at the same time Kant turns the upper floor into something
empty or inhabited, and he isolates the two floors such that in his own
way he refashions two worlds, one now having nothing more than a
regulatory value. Leibniz's solution is entirely different.
For Leibniz, the two floors are and will remain inseparable; they are
really distinct and yet inseparable by dint of a presence of the upper in the
lower. The upper floor is folded over the lower floor. One is not acting
upon the other, but one belongs to the other, in a sense of a double
belonging. The soul is the principle of life through its presence and not
through its action. Force is presence and not action. Each soul is inseparable
from a body that belongs to it, and is present to it through projection.
Every body is inseparable from the souls that belong to it, and that are
present to it by requisition. These appurtenances do not constitute an
action, and even the souls of the body do not act upon the body to which
they belong. But the belonging makes us enter into a strangely
intermediate, or rather, original, zone, in which every body acquires
individuality of a possessive insofar as it belongs to a private soul, and
136
THE TWO FLOORS
souls accede to a public status; that is, they are taken in a crowd or in a
heap, inasmuch as they belong to a collective body. Is it not in this zone,
in this depth or this material fabric between the two levels, that the upper
is folded over the lower, such that we can no longer tell where one ends
and the other begins, or where the sensible ends and the intelligible
begins? 43
Many different answers can be made to the question, W here is the fold
moving? As we have seen, it moves not only between essences and
existences. It surely billows between the body and the soul, but already
between the inorganic and the organic in the sense of bodies, and still
between the 'species' of monads in the sense of souls. It is an extremely
sinuous fold, a zigzag, a primal tie that cannot be located. And there are
even regions in this zone where the vinculum is replaced by a looser,
instantaneous linkage. The vinculum (or its replacement) only binds
souls to souls. But that is what inaugurates the inverse double belonging
by which it ties them together. It links to a soul that possesses a body
other souls that this body possesses. Having jurisdiction only over souls,
the vinculum thus engages a movement going to and from the soul to the
body and from bodies to souls (whence the perpetual overlappings of the
two floors). If, now, we can find in the body an 'ideal cause' for what
happens in the soul and, then, find in the soul an ideal cause of what
happens to the body, it works only by virtue of this coming-and-going.
Furthermore, souls can be said to be material — or forces can be said to be
mechanical — not because they act upon matter, but inasmuch as they
belong to it. Matter is what continues to make syntheses in accord with its
laws of exteriority, while souls make up units of synthesis, under the
vinculum or instantaneously, in the flash of an instant. Inversely, bodies
can be not only animal but also animated: not because they act upon
souls, but to the extent they belong to them; only souls have an inner
action that follows their own laws, while bodies are forever 'realizing' this
action in accord with their own laws.
Thus we see exactly how the two floors are allotted in relation to the
world they are conveying. The world is actualized in souls, and is realized
in bodies. It is therefore folded over twice, first in the souls that actualize
it, and again folded in the bodies that realize it, and each time according
to a regime of laws that corresponds to the nature of souls or to the
determination of bodies. And between the two folds, in the in-between of
the fold, the Zweifalt, the bending of the two levels, the zone of
137
THE FOLD
inseparability that produces the crease or seam. To state that the bodies
realize is not to say that they are real: they become real with respect to
what is actual in the soul (inner action or perception). Something completes
or realizes it in the body. A body is not realized, but what is realized in the
body is currently perceived in the soul. The reality of the body is the
realization of phenomena in the body. What is realized is the fold of the
two levels, the vinculum itself or its replacement." A Leibnizian
transcendental philosophy, which bears on the event rather than the
phenomenon, replaces Kantian conditioning by means of a double
operation of transcendental actualization and realization (animism and
materialism).
9
The new harmony
If the Baroque is defined by the fold that goes out to infinity, how can it
be recognized in its most simple form? The fold can be recognized first of
all in the textile model of the kind implied by garments: fabric or clothing
has to free its own folds from its usual subordination to the finite body it
covers. If there is an inherently Baroque costume, it is broad, in
distending waves, billowing and flaring, surrounding the body with its
independent folds, ever-multiplying, never betraying those of the body
beneath: a system like rhingrave-canons — ample breeches bedecked with
ribbons — but also vested doublets, flowing cloaks, enormous flaps,
overflowing shirts, everything that forms the great Baroque contribution
to clothing of the seventeenth century.'
Yet the Baroque is not only projected in its own style of dress. It
radiates everywhere, at all times, in the thousand folds of garments that
tend to become one with their respective wearers, to exceed their
attitudes, to overcome their bodily contradictions, and to make their
heads look like those of swimmers bobbing in the waves. We find it in
painting, where the autonomy conquered through the folds of clothing
that invade the entire surface becomes a simple, but sure, sign of a
rupture with Renaissance space (Lanfranc, but already Il Rosso
Fiorentino). Zurburan adorns his Christ with a broad, puffy loincloth in
the rhingrave style, and his Immaculate Conception wears an immense
mantle that is both open and cloaked. And when the folds of clothing spill
out of painting, it is Bernini who endows them with sublime form in
sculpture, when marble seizes and bears to infinity folds that cannot be
explained by the body, but by a spiritual adventure that can set the body
138
139
THE FOLD
ablaze. His is not an art of structures but of textures, as seen in the twenty
marble forms he fashions.
This liberation of folds that are no longer merely reproducing the finite
body is easily explained: a go-between — or go-betweens — are placed
between clothing and the body. These are the Elements. We need not
recall that water and its rivers, air and its clouds, earth and its caverns,
and light and its fires are themselves infinite folds, as El Greco's painting
demonstrates. We have only to consider the manner by which the
elements are now going to mediate, distend, and broaden the relation of
clothing to the body. It may be that painting needs to leave the frame and
become sculpture in order fully to attain these effects. A supernatural
breeze, in Johann Joseph Christian's Saint Jerome, turns the cloak into a
billowing and sinuous ribbon that ends by forming a high crest over the
saint. In Bemini's bust of Louis XIV the wind flattens and drapes the
upper part of the cloak in the image of the Baroque monarch confronting
the elements, in contrast to the 'classical' sovereign sculpted by Coysevox.
And especially, is it not fire that can alone account for the extraordinary
folds of the tunic of Bernini's Saint Theresa? Another order of the fold
surges over the Blessed Ludovica Albertoni, this time turning back to a
deeply furrowed earth. Finally, water itself is creased, and closely woven,
skintight fabric will still be a watery fold that reveals the body far better
than nudity: the famous 'wet folds' flow over Jean Goujon's bas-reliefs to
affect the entire volume, to create the envelope and the inner mold and
the spiderweb of the whole body, including the face, as in Spinazzi's and
Corradini's late masterpieces, Faith and Modesty. 2 In every instance folds
of clothing acquire an autonomy and a fullness that are not simply
decorative effects. They convey the intensity of a spiritual force exerted on
the body, either to turn it upside down or to stand or raise it up over and
again, but in every event to turn it inside out and to mold its inner
surfaces.
The great elements thus intervene in many ways: as whatever assures the
autonomy of folds of fabric in relation to the finite wearer; as themselves
raising the material fold up to infinity; as 'derivative forces' that
materialize an infinite spiritual force. It is seen not only in the
masterworks of the Baroque period, but also in its stereotypes, in its
standard formulas or its everyday productions. In fact. if we want to test
the definition of the Baroque — the fold to infinity — we cannot be limited
140
THE NEW HARMONY
to masterpieces alone; we must dig into the everyday recipes or modes of
fashion that change a genre. For example, the object of the still life is the
study of folds. The usual formula of the Baroque still life is: drapery,
producing folds of air or heavy clouds; a tablecloth, with maritime or
fluvial folds; jewelry that burns with folds of fire; vegetables, mushrooms,
or sugared fruits caught in their earthy folds. The painting is so packed
with folds that there results a sort of schizophrenic 'stuffing.' They could
not be unraveled without going to infinity and thus extracting its spiritual
lesson. It seems that this ambition of covering the canvas with folds is
discovered again in modern art, with the all-over fold.
The law of extremum of matter entails a maximum of matter for a
minimum of extension. Thus, matter tends to flow out of the frame, as it
often does in trompe l'oeil compositions, where it extends forward
horizontally. Clearly some elements, such as air and fire, tend to move
upward, but matter generally always tends to unfold its pleats at great
length, in extension. Wallin underscored this 'multiplication of lines in
width,' this taste for masses and this 'heavy broadening of mass,' this
fluidity or viscosity that carries everything along an imperceptible slope,
in a great conquest of abstraction. 'The Gothic underlines the elements of
construction, closed frames, airy filling; Baroque underlines matter:
either the frame disappears totally, or else it remains, but, despite the
rough sketch, it does not suffice to contain the mass that spills over and
passes up above.' 3
If the Baroque establishes a total art or a unity of the arts, it does so first of
all in extension, each art tending to be prolonged and even to be
prolonged into the next art, which exceeds the one before. We have
remarked that the Baroque often confines painting to retables, but it does
so because the painting exceeds its frame and is realized in polychrome
marble sculpture; and sculpture goes beyond itself by being achieved in
architecture; and in turn, architecture discovers a frame in the facade, but
the frame itself becomes detached from the inside, and establishes
relations with the surroundings so as to realize architecture in city
planning. From one end of the chain to the other, the painter has become
all urban designer. We witness the prodigious development of a
continuity in the arts, in breadth or in extension: an interlocking of
frames of which each is exceeded by a matter that moves through it.
This extensive unity of the arts forms a universal theater that includes
air and earth, and even fire and water. In it sculptures play the role of real
141
THE FOLD
characters, and the city a decor in which spectators are themselves
painted images or figurines. The sum of the arts becomes the Socius, the
public social space inhabited by Baroque dancers. Perhaps we rediscover
in modern abstract art a similar taste for a setting 'between' two arts,
between painting and sculpture, between sculpture and architecture, that
seeks to attain a unity of arts as 'performance,' and to draw the spectator
into this very performance (minimal art is appropriately named following
a law of extremum). 4 Folding and unfolding, wrapping and unwrapping
are the constants of this operation, as much now as in the period of the
Baroque. This theater of the arts is the living machine of the 'new system'
as Leibniz describes it, an infinite machine of which every part is a
machine, 'folded differently and more or less developed.'
Even compressed, folded, and enveloped, elements are powers that
enlarge and distend the world. It hardly suffices to speak of a succession of
limits or of frames, for every frame marks a direction of space that coexists
with the others, and each form is linked to unlimited space in all
directions at once. It is a broad and floating world, at least on its base, a
scene or an immense plateau. But this continuity of the arts, this
collective unity in extension, goes out and beyond, toward an entirely
different unity that is comprehensive and spiritual, punctual, is indeed
conceptual: the world as a pyramid or a cone, that joins its broad material
base, lost in vapors, to an apex, a luminous origin or a point of view.
Leibniz's world is one that encounters no difficulty in reconciling full
continuity in extension with the most comprehensive and tightly knit
individuality. 5 Bernini's Saint Theresa does not find her spiritual unity in
the satyr's little arrow, that merely spreads fire, but in the upper origin of
the golden rays above.
The law of the cupola, a Baroque figure par excellence, is double: its
base is a vast ribbon, at once continuous, mobile, and fluttering, that
converges or tends toward a summit as its closed interiority (Lanfranc's
cupola, for Sant'Andrea della Valle). The apex of the cone is probably
replaced by a rounded point that inserts a concave surface in the place of
an acute angle. It is not only in order to soften the point, but also
because the latter must still be in an infinitely folded form, bent over a
concavity, just as the base is of a matter that can be unwrapped and
folded over again. This law of the cupola holds for all sculpture; it shows
how all sculpture amounts to architecture, and to city planning. The
sculpted body, taken in an infinity of folds of marble cloth, goes back, on
the one hand, to a base made of personages or powers, genuine
142
THE NEW HARMONY
elements of bronze that mark not so much limits as directions of
development. On the other, it refers to the upper unity, the obelisk, the
monstrance or stucco curtain, from which falls the event that affects it.
Thus the derivative forces are allotted to the lower area and primal force
to the upper reaches.
It even happens that an organized group that follows the vertical tends
to topple in an optical sense, and to place its four powers on a fictive
horizontal plan, while the sculpted body appears to be inclined by half of
a right angle, in order to acquire height in relation to this base (the tomb
of Gregory XV). The world as cone brings into coexistence, for the arts
themselves, the highest inner unity and the broadest unity of extension.
It is because the former could not exist without the latter. For some time
now the idea of an infinite universe has been hypothesized, a universe
that has lost all center as well as any figure that could be attributed to it;
but the essence of the Baroque is that it is given unity, through a
projection that emanates from a summit as a point of view. For some time
the world has been understood on a theatrical basis, as a dream, an
illusion — as Harlequin's costume, as Leibniz would say.
But the essence of the Baroque entails neither falling into nor
emerging from illusion but rather realizing something in illusion itself, or
of tying it to a spiritual presence that endows its spaces and fragments with
a collective unity. 6 The prince of Hamburg, and all of Kleist's characters,
are not so much Romantic as they are Baroque heroes. Prey to the
giddiness of minute perceptions, they endlessly reach presence in illusion,
in vanishment, in swooning, or by converting illusion into presence:
Penthesilea-Theresa? The Baroque artists know well that hallucination
does not feign presence, but that presence is hallucinatory.
Walter Benjamin made a decisive step forward in our understanding of
the Baroque when he showed that allegory was not a failed symbol, or an
abstract personification, but a power of figuration entirely different from
that of the symbol: the latter combines the eternal and the momentary,
nearly at the center of the world, but allegory uncovers nature and
history according to the order of time. It produces a history from nature
and transforms history into nature in a world that no longer has its
center.' If we consider the logical relation of a concept to its object, we
discover that the linkage can be surpassed in a symbolic and an allegorical
way. Sometimes we isolate, purify, or concentrate the object; we cut all
its ties to the universe, and thus we raise it up, we put it in contact no
143
THE FOLD
longer with its simple concept, but with an Idea that develops this
concept morally or esthetically.
Sometimes, on the contrary, the object itself is broadened according to
a whole network of natural relations. The object itself overflows its frame
in order to enter into a cycle or a series, and now the concept is what is
found increasingly compressed, interiorized, wrapped in an instance that
can ultimately be called 'personal.' Such is the world as cone or cupola,
whose base, always in extension, no longer relates to a center but tends
toward an apex or a summit. The world of allegory is especially projected
in devices and emblems; for example, a porcupine is drawn to illustrate
the inscription 'From near and afar' because the porcupine stands its
quills on end when near, but it also shoots them from afar. Devices or
emblems have three elements that help us understand the basis of
allegory: images or figurations, inscriptions or maxims, and personal
signatures or proper names of owners. Seeing, reading, dedicating (or
signing).
First, basic images tend to break their frames, form a continuous fresco,
and join broader cycles (either of other aspects of the same animal, or
aspects of other animals) because the pictured form — an animal or
whatever — is never an essence or an attribute, as in a symbol, but an
event, which is thus related to a history or to a series. Even in the worst of
representations, 'Fidelity Crowns Love,' we find the charm of allegory,
the presence of the event that makes an appeal to an antecedent and a
sequel. Second, inscriptions, which have to keep a shrouded relation with
images, are themselves propositions akin to simple and irreducible acts,
which tend toward an inner concept, a truly propositional concept. A
judgment is not broken down into a subject and an attribute; rather, the
whole proposition is a predicate, as in 'From near and afar.' Finally, the
many inscriptions or propositions — that is, the propositional concept itself
— is related to an individual subject who envelops it, and who allows
himself or herself to be determined as the owner: allegory offers us
Virtues, but these are not virtues in general. They belong to Cardinal
Mazarin and figure among his effects. Even the Elements are put forth as
belongings pertaining to Louis XIV or to someone else.
The concept becomes a 'concetto,' or an apex, because it is folded in the
individual subject just as in the personal unity that amasses for itself the
many propositions, but that also projects them in the images of the cycle
or the series. 8 Although practicians and theorists of concettism had rarely
144
THE NEW HARMONY
been philosophers, they developed rich materials for a new theory of the
concept reconciled with the individual. They fashioned the world in the
shape of a cone that becomes manifest and is imposed in the Baroque
world. This world even appears — in the frontispiece to Emmanuel
Tesauro's La lunette d'A ristote (1655) — as an allegory of allegory. 'At the
center of this frontispiece we find a conical anamorphosis, that is, an
image projected in the shape of a cone. The maxim "Omnis in unum" has
thus become legible; this deformed moral is written by an allegorical
figure who represents Painting. According to Tesauro, Painting would
have the power of transforming the real into figured shapes, but the cone
is what allows the real to be recovered.' 9
How much Leibniz is part of this world, for which he provides the
philosophy it lacks! The principal examples of this philosophy are shown
in the transformation of the perceptible object into a series of figures or
aspects submitted to a law of continuity; the assignation of events that
correspond to these figured aspects, and that are inscribed in propositions;
the predication of these propositions to an individual subject that
contains their concept, and is defined as an apex or a point of view, a
principle of indiscernibles assuring the interiority of the concept and the
individual. Leibniz occasionally sums it up in the triad, 'scenographiesdefinitions-points of view.' 1° The most important consequence that
ensues concerns the new relation of the one and the multiple. Always a
unity of the multiple, in the objective sense, the one must also have a
multiplicity 'of' one and a unity 'of' the multiple, but now in a subjective
sense. Whence the existence of a cycle, 'Omnis in unum,' such that the
relations of one-to-multiple and multiple-to-one are completed by a oneto-one and a multiple-to-multiple, as Michel Serres has shown. I l This
square finds its solution in the distributive character of the one and an
individual unit or Every, and in the collective character of the multiple as
a composite unit, a crowd or a mass. The belonging-to and its inversion
show how the multiple belongs to a distributive unity, but also how a
collective unity pertains to the multiple.
And if it is true that appertaining — belonging to — is the key to
allegory, then Leibniz's philosophy must be conceived as the allegory of
the world, the signature of the world, but no longer as the symbol of a
cosmos in the former manner. In this respect the formula of the
Monadologie, that 'components symbolize with simple units,' far from
marking a return to the symbol, indicates the transformation or
translation of the symbol into allegory. The allegory of all possible worlds
145
THE NEW HARMONY
THE FOLD
one
one
•
multiple
multiple
appears in the story of the Thiodicee — which might be called a pyramidal
anamorphosis — which combines figures, inscriptions or propositions,
individual subjects or points of view with their propositional concepts
(thus, 'to violate Lucretia' is a proposition-predicate, this Sextus is its
subject as a point of view, and the inner concept contained in the point of
view is the 'Roman Empire,' whose allegory Leibniz thus puts before
us).' 2 The Baroque introduces a new kind of story in which, following the
three traits above, description replaces the object, the concept becomes
narrative, and the subject becomes point of view or subject of expression.
The basic unity, the collective unity in extension, the horizontal
material process that works by exceeding the frame, the universal theater
as a continuity of the arts, tends toward another, now a private, spiritual,
and vertical unity of the summit. And a continuity exists not only at the
base, but all the way from the base to the summit because it cannot be
said where one begins and the other ends. Perhaps Music is at the apex,
while the theater that moved in that direction is revealed as opera,
carrying all the arts toward this higher unity. Music is in fact not without
ambiguity — especially since the Renaissance — because it is at once the
intellectual love of an order and a measure beyond the senses, and an
affective pleasure that derives from bodily vibrations.' 3 Furthermore, it is
at once the horizontal melody that endlessly develops all of its lines in
extension, and the vertical harmony that establishes the inner spiritual
unity or the summit, but it is impossible to know where the one ends and
the other begins. But, precisely, Baroque music is what can extract
harmony from melody, and can always restore the higher unity toward
which the arts are moving as many melodic lines: this very same
elevation of harmony makes up the most general definition of what can
be called Baroque music.
146
Many critics reckon that Leibniz's concept of harmony remains quite
general, almost as a synonym of perfection, and refers to music only
metaphorically: 'unity in variety,' 'harmony exists when a multiplicity is
linked to a determinable unity,' 'ad quamdam unitatem.' 14 Two reasons
may, however, lead us to believe that the musical allusion is both exact
and reflective of what is happening in Leibniz's time. The first is that
harmony is always thought to be preestablished. which specifically implies
a very new state of things. And if harmony is so strongly opposed to
occasionalism, it is to the degree that occasion plays the role of a sort of
counterpoint that still belongs to a melodic and polyphonic conception of
music. It is as if Leibniz were attentive to the innovations happening in
Baroque music all the while his adversaries remained attached to older
conceptions.
The second reason stands because harmony does not relate multiplicity to some kind of unity, but to 'a certain unity' that has to offer
distinctive or pertinent traits. In effect, in a programmatic text that
appears to take up in detail a writing by the neo-pythagorean Nicolas of
Cusa, Leibniz suggests three traits: Existence, Number, and Beauty.
Harmonic unity is not that of infinity, but that which allows the existant
to be thought of as deriving from infinity; it is a numerical unity insofar as
it envelops a multiplicity ('to exist means nothing other than to be
harmonic'); it is extended into the affective domain insofar as the senses
apprehend it aesthetically, in confusion.' 5 The question of harmonic
unity becomes that of the 'most simple' number, as Nicolas of Cusa.
states, for whom the number is irrational. But, although Leibniz also
happens to relate the irrational to the existant, or to consider the
irrational as a number of the existant, he feels he can discover an infinite
series of rationals enveloped or hidden in the incommensurable, in a
particular form. Now this form in its most simple state is that of the inverse
or reciprocal number, when any kind of denominator shares a relation with
the numerical unity as a numerator:
1
Ti
the inverse of n.' 6
We can consider the different appearances of the word 'harmonic.' They
constantly refer to inverse or reciprocal numbers: the harmonic triangle
of numbers that Leibniz invented to complete Pascal's arithmetical
triangle; the harmonic mean that retains the sums of inverses; but also
147
THE FOLD
THE NEW HARMONY
harmonic division, harmonic circulation, and what will later be
discovered as the harmonics of a periodic movement."
However simple these examples, they allow us to understand certain
traits of the theory of monads, and first of all why we go, not from
monads to harmony, but from harmony to monads. Harmony is
monadological, but because monads are initially harmonic. The programmatic text states the point clearly: when the infinite Being judges
something to be harmonic, it conceives it as a monad, that is, as an
intellectual mirror or expression of the world. Thus the monad is the
existant par excellence. It is because, conforming to Pythagorean and
Platonic traditions, the monad is clearly a number, a numerical unit. For
Leibniz the monad is clearly the most 'simple' number, that is, the
inverse, reciprocal, harmonic number. It is the mirror of the world
because it is the inverted image of God, the inverse number of infinity,
contrary, attests to the irreducibility of 'particular breezes' distributed
through many pipes; the world's soul implies a confusion that belongs to
pantheism, between the number and its inverse, between God and the
monad. 19 The mathematician Abraham Robinson has proposed considering Leibniz's monad as an infinite number quite different from
transfinites, as a unit surrounded by a zone of infinitely small numbers
tbat reflect the convergent series of the world. 2° And the point is
effectively that of knowing how the unit of a numerator is at once
combined with the infinite of the denominator,
1
(
but with a distinctive variable value
1
1
1
1
(— , necessarily holding for —, —, or — ...):
4
2 3
n
instead of
each monad expresses the world, but 'cannot equally well express
everything; for otherwise there would be no distinction between souls.' 21
We have seen how Leibniz was able to implement the conciliation on his
own account: each monad expresses the world
(even though sufficient reason is the inverse of infinite identity). God
thinks the monad as his own inverse, and the monad conveys the world
only because it is harmonic. From then on preestablished harmony will
be an original proof of the existence of God, to the degree that the divine
formula,
oo
1
can be found: it is a proof by the inverse. 18
The inverse number has special traits; it is infinite or infinitely small,
but also, by opposition to the natural number, which is collective, it is
individual and distributive. Units taken as numerators are not identical
among each other because they receive from their respective denominators a distinctive mark. That is why harmony does not at all confirm the
hypothesis of a soul of the world or of a universal spirit but, to the
148
1
00
but clearly expresses only one particular zone of the world
1
n
(with n in each case having a specific value). Each monad includes the
world as an infinite series of infinitely small units, but establishes
differential relations and integrations only upon a limited portion of the
series, such that the monads themselves enter in an infinite series of
inverse numbers. In its own portion of the world or in its clear zone, each
monad thus presents accords, inasmuch as an 'accord' can be called the
relation of a state with its differentials, that is, with the differential
relations among infinitely small units that are integrated into this state.
149
THE FOLD
Whence the double aspect of the accord, insofar as it is the product of an
intelligible calculus in an affective state. To hear the noise of the sea is
tantamount to striking a chord, and each monad is intrinsically
distinguished by its chords. 22 Monads have inverse numbers, and chords
are their 'inner actions.'
Conveying the entire world, all monads include it in the form of an
infinity of tiny perceptions, little solicitations, little springs or bursts of
force: the presence of the world within me, my being-for the world, is an
'anxiousness' (being on the lookout). I produce an accord each time I can
establish in a sum of infinitely tiny things differential relations that will
make possible an integration of the sum — in other words, a clear and
distinguished perception. It is a filter, a selection. Now, on the one hand, I
am not always capable of doing so at all times, but only in a particular
zone that varies with each monad, and such that, for each monad, the
greatest part remains in a state of detached dizziness, undifferentiated,
unintegrated, in an absence of accord. All that can be said, to the
contrary, is that no part of the world can be taken in the zone of a
determinable monad, and that does not carry accords produced by this
monad. But on the other hand especially, the linkages produced by a
monad can be very different. Leibniz's writings clearly guarantee a
classification of accords.
It would be wrong to seek a direct transposition of musical chords in
the way they are developed in the Baroque; and yet it would also be
erroneous to conclude with Leibniz's indifference in respect to the
musical model: the question, rather, involves analogy. And we know that
Leibniz was always trying to bring it to a new rigor. At its highest degree,
a monad produces major and perfect accords: these occur where the small
solicitations of anxiety, far from disappearing, are integrated in a pleasure
that can be continued, prolonged, renewed, multiplied; that can
proliferate, be reflexive and attractive for other accords, that give us the
force to go further and further. This pleasure is a 'felicity' specific to the
soul; it is harmonic par excellence, and can even be felt in the midst of the
worst sufferings, such as in the joy of martyrs. In this sense the perfect
accords are not pauses, but, on the contrary, dynamisms, which can pass
into other accords, which can attract them, which can reappear, and
which can be infinitely combined. 23 In the second place, we speak of
mirror accords when the differential relations among the infinitely small
parts only allow integrations or instable combinations, simple pleasures
that are inverted into their contrary, unless they are attracted by a perfect
150
THE NEW HARMONY
accord. For, in the third place, integration can be made in pain. That is the
specific character of dissonant accords, the accord here consisting in
preparing and resolving dissonance, as in the double operation of
Baroque music. The preparation of dissonance means integrating the
half-pains that have been accompanying pleasure, in such ways that the
next pain will not occur 'contrary to all expectations.' Thus the dog was
musical when it knew how to integrate the almost imperceptible
approach of the enemy, the faint hostile odor and the silent raising of
the stick just prior to its receiving the blow. 24 The resolution of
dissonance is tantamount to displacing pain, to searching for the major
accord with which it is consonant, just as the martyr knows how to do it
at the highest point and, in that way, not suppress pain itself, but suppress
resonance or resentment, by avoiding passivity, by pursuing the effort to
suppress causes, even if the martyr's force of opposition is not attained. 25
All of Leibniz's theory of evil is a method to prepare for and to resolve
dissonances in a 'universal harmony.' A counterexample would be
furnished by the damned, whose souls produce a dissonance on a unique
note, a breath of vengeance or resentment, a hate of God that goes to
infinity; but it is still a form of music, a chord — though diabolical — since
the damned draw pleasure from their very pain, and especially make
possible the infinite progression of perfect accords in the other souls. 26
Such is the first aspect of harmony, which Leibniz calls spontaneity. The
monad produces accords that are made and are undone, and yet that
have neither beginning nor end, that are transformed each into the other
or into themselves, and that tend toward a resolution or a modulation.
For Leibniz even the diabolical accord can be transformed. It is because
the monad is expression; it expresses the world from its own point of view
(and musicians such as Rameau forever underscore the expressive
character of the chord). Point of view signifies the selection that each
monad exerts on the whole world that it is including, so as to extract
accords from one part of the line of infinite inflection that makes up the
world.
Thus the monad draws its accords from its own depths. It matters little if
for Leibniz the inner selection is still not made through the first harmonics,
but through differential relations. In any event the soul sings of itself and is
the basis of self-enjoyment. The line of the world is inscribed vertically upon
the unitary and inner surface of the monad, that then extracts the accords
that are superimposed. That is why it can be said that harmony is a vertical
151
THE FOLD
THE NEW HARMONY
writing that conveys the horizontal line of the world: the world is like the
book of music that is followed successively or horizontally by singing. But
the soul sings of itself because the tablature of the book has been engraved
vertically and virtually, 'from the beginning of the soul's existence' (the
first musical analogy of Leibnizian harmony). 27
There exists a second aspect of harmony. Monads are not only
expressions, but they also express the same world that does not exist
outside of its expressions. 'All simple substances will always have a
harmony among each other because they always represent the same
universe'; monads have no reason to be closed; they are not monastic,
and they are not the cells of monks because they include the same —
solidary but not solitary — world. 28 We can call concertation this second
aspect. Many musicologists prefer to speak of the 'concertant' style
instead of Baroque music. This time, insofar as what is expressed is a
single and same world, the issue concerns an accord of spontaneities
themselves, an accord among accords. But among what, in fact, is there
accord? For Leibniz preestablished harmony has many formulas, each in
respect to the spot through which the fold is passing: sometimes it is
among principles, mechanism, or finality, or even continuity and
indiscernibles; at others, between the floors, between Nature and Grace,
between the material universe and the soul, or between each soul and its
organic body; and at others again, among substances, simple substances
and corporal or composite substances. But it is easy to see that in every
event harmony is always between souls themselves or monads.
Organic bodies are inseparable from monads taken in crowds, and
harmony appears between the inner perceptions of these monads and
those of their dominant monad. And even inorganic bodies are
inseparable from monads made instantaneous, among which harmony
exists. 29 But, if there is a preestablished accord among all these monads
that express a single and same world, it is no longer in the way that the
accords of the one might be transformed into the accords of another, or
that one monad might produce accords in the other. Accords and their
transformations are strictly on the inside of every monad; vertical,
absolute 'forms' that make up the monads remain disconnected, and thus
we do not go from one to the other one after the other by resolution or
modulation. Following a second and strictly Baroque analogy, Leibniz
appeals to the conditions of a choir in which two monads each sing their
part without either knowing or hearing that of the other, and yet they are
'in perfect accord.' 3°
152
Of what does this concertation consist? We know that the bottom of a
monad resembles a lapping of the infinitely little things that it cannot
clarify, or from which it cannot extract accords. Its clear region is
effectively quite selective and partial, and only constitutes a small zone of
the world that it includes. However, since this zone varies from one
monad to another, there is nothing obscure in a given monad about
which it cannot be said: that it is taken in the clear region of another
monad, that it is taken in an accord inscribed on another vertical surface.
Thus we have a sort of law of the inverse: there exists for monads that
convey obscurely at least one monad that conveys clearly. Since all
monads convey the same world, we could state that the one that clearly
expresses an event is a cause, while the one that expresses it obscurely is
an effect: the causality of one monad upon another, but a purely 'ideal'
causality, without real action, since what each of the two monads is
expressing only refers to its own spontaneity.
In any event this law of the inverse would have to be less vague; it
would have to be established among monads that are better determined.
If it is true that each monad is defined by a clear and distinguished zone,
this zone is not unchanging, but has a tendency to vary for each monad,
in other words, to increase or diminish according to the moment: in every
flash of an instant, the privileged zone offers spatial vectors and temporal
tensors of augmentation or diminution. A same event can thus be
expressed clearly by two monads, but the difference nonetheless subsists
at every instant, for the one expresses the event more clearly or with less
confusion than the other, following a vector of augmentation, while the
other expresses it following a vector of diminution.
Now we can return to the level of bodies or of corporal substances:
when a boat moves ahead on the water, we say the vessel's movement is
the cause for the movements of the water that fills the area it has just
passed through. That is only an ideal cause, because the proposition, 'the
prow cuts the water,' is clearer than the proposition, 'the water pushes
the stern.' Causality always moves not just from the clear to the obscure,
but from the clearer (or more-clear) to the less-clear, the more-confused.
It goes from what is more stable to what is less. Such is the requirement of
sufficient reason: clear expression is what increases in the cause, but also
what diminishes in the effect?' When our soul feels pain, we say that
what happens in the body is the cause, because it is a clearer and stable
expression that pain in the soul can only resemble. Inversely, it is the soul
that is the cause when our body makes what is called a voluntary
1
153
THE FOLD
movement. Concertation is the sum of ideal relations of causality. Ideal
causality is concertation itself, and therefore is perfectly reconciled with
spontaneity: ideal causality goes from the more-clear to the less-clear, but
what is clearer in a substance is produced by that substance by virtue of
its own spontaneity, and the same holds for the less-clear in the other,
when the other substance produces it by virtue of its own. 32
The two aspects of harmony are perfectly linked. Spontaneity is
tantamount to the production of each monad's inner accords on its
absolute surface. Concertation amounts to the correspondence according
to which there can be no major and perfect accord in a monad unless there is a
minor or dissonant accord in another, and inversely. All combinations are
possible without there ever being same accord in two monads. Each
monad spontaneously produces its accords, but in correspondence with
those of the other. Spontaneity is the inner or sufficient reason applied to
monads. And concertation is this same reason applied to spatiotemporal
relations that follow from the monads. If space-time is not an empty area,
but the order of coexistence and the succession of monads themselves,
the order has to be marked out, oriented, vectored; in the instance of each
monad movement has to go from the more-clear monad to the less-clear
monad, or from the perfected accord to the less-perfected accord, for the
clearest or the most perfected is reason itself. In the expression
'preestablished harmony,' 'preestablished' is no less important than
'harmony.' Harmony is twice pre-established: by virtue of each
expression, of each expressant that owes only to its own spontaneity or
interiority, and by virtue of the common expression that establishes the
concert of all these expressive spontaneities. It is as if Leibniz were
delivering us an important message about communication: don't
complain about not having enough communication, for there is always
plenty of it. Communication seems to be of a constant and preestablished
quantity in the world, akin to a sufficient reason.
The most general given has vertical harmony in accords in a position
subordinate to horizontal melody, to the horizontal lines of melody.
These lines do not disappear, obviously, but they do submit to a harmonic
principle. It is true that this subordination implies something other than
preestablished harmony: it is the vinculum that acts as a 'continuous bass'
and prepares a tonality. Thus it can be stated that each dominant monad
has a vinculum, a continuous bass, as well as a tonality that carries its
inner chords. But, as we have seen, under every vinculum infinities of
154
THE NEW HARMONY
'dominated' monads begin to group into clusters that can organize
material aggregates (these aggregates can move from one tonality to
another, from one vinculum to another, while reorganizing, or even
reproducing themselves from one instant to another). In short, the
continuous bass does not impose a harmonic law upon the lines of
polyphony without having the melody retrieve a new freedom and unity,
or a flux.
In effect, in polyphony lines were as if screwed down by points, and as
if counterpoint only affirmed bi-univocal correspondences among points
on diverse lines: Malebranche's occasionalism remains precisely a
philosophical polyphony, in which occasion plays the role of counterpoint, in a perpetual miracle or a constant intervention of God. In the
new system, on the contrary, melody, freed of this modal counterpoint,
gains a force of variation that consists in introducing all kinds of foreign
elements in the realization of the accord (delays, interweavings,
appoggiaturas, etc., whence ensues a new tonal or 'luxuriant' counterpoint), but also a force of continuity that will develop a unique motif,
even across eventual tonal diversities ('continuo homophone'). 33 At its
limit the material universe accedes to a unity in horizontal and collective
extension, where melodies of development themselves enter into
relations of counterpoint, each spilling over its frame and becoming the
motif of another such that all of Nature becomes an immense melody and
flow of bodies. 34 And this collective unity in extension does not
contradict the other unity, the subjective, conceptual, spiritual, harmonic, and distributive unity.
To the contrary, the former depends upon the latter by furnishing it
with a body, exactly in the way the monad requires a body and organs,
without which it would have no inkling of Nature. The 'conformity of the
senses' (melody) indicates where I recognize harmony in the rea1. 35 There
is not only harmony in harmony, but harmony between harmony and
melody. In this sense harmony goes from the soul to the body, from the
intelligible to the sensible, and extends into the sensible. Rameau will say
that it goes by principle and by instinct. When the Baroque house
becomes musical, the upper floor includes vertical harmonic monads,
inner accords that each one produces in its respective chamber, and the
correspondence or concertation of these accords; the lower floor stretches
out along an infinity of horizontal melodic lines drawn into each other,
where at the same time it embroiders and develops its sensible variations
and continuity. Yet, because the upper floor is folded over the lower floor,
155
THE FOLD
following tonality, the accords are realized. It is in melody that harmony
is achieved.
It seems difficult not to be moved by the totality of exact analogies
between Leibnizian harmony and the harmony on which, at the same
time, Baroque music is based. Even the concert of monads, which Leibniz
invokes in his second analogy, not only brings in harmony but also a state
of inexplicable melody lacking any Baroque reference. Such are the
principal traits by which musicologists have been able to define a Baroque
music: music as expressive representation, expression here referring to
feeling as if to an affect of accord (for example, an unprepared dissonance,
an expression of despair and of fury); vertical harmony, the first in line in
respect to horizontal melody, insofar as it is in chords, but no longer in
intervals, and treats dissonance as a function of chords themselves; the
concertant style that moves by contrasts among voices, instruments or
groups of different density; melody and counterpoint that change their
nature (luxuriant counterpoint and continuo homophone); continuous
bass, preparing or consolidating a tonality that the accords include and in
which they are resolved, but also submitting the melodic lines to the
harmonic principle. 3 6
Every one of these traits that does not fail to attest to a 'preestablishment' of harmony also has its analogy in Leibnizian harmony.
Leibniz loves to compare diverse conceptions of the body-and-soul to
modes of correspondence between two clocks that include influx, chance,
or even harmony (that he judges to be superior). These too are the three
'ages' of music, which go from monody, to unison, to harmonic
polyphony or counterpoint in accords — in other words, the Baroque.
We could hardly be satisfied in establishing binary relations between
the text and music that would inevitably be arbitrary. How to fold the text
so that it can be enveloped in music? This problem of expression is not
fundamental to opera alone. Baroque musicians count among the first,
perhaps, to propose a systematic answer: accords are what determine the
affective states that conform to the text, and that furnish voices with the
necessary melodic inflections. Whence Leibniz's idea that our souls sing
of themselves — spontaneously, in chords — while our eyes read the text
and our voices follow the melody. The text is folded according to the
accords, and harmony is what envelops the text. The same expressive
problem will animate music endlessly, from Wagner to Debussy and now
up to Cage, Boulez, Stockhausen, and Berio.
156
THE NEW HARMONY
The issue is not one of relation, but of 'fold-in,' or of 'fold according to
fold.' What has happened to cause the answer — or rather, the quite
diverse range of answers — to change since the Baroque musicians?
Solutions no longer pass through accords. It is because the conditions of
the problem itself have changed: we have a new Baroque and a neoLeibnizianism. The same construction of the point of view over the city
continues to be developed, but now it is neither the same point of view
nor the same city, now that both the figure and the ground are in
movement in space. 37 Something has changed in the situation of monads,
between the former model, the closed chapel with imperceptible
openings, and the new model invoked by Tony Smith, the sealed car
speeding down the dark highway. In summary we can attribute what has
changed to two principal variables.
Leibniz's monads submit to two conditions, one of closure and the
other of selection. On the one hand, they include an entire world that
does not exist outside of them; on the other, this world takes for granted a
first selection, of convergence, since it is distinguished from other possible
but divergent worlds, excluded by the monads in question; and it carries
with it a second selection of consonance, because each monad in question
will fashion itself a clear zone of expression in the world that it includes
(this is the second selection that is made by means of differential relations
or adjacent harmonics). Now the selection is what tends to be
disappearing, first of all and in every way. If harmonics lose all privilege
of rank (or relations, all privilege of order), not only are dissonances
excused from being 'resolved,' divergences can be affirmed, in series that
escape the diatonic scale where all tonality dissolves. But when the
monad is in tune with divergent series that belong to incompossible
monads, then the other condition is what disappears: it could be said that
the monad, astraddle over several worlds, is kept half open as if by a pair
of pliers.
To the degree that the world is now made up of divergent series (the
chaosmos), or that crapshooting replaces the game of Plenitude, the
monad is now unable to contain the entire world as if in a closed circle
that can be modified by projection. It now opens on a trajectory or a spiral
in expansion that moves further and further away from a center. A
vertical harmonic can no longer be distinguished from a horizontal
harmonic, just like the private condition of a dominant monad that
produces its own accords in itself, and the public condition of monads in a
crowd that follow lines of melody. The two begin to fuse on a sort of
157
THE FOLD
diagonal, where the monads penetrate each other, are modified,
inseparable from the groups of prehension that carry them along and
make up as many transitory captures.
The question always entails living in the world, but Stockhausen's
musical habitat or Dubuffet's plastic habitat do not allow the differences
of inside and outside, of public and private, to survive. They identify
variation and trajectory, and overtake monadology with a 'nomadology.'
Music has stayed at home; what has changed now is the organization of
the home and its nature. We are all still Leibnizian, although accords no
longer convey our world or our text. We are discovering new ways of
folding, akin to new envelopments, but we all remain Leibnizan because
what always matters is folding, unfolding, refolding.
Notes
A Note on References
When referring to Leibniz and other works, Deleuze can appear cryptic or
allusive. To make his references clear for readers of English, I have
arranged the bibliographical materials in an order that can be conceived
as being arranged in three tiers.
The first includes the works of Leibniz to which Deleuze refers. We
know that Leibniz developed his philosophy in fragments, in private
correspondence, in transit, and in the toss of circumstance between the
end of the seventeenth century and the early years of the Enlightenment;
that he worked with ease in Latin, German, and French; and that he
never intended to finish a complete work. Further; the heritage of his
writing is affected by the tumultuous relations that France and Germany
have experienced since the eighteenth century. Wars have interrupted
completion of any final critical edition. For Deleuze, the history and
condition of writing bear resemblance to fragmentary activity that
characterizes the oeuvre of Balzac and Proust, for whom, as he explained
in Proust et les signes ( [Paris: PUF, 1979 reed.], 197) a 'work' amounts to an
effect that exceeds the material totality of a body.
Readers of Leibniz are thus required to consult a variety of editions
published over the last two centuries. Deleuze uses many of them, but he
ostensibly prefers to consult, where possible, current and readily available
reprints. For French readers these include:
158
159
NOTES
THE FOLD
Nouveaux essais sur l'entendement humain. Ed. Jacques Brunschwig.
Paris: Garnier/Flammarion, 1966.
Essais de theodicie sur la bowl de Dieu, la liberte" de 1' homme et Vorigine
du mal. . . . suivi de la Monadologie. Ed. Jacques Brunschwig. Paris:
Garnier/Flammarion, 1969.
Deleuze often cites the number of the paragraph (indicated by §) to allow
for cross-reference with other editions. French editions of Leibniz often
include numerical ciphers for each movement or paragraph. Some
English translations (such as New Essays on Human Understanding and the
Monadology) are thus equipped, but others are not (On Liberty, The
Correspondence with A rnauld, etc.). Wherever Deleuze quotes the principal
texts of Leibniz, for sake of clarity and thoroughness I refer to the most
current and definitive English versions. I have chosen G. H. R.
Parkinson's carefully selected anthology of Leibniz's philosophical
writings to serve as an accompaniment to The Fold. It is easily obtained
and modestly priced. I also refer to H. T. Mason's concise translation of
the Leibniz/A rnauld Correspondence, as well as Peter Remnant and
Jonathan Bennett's translation of the New Essays on Human Understanding.
Both works are prepared with equal precision and elegance. The
translators provide indications of volume, book, page, and paragraph
that concur with Deleuze's French editions. Whenever Deleuze cites texts
that can be located in these editions, I refer to them and cite their English
translations. The following abbreviations and sources are used:
Mason
H. T. Mason, ed. and trans., The Leibniz/A rnauld
Correspondence. New York: Garland, 1985.
Parkinson
G. H. R. Parkinson, ed., and trans. (with Mary
Morris), Gottfried W ilhelm Leibniz: Philosophical W ritings. London: J. M. Dent and Sons (Everyman
Library), 1973 (1990 reprint).
Remnant/Bennett Peter Remnant and Jonathan Bennett, ed. and
trans., Leibniz: New Essays on Human Understanding.
Cambridge: Cambridge University Press, 1981.
In each instance where material is quoted, the appropriate abbreviation
160
and page number can be found in the notes. They follow the citation and
are set between brackets.
The second tier involves works of Leibniz that are not easily correlated
with English translations. La theodicie, for example, is often abridged or
fragmented in English anthologies. Other important pieces — the letters to
Des Bosses or Lady Masham, The Clarification of Difficulties that Bayle found
in the New System, etc. — are available in works that constitute the primary
bibliography of Leibniz's writings. Deleuze refers to them often and
consistently. They are as follows:
GPh
Die philosophischen Schriften von G. W . Leibniz. Ed. C. I. Gerhardt. 7
vols. Berlin, 1875-90.
Louis Couturat, ed., Opuscules et fragments inerdits de Leibniz. Paris,
1903.
Dutens Louis Dutens, ed., Gothofredi Guillelmi Leibnitii . . . opera amnia. 6
vols. Geneva, 1768.
GM
Leibnizens mathematische Schriften. 7 vols. Berlin and Halle, 184963.
F
Foucher de Careil, ed., Nouvelles lettres et opuscules inidits de
Leibniz. Paris: 1857-75.
I. Jagodinsky, ed., Leibnitiana: Elementa philosophiae arcanae de
J
summa rerum. Kazan, 1913.
P
Yvan Belaval, ed., Leibniz: Profession de foi du philosophe. Paris:
Vrin, 1961.
C
I have directly translated Deleuze's quotations or translations of material
taken from these texts. Because no handy edition of La theodicie is
available in English (except for E. M. Huggard's translation, London,
1952), I have taken the liberty of translating Deleuze's quotations from
his French copies. Other materials from other sources, both primary and
secondary, in French, or in non-English sources, are translated directly
from Deleuze's citations. Wherever Deleuze refers to French translations
of works in English, I cite the original. Rather than retranslating the titles
of many of Leibniz's works back into English, because they are clear, I
have retained them in the way he notes them. The French titles convey
well, it seems, the spirit of Deleuze's relation with Leibniz.
Finally, on a third tier, are placed other significant materials that
belong to contemporary sources. These often include the fine arts,
mathematics, logic, literature, military strategy, music, and philosophy.
161
THE FOLD
NOTES
Deleuze refers to many works that circulate in these contexts - often in
Parisian editions, gallery catalogues, brochures, or in works pertaining to
the French academic system - but are not easily located in libraries
elsewhere. I have attempted to provide additional information concerning date and place of the publication of these works. Some items have not
been located in American libraries and, therefore, must be taken on faith.
For these and other inconsistencies in the notes below, the translator begs
the reader's indulgence and generosity.
7.
8.
9.
Translator's foreword: a plea for Leibniz
1.
The A rt of the W est, 2 vols. (London: Phaidon, 1970 reprint), first appeared in
1933, without its now-familiar title, as the third part of a work entitled
Histoire du moyen age, whose first two sections included, first, economic and
social history (by Henri Pirenne) and, second, intellectual, moral, and
literary movements (by Gustave Cohen). Focillon's section went under the
title of 'Les mouvements artistiques.' The compendium was the eighth
volume of an Histoire gine rale under the direction of Gustave Glotz (Paris:
PUF). V ie des formes was published in 1934 (Paris: PUF). Charles Beecher
Hogan and George Kubler's translation, The Life of Forms in A rt, appeared in
1942 (New Haven: Yale University Press).
2. The development of the historical 'grid' of literature, or the adjacent lists of
dates and significant events in the life of given authors, the concurrent
political spheres, and in international history parallels that of the
educational mission of 'surveillance' that Michel Foucault studies in
Surveiller et punir (Paris: Gallimard, 1975). For Foucault a key term is
quadrillage, or gridding; its meaning, developed through a history of
incarceration, shares traits with traditions in the pedagogy of literature,
art, and philosophy. See also note 11 below.
3. Included are profusions of moving shapes, the loss of function, search for
picturesque effect, the mix of architecture, and a proclivity for anecdote.
Sculpture of the twelfth century, he notes, dessicates 'through an excess of
confidence in formulas, through a necessary consequence of serial production,
and industrial fabrication' (Histoire gine rale, 514, stress added). For Focillon,
what would be mistaken as impoverishment is, on the contrary, a sign of
living form (515).
4. The Life of Forms in A rt, 15.
5. Michel de Certeau, 'Mystique,' in Encyclopaedia universalis, vol. 12 (Paris:
Encyclopaedia Universalis, 1985), 873-78. [English translation by Marsanne
Brammer, forthcoming in Diacritics].
6. Gilles Deleuze, Proust et les signes (Paris: PUF, 1979 reedition), 185 (Deleuze's
emphasis).
-
-
162
10.
11.
12.
Qu'est-ce que la philosophie? [W hat is Philosophy?] (Paris: Minuit, 1991), 91.
A more complete explanation of Deleuze's theory of music is found in
Ronald Bogue, 'Rhizomusicology,' Substance, 20:3 (1991), 89-101. The
entire issue, edited by Charles Stivale, offers an excellent introduction and
overview of Deleuze and Guattari's writings of the last decade. It also deals
extensively with A Thousand Plateaus, a work that inspires much of the work
on the fold.
David Harvey calls the idealization of nature and invention of the worldpicture (in the aftermath of Descartes) crucial for the beginnings of
compression of time and space in our time, in The Condition of Postmodernity
(London: Blackwell, 1989). It could be said that the 'deterritorializing'
effects of monadic philosophy are also apt to be co-opted. Deleuze notes that
the Baroque has been linked with capitalism because it is associated with 'a
crisis of property, a crisis that appears at once with the growth of new
machines in the social field and the discovery of new living beings in the
organism' (p. 110).
Qu 'est-ce que la philosophie, 95-96.
As Samuel Y. Edgerton, Jr. , notes about the quincunx in designs of the body
and the world, in 'From Mental Matrix to Mappamundi to Christian Empire:
The Heritage of Ptolemaic Cartography in the Renaissance,' in David
Woodward, ed., A rt and Cartography: Six Historical Essays (Chicago: University
of Chicago Press, 1987), 12-13.
The Life of Forms in A rt, 15.
1. The pleats of matter
I. Systime nouveau de la Nature et de la communication des substances, §
7
[Parkinson, 119].
2. Monadologie. § 61 [Parkinson, 189]. And Principes de la Nature et de la GI eke
fonde's en raison. § 13 [Parkinson, 201].
3. De la liberte" (Nouvelles lettres et opuscules) [Parkinson, 112-14].
4. On cryptography as an 'art of inventing the key to an enveloped thing,' see
Fragment, Un livre sur l'art combinatoire ... (C, Opuscules). And the Nouveaux
essais sur l'entendement humain. IV, chap. 17, § 8: the fold of Nature and the
'summaries.'
5. Nouveaux essais, II, chap. 12, § 1. In this book Leibniz 'refashions' Locke's
Essays; thus the camera obscura was clearly invoked by Locke, but its
curtains were not.
6. See WOlfflin, Renaissance et Baroque, trans. Guy Ballange (Paris: Poche, 1967).
7. Nouveaux essais, preface [Remnant/Bennett, 59].
8. Letter to Des Billettes, December 1696 (GPh, VII, 452).
9. Table de definitions (C, 486). And Nouveaux essais, II, chap. 23, § 23.
-
163
NOTES
THE FOLD
10. Pacidus Philalethi (C, 614-15).
11. Letter to Des Billettes, 453.
12. Protogaea (Dutens II). On veins and conical forms, see chap. 8.
13. William Gibbs will develop this theme. Leibniz supposes that God does not
trace 'the first lineaments of the still-tender globe' without producing
'something analogous to the structure of the animal or plant' (Protogaea,
chap. 8).
14. Letter to Des Billettes; and his Letter to Bayle, December 1698 (GPh, III, 57).
See Gueroult, Dynamique et melaphysique leibniziennes (Paris: Les Belles
Lettres, 1934), 32: 'How can we conceive the motivating force if we fail to
suppose that the body is composite, and that thus it can be shrunk in
flushing out of its pores the subtle particles of matter that penetrate it, and
that in turn this more refined matter must be capable of expulsing from its
pores another, even more refined matter, etc., ad infinitum?'
15. On elasticity and detonation, which inspire the concept that Willis (16211675) proposes for reflexivity, and on how this model differs from that of
Descartes, see Georges Canguilhem, La formation du concept de reflexe aux
xvir et au X VIII' siicles (Paris: PUF,), 60-67.
16. Letter to Lady Masham, July 1705 (GPh, III, 368). And Considerations sur les
principes de vie et sur la natures plastiques (GPh, VI, 544 and 553): principles of
life are immaterial, but 'plastic faculties' are not. See Protogaea, chap. 28, on
fossils.
17. See Systeme nouveau de la Nature, § 10. Monadologie, § 64: 'The tooth of a
metal wheel has parts or fragments which as far as we are concerned are not
artificial and which have about them nothing of the character of a machine,
in relation to the use for which the wheel was intended. But machines of
nature, that is to say, living bodies, are still machines in the least of their
parts ad infinitum' [Parkinson, 189]. And the letter to Lady Masham, 374:
'Plastic force is in the machine.'
18. On Leibniz's technological conception, its modernity, and its opposition to
Descartes, see Michel Serres, Le systeme de Leibniz, 2 (Paris: Seuil, 1982), 491510, 621 (2d ed.).
19. Letter to Arnauld, Apri11687 (GPh, II, 99) [Mason, 125].
20. Nouveaux essais, III, chap. 6, § 23 [RemnantlBennett, 314-17]. Consequently, in Palingene'sie philosophique, Bonnet wrongly reproaches his
teacher, Leibniz, for holding to variations of size.
21. Monadologie, § 67 [Parkinson, 190].
22. See Serres, I, 371.
23. Letter to Arnauld, September 1687 [Mason, 144 (October 9, 1687)].
24. In the name of epigenesis Albert Dalcq can state, 'A caudal fin can be obtained
from a system of action and reaction ... where nothing caudal is a prior,' in
L'oeuf et son dynamisme organisateur (Paris: Albin Michel, 1941), 194.
164
25. Geoffroy Saint-Hilaire, a partisan of epigenesis, remains one of the greatest
philosophers of organic folding. Given the modifications of a same Animal,
he esteems that one can still move from one to the other by way of folding
(a unity of the plan of composition). If a vertebrate is folded 'in such a
fashion that the two parts of its spinal column are turned toward each
other, its head goes toward its feet, the lower area toward the neck, and its
viscera arranged as they are in a cephalopod.' This is what prompts Baer's
opposition in the very name of epigenesis, and already the anger of Cuvier,
who posits the diversity of axes of development or of plans of organization
(see Geoffroy, Principes de philosophie zoologique). Despite his monism, in
every event Geoffroy can be called Leibnizian in other respects: he explains
the organism in terms of a material force that does not change the nature
of bodies, but adds to them new forms and new relations. It is an impulsive
or tractive electric force in the style of Kepler. It can refold elastic fluids,
and it operates in very short distances in the 'world of details' or in
infinitely small areas, no longer by the summation of homogenous parts,
but by the confrontation of homologous parts (Notions synthetiques et
historiques de philosophie naturelle).
26. Letter to Des Bosses, March 1706, in Christiane Fremont, L'etre et la relation
(Paris: Vrin, 1981). And the letter to Arnauld, April 1687: 'As regards an
insect which one cuts in two, the two parts do not necessarily have to
remain animate, although a certain movement remains in them. At least the
soul of the whole insect will remain only in one part. ... It will also remain
after the destruction of the insect in a certain part that is still alive, which
will always be as small as is necessary to be sheltered from whoever tears or
scatters the body of this insect' [Mason, 125-26].
27. Letter to Lady Masham, June 1704 (357).
28. Principes de la Nature et de la Grdce, § 4: 'infinite degrees' in souls [Parkinson,
196], and in the Systeme nouveau de la Nature, § H.
29. Monadologie, § 74 [Parkinson, 191].
30. La cause de Dieu plaide'e par sa justice. §§ 81-85. And the Theodicee. § 91, 397.
31. Eclaircissement des difficultes que M. Bayle a trouvees dans le systime nouveau .
(GPh, IV, 544, 558). Gueroult has shown how external determinism and
internal spontaneity are already perfectly reconciled in respect to physical
bodies ('elasticity is now considered as the expression of the first
spontaneity, of the active primitive force,' 203-7 and 163).
32. Systeme nouveau de la Nature. § 18; De la reforme de la philosophie premiere et de
la notion de substance.
2. The folds in the soul
1. Paul Klee, Theorie de l'art moderne (Paris: Gonthier, 1963), 73.
165
THE FOLD
Letter to Arnauld, September 1687 (GPh, II, 119) [Mason, 152 (October 9,
1687)].
3. Bernard Cache, L'ameublement du territoire (forthcoming). Inspired by
geography, architecture, and the decorative arts, in my view this book
seems essential for any theory of the fold.
4. On the relation between catastrophe theory and an organic morphogenesis,
see Rene Thorn, Morphologie et imaginaire, Circe 8-9, and the presentation of
the seven singularities or • catastrophe-events, (Paris: Lettres modernes,
1978) 130.
5. [Homothesis (homothetie), a term belonging to geometry, indicates a
similarity of form and position between two figures in respect to a given
point. Homothesis is said to be direct if two figures are in the same direction
at a given point, and inverse when on either side of that point. The given
point is the center of homothesis. - Trans.]
6. Mandelbrot, Fractals: Form, Chance, and Dimension (San Francisco: W. H.
Freeman, 1977). On the porous or cavernous qualities, see Jean Perrin's
text, cited by Mandelbrot, pp. 4-9. From different points of view, both
Mandelbrot and Thorn are strongly influenced by Leibniz.
7. Hocquenghem and Scherer thus describe the Baroque spiral, according to
Permozer's statue, in the 'Apotheosis of Prince Eugene' (1718-1721), in
L'dme atomique (Paris: Albin Michel, 1986), 196-97.
8. From inflection to turbulence, see Mandelbrot, chap. 8, and Cache, who
emphasizes the phenomena of differences.
9. Justification du calcul des infinitesimales par celui de l'algebre ordinaire. GM, IV,
104.
10. Michel Serres, I, 197. Leibniz's two principal texts are GM, V: D'une ligne
issue de lignes and Nouvelle application du calcul diffirentiel ('by comparing the
curves of a series among each other, or by considering the crossing of one
curve on another curve, certain coefficients are quite constant or
permanent, that do not remain solely on one but on all the curves of the
series, the others being variable. And clearly, so that the law of the series of
curvatures can be given, a unique variability has to subsist in the
coefficients, to such a point that, if several variables appear for all the
curves in a principal equation explaining their common nature, other
accessory equations are needed to express the dependency of variable
coefficients, by which all the variables could be removed from the principal
equation, except one,' tr. Jean Peyroux, Oeuvre mathematique de Leibniz autre
que le calcul infinitesimal (Paris: Blanchard, 1986).
11. Gilbert Simondon, L'individu et sa genese physico-biologique (Paris: PUF, 1964),
41-42.
12. On anamorphosis see the Thiodicee, § 147; Nouveaux essais. II, chap. 29, § 8
[Remnant/Bennett, 257-58]. [A namorphosis pertains to distorted projections
2.
166
NOTES
of images that are seen correctly from an oblique point of view or in
reflection on a mirror placed at an indicated area. Anamorphic perspective
characterizes the celebrated death's head that Hans Holbein inserts in a
diagonal fashion in The A mbassadors. It became, as Jurgis Baltrugaitis has
noted, a field of experiment in perspective in early seventeenth-century
France, and a mode of visual trickery that can be seen in pictures that
constitute 'parlor games' in French society of the same period, in
A namorphoses (Paris: Musee des Arts Decoratifs, 1976). Anamorphosis is
synonymous with Baroque art and literature. - Trans.]
13. Following Russell, Gueroult has often insisted on a so-called contradiction of
continuity-indiscernibles (cf. Descartes selon l'ordre des raisons. vol. 1 [Paris:
Aubier] 284). Even more curiously, elsewhere he takes up Russell's thesis,
according to which Leibniz would have sketched the notion of distance as a
relation indivisible, irreducible to length and measure: space is made of
relations of distance, while extension consists of measurable sizes. Thus this
thesis assures a perfect conciliation of points of view with the continuous
(see Gueroult, 'Espace, point et vide chez Leibniz,' Revue philosophique, 1946,
and already Russell himself, in The Philosophy of Leibniz (London: Allen and
Unwin, 1937), 124-30.
14. Entretien de Philarete et d 'A riste: 'Thus extension, when it is the attribute of Space.
is the diffusion or continuation of the situation or locality, as the extension
of the body is the diffusion of the antitype or of materiality' (GPh, VI, 585).
15. On the equation with an ambiguous sign that includes the different cases of
the conic section, see De la mithode de l'universalite C, 97 sq.
16. See Rene Taton, L'oeuvre mathematique de Desargues (Paris: Vrin), 110.
Yvonne Toros comments on Desargues's notion of involution, not only in
respect to Leibniz but also to Spinoza, by which she proves all the interest
that he had for the theory of conic sections. New light is cast on Spinozism
and 'parallelism' (L'optique de Spinoza, forthcoming).
17. Serres, I, 156-63; II, 665-67,690-93.
18. Letter to Princess Sophie, June 1700 (GPh, VII, 554). The Justification du
calcul would even show point A contained and held the relation
c
e
19. This is how Leibniz distinguishes: virtuality or idea; modification, disposition, or habit, which resembles the act of force in the soul; the tendency to
action and action itself as the ultimate actualization of the act. One could
say, following the sculptural metaphor: the figure of Hercules; the veins of
the marble; labor exerted on the marble to bring out these veins. See the
preface and part II, chap. 1, § 2 ('beyond disposition, there is a tendency to
action ...') in the Nouveaux essais.
167
THE FOLD
20. Systeme nouveau de la Nature. § II [Parkinson, 120-21]. On the scholastic
21.
22.
23.
24.
25.
26.
27.
conceptions of the point, and of the different cases that inspire Leibniz, see
Boehm, Le vinculum substantiale chez Leibniz (Paris: Vrin, 1962), 62-81.
Letter to Lady Masham, June 1704: 'The soul must be placed in the body
where its point of view is located, according to which the soul presently
represents the universe to itself. ... To wish for something more and to
enclose souls within the dimensions is to desire to imagine souls as bodies'
(GPh, III, 357).
See Proclus, Elements de theologie (Paris: Aubier, n.d.), 204, § 21.
Giordano Bruno, De triplici minima. The theory of 'complicatio' had already
been developed by Nicolas of Cusa. See Maurice de Gandillac, La philosophic
de Nicolas de Cues (Paris: Aubier-Montaigne, 1941).
Considerations sur la doctrine d'un esprit universel (GPh, VI). That is why Leibniz
does not take up the term 'complicatio' despite the attraction he has for
words and notions that translate the fold.
Cf. Plotinus's concise sentence: 'We multiply the city without its founding
this operation' (Enneades, VI, 6, 2).
Discours de mitaphysique. § 15 and 16 [Parkinson, 146]. Monadologie, § 60,61,
83 ('each mind being as it were a little divinity in its own department')
[Parkinson, 193].
Monadologie, § 37 [Parkinson, 185]. On the 'law of curvatures' see
Eclaircissement des difficultes que M. Bayle a trouve'es dons le systeme nouveau
(GPh, IV, 544): surely we can say that the law of seriality is enveloped in the
soul in confusion; but what is in the soul in this sense is less the law than the
'means of executing it.'
28. Heidegger: 'As monad, Dasein does not require a window to see what is
outside, not, as Leibniz believes, because everything that is is already
accessible inside the box ... but because the monad, the Dasein, is already
outside, in conformity with its own being,' in Les problemes fondamentaux de
la phe'nomenologie (Paris: Gallimard, 1985), 36. Merleau-Ponty has a much
stronger understanding of Leibniz when he merely posits that 'our soul
does not have windows, which means In der W elt Sein . . .' in Le visible et
l'invisible (Paris: Gallimard, 1966),264 and 276. As of La phinomenologie de
la perception Merleau-Ponty invoked the fold in order to oppose it to
Sartrian holes; and in Le visible et l'invisible, his task is one of interpreting
the Heideggerian fold as a 'chiasm or interlace' between the visible [visible]
and the seeing [voyant].
3. What is baroque?
1. Monadologie. § 7 [Parkinson, 179]; Letter to Princess Sophie, June 1700
(GPh, VII, 554).
168
NOTES
2.
Leo Steinberg, 'The Flatbed Plan of the Painting,' in Other Criteria (New York:
Oxford University Press, 1972).
3. For the Baroque city and the importance of the urban world in the Baroque,
see Lewis Mumford, The City in History (New York, 1961), and Severo
Sarduy, 'Le Caravage, la ville bourgeoise,' in Barroco. trans. Jacques Henric
(Paris: Seuil, 1975), 61-66.
4. See Gravesande's 'Use of the camera obscura' that Sarah Kofman takes up in
her Camera obscura (Paris: Galilee, 1978), 79-97.
5. Michel Serres, II, 762.
6. Jean Rousset, La litterature de l'dge baroque en France (Paris: Corti, 1953), 16871. And, by the same author, L'interieur et l'exterieur (Paris: Corti, 1968).
7. Regis Debray, 'Le Tintoret ou le sentiment panique de la vie,' in Eloges (Paris:
Gallimard, 1986), 13-57. (Debray takes Sartre to task for having seen only
the lower level in Tintoretto.) Also Jean Paris, L'espace et le regard (Paris:
Seuil, 1963), on the analysis of 'ascensional space' in El Greco ('like
Cartesian divers, men thus balance earthly gravity and divine attraction'),
226-28.
8. Andre Scala has studied this in La genese du pli chez Heidegger (forthcoming).
The notion springs up between 1946 and 1953, especially in 'Moira,' in
Essais et conferences (Paris: Gallimard, 1980); it follows the entre-deux or the
incident, the Zwischen-fall, that had rather marked a thing fallen. This is the
'Greek' fold, especially related to Parmenides. Scala notes one of Riezler's
comments that, as of 1933, he found in Parmenides 'a pleat of being,' 'a fold
of one in being and non-being, the two being narrowly stretched into each
other' (Faltung); when Kurt Goldstein discovers that he is Parmenidian
when he comprehends the living, appeals to Riezler [La structure de
l'organisme (Paris: Gallimard), 325-29]. According to Scala another source
puts in play the stakes of new perspective, and the projective method that
already appeared in Diirer, in the name of 'zweifalten cubum.' Cf. Erwin
Panofsky on Diirer's treatment of solids: 'Instead of representing the solids in
perspective or stereographic images, he devised the apparently original and,
if one may say so, proto-topological method of developing them on the
plane surface in such a way that the facets form a coherent 'net' which,
when cut out of paper and properly folded where the two facets adjoin, will
form an actual, three-dimensional model of the solid in question' The Life
and A rt of A lbrecht Ddrer (Princeton: Princeton University Press, 1955), 259.
9. 'Every body is sensitive to everything which is happening in the universe, so
much so that one who saw everything could read in each body what is
happening everywhere. ... But a soul can read in itself only what is
distinctly represented there,' Monadologie, § 61 [Parkinson, 189].
10. On Leibniz's invention of binary arithmetic, on its two characters, 1 and 0,
light and shadow, on the analogy with 'Fohy's Chinese figures,' see the
169
THE FOLD
NOTES
Invention de l'arithmetique binaire, Explication de V arithmetique binaire (GM,
VII). Reference can be made to Christiane Fremont's annotated edition,
Leibniz, Discours sur la theologie naturelle des Chinois (Paris: L'Herne).
11. Cf. Goethe, Traite des couleurs (Paris: Editions Triades, 1983), § 902-9.
12. Preceptes pour avancer les sciences (GPh, VII, 169). And Nouveaux essais II, chap.
9, § 8 [Remnant/Bennett, 134-38].
13. Black, the dark background (fuscum subnigrum), colors, white and light are
defined in the Table de definitions, C, 489.
14. Nietzsche, Beyond Good and Evil. chap. 8, § 244.
15. Cited by Ernst Bertram, in Nietzsche (Paris: Rieder, 1932), 233.
16. Herbert Knecht, La logique de Leibniz. essai sur le rationalisme baroque
(Lausanne: L'Age d'homme, 1982); Christine Buci-Glucksmann, La folie
du voir, De V esthetique baroque (Paris: Galilee, 1987). The author develops a
conception of the Baroque that appeals to Lacan and Merleau-Ponty.
17. Marcel Schwob, V ies imaginaires (Paris: Union generale d'editions 10/18),
229-31.
18. Jurgis Baltrusaitis, Formations, deformations (Paris: Editions Flammarion,
1986), chap.9.
19. Bernard Cache, L'ameublement du territoire [see chap. 2, n. 3 - Tr.]
20. On the 'two orders,' the material and the immaterial, see Jean Dubuffet,
Prospectus et tous ecrits suivants, II (Paris: Gallimard, 1967), 79-81.
21. On Hantai and his method of folding, see Marcelin Pleynet, Identite de la
lumiire, catalogue of the Arca Marseille. And also Dominique Fourcade, Un
coup de pinceau c'est la pensee, catalogue of the Pompidou Center; Yves
Michaud, Melaphysique de Hantai; catalogue of Venice; Genevieve Bonnefoi,
Hantai' (Abbaye Beaulieu, coll. Artistes d'aujourd'hui, 1973).
22. Leibniz counted on his binary arithmetic for the discovery of a periodicity in
numerical series. Nature would perhaps hide this periodicity 'in its foldings,'
as in the instance of first numbers (Nouveaux essais, IV, chap. 17, § 13).
23. For textures see the letter to Des Bosses, August 1715. Leibniz's physics
attests to a constant interest in the problems of the resistance of materials.
24. [Hysteresis, which literally means a lagging, or deficiency, is used in
describing magnetic fields (and in electronics) to denote the lapse of
magnetic effects after their causes. - Trans.]
25. Jeanclos-Mosse, sculptures et dessins, Maison de la culture d'Orleans.
26. See De la liberte (F, 178) for the presence or absence of a 'common measure.'
27. Cf. Papetti, Valier, Freminville and Tisserson, La passion des etoffes chez un
neuropsychiatrie, G. G. de Cle'rambault (Paris: Editions Solin, 1981), with its
photographic reproductions and two lectures on drapery (49-57). A reader
might be led to believe that these photos of overabundant folds refer to
pages chosen by Clerambault himself. But the postcards at the time of the
colonial empire also reveal these systems of folds, which dictate all the
170
clothing of Moroccan women, including that of the face: an Islamic
Baroque.
4. Sufficient reason
1. Letter to Arnauld, July 14,1686 [Mason, 67-72].
Discours de mitaphysique. § 14 [Parkinson, 27].
3. Cf. Discours de metaphysique, § 8 and 13 [Parkinson, 18, 24].
4. 'Instead, the analysis proceeds to infinity. God alone seeing - not, indeed,
the end of the analysis, since it has no end - but the connexion of terms or
the inclusion of the predicate in the subject, for he sees whatever is in the
series,' De la liberte (F, 180-81) [Parkinson, 109].
5. See De la liberte (F. 183) [Parkinson, 109], but also Sur le principe de raison (C,
II), W rites necessaires et veritis contingentes (C, 17-18), or Fragment X (GPh,
VII, 300). These texts invoke analogous arithmetical examples and use
synonymous terms ('latebat' or 'tecte' as well as 'virtualiter'). Couturat is
thus correct in stating, 'Necessary truths are identical, some explicitly ..., the
others virtually or implicitly,' in La logique de Leibniz, 206.
6. Nouveaux essais, IV. chap. 7. § 10 [Remnant/Bennett, 414].
7. Ortega y Gasset, L'evolution de la theorie deductive, Vickee de principe chez Leibniz
(Paris: Gallimard, 1970), 10-12.
8. On this criterion or this proof of elevation to infinity, and on the condition
of 'neither whole nor part,' cf. Nouveaux essais, II, chap. 17. § 2-16
[Remnant/Bennett, 159]. And Meditations sur la connaissance, la veriti et les
idees. The two texts admit an absolute extension, 'extensio absoluta,' as an
infinite absolute form. But it is in a very special sense, because at stake is
neither space, which is relative, nor properly Leibnizian extension, which
enters into relations of the wholes and parts: in question is immensity, which
is the 'idea of the absolute, with reference to space' [Remnant/Bennett,
159].
9. On the impossibility of being contradicted, for absolutely simple forms that
are necessarily 'compatible,' cf. the Letter to Princess Elisabeth, 1678, and
especially Qu'il existe un Etre infiniment parfait (GPh, VIII, 261-62). In the
latter writing Leibniz claims having taught this demonstration to Spinoza.
This is questionable, since it also belongs to the first ten propositions of the
Ethics: it is because attributes have nothing in common that they can be said
to be of a sole and same Being ... And all the more in that Spinoza and
Leibniz have a same source in Duns Scotus, who showed that formally
distinct quiddities compose a sole and same Being. Cf. Etienne Gilson: 'The
formal distinction of essences is not an obstacle for the perfect ontological
unity of infinity,' in Jean Duns Scot (Paris: Vrin, 1952), 243-54.
10. Recherches ginerales sur l'analyse des notions et virites (C, 358-59). On the
2.
171
THE FOLD
'vinculum' as a relation among the definers of a magnitude, see De la
mithode de l'universalite (C, 101).
11. See the early work, Sur l'art combinatoire, along with Couturat's commentary, in La logique de Leibniz (560). We have simplified the example of the
line that in fact belongs to level IV.
12. Spinoza also distinguishes three infinities in Letter XII, one by itself, the
other by its cause, the third finally understood within limits. Leibniz
congratulates Spinoza in this respect although, on his account, he conceives
otherwise the relation of the limit and infinity. Cf. GPh, I, 137.
13. For the texture of gold or the connection of its characters, see the Nouveaux
essais, II, chap. 31, § 1; III, chap. 3, § 19 (Remnant/Bennett, 266; 295-96].
14. Nouveaux essais, IV, chap. 2, § 7: on the category of problem.
15. Nouveaux essais, I, chap. I, § 4 and 19. On the enthymeme, see Aristotle,
First A nalytics, II, 27 ('If a single premise is uttered, only one sign is
obtained').
16. On the question of attaining (or not) the connection of characters (the case
of gold): see the Nouveaux essais, III, chap. 4, § 16; III, chap. 11, § 22-24; IV,
chap. 6, § 8-10.
17. Nouveaux essais, IV, chap. 17, § 4 (theory of the 'fabric'). [With enthymemes,
'the inference lies partly in what is being suppressed,' 79, 479; 'it is therefore
only too necessary that they should have a strict logic, though of a different
type from the scholastic one,' Remnant/Bennett, 482].
18. Nouveaux essais, III, chap. 3, § 6.
19. Nouveaux essais, III, chap. 4, § 16.
20. Cf. the beginning of L'origine radicale des choses (On the Ultimate Origination of
Things]. And the Monadologie, § 36-37: 'Ultimate reason ... must certainly be
greater, higher and prior to the world itself' [Parkinson, 140]. The latter text
has the advantage of moving through souls or monads, that contain final
reason no more than the states of the world. If serial reason is outside of the
series, it appears to us that in this instance it has to be taken literally. Here is
one of the few points on which we do not concur with Michel Serres (I,
262). An argument often invoked by Leibniz is that a 'series enclosing sin'
cannot have its reason in the monad.
21. De la liberte: 'For demonstration consists simply in this: by the analysis of the
terms of a proposition, and by substituting for a defined term a definition or
part of a definition, one shows a certain equation or coincidence of predicate
with subject in a reciprocal proposition, or in other cases at least the
inclusion of the predicate in the subject, in such a way that what was latent
in the proposition and as it were contained in it virtually is rendered evident
and express[ed] by the demonstration' [Parkinson, 108].
22. 'The concept of an individual, regarded as possible (sub ratione possibilitatis),
contains what in fact exists or what is related to the existences of things and
172
NOTES
23.
24.
25.
26.
27.
28.
29.
to time,' in the correspondence with Arnauld, 'Remarks on M. Arnauld's
letter' (May 13, 1686). [Mason, 41.]
Arnauld and Nicole, La logique ou l'art de penser, II (Paris: Flammarion, 1970
reprint), chap.2.
See the texts quoted by Couturat in La logique de Leibniz (Hildesheim: Olms,
1961), 70.
Letter to Arnauld, July 1686: inclusion is offered as a direct connection
'between me, I who am the subject, and the accomplishment of the journey,
which is the predicate' [Mason, 58].
On the first Stoics' conception of the event, Emile Brehier, La thiorie des
incorporels dans l'ancien stoicisme (Paris: Vrin, 1970), chaps. 1 and 2, is still a
basic study. And on the substitution of 'to follow' for 'to be,' see Brochard,
Etudes de philosophic ancienne et de philosophic moderne (Paris: Vrin, 1974),
226-27. This substitution is found in Leibniz.
'The kinds and degrees of perfection vary up to infinity, but as regards the
foundation of things. The foundations are everywhere the same; this is a
fundamental maxim for me, which governs my whole philosophy. But if
this philosophy is the simplest in resources it is also the richest in kinds [of
effects],' Nouveaux essais, IV, chap. 17, § 16 [Remnant/Bennett, 490].
That is why, sometimes, Leibniz briefly presents the inherence of the
predicate in conformity with opinion in general ('ut aiunt'), or to Aristotle
in particular.
Cf. the letter to Arnauld (March 4, 1687), and the letter to Arnauld dated
April 30 [Mason, 105-29]. Andre Robinet shows that for a long time, up to
1696, Leibniz avoids speaking of 'simple substance,' in A rchitectonique
disjonctive, automates systemiques et idealize transcendantale dans l'oeuvre de
Leibniz (Paris: Vrin, 1986), 355, and Anne Becco's study, Du simple selon
Leibniz (Paris: Vrin, 1975).
30. On local movement and qualitative change, see De la nature en elle-meme, §
13.
31. 'If separability is a consequence of the real distinction,' Letter to
Malebranche (GPh, I, 325-26).
32. On Leibniz against the Cartesian attribute, see the Correspondence with De
Voider (GPh, II), especially June 30, 1703.
33. Eclaircissement des difficultes que M. Bayle a trouvies dans le systeme nouveau
(GPh, IV, 532, 546-47).
34. A ddition a l'explication du systime nouveau (GPh, IV, 586).
35. Whence the Monadologie, § 36: 'Sufficient reason has a duty also to find in
contingent truths ...' [Parkinson, 1401, which implies that it already held for
necessary truths. And the The'odicie 'Remarques sur le livre de l'origine du
mal,' § 14.
36. 'The principle of identity affirms that every identical proposition is true,
173
THE FOLD
NOTES
while the principle of reason affirms to the contrary that every true
proposition is analytical, that is, virtually identical,' notes Couturat (in La
logique de Leibniz, 215).
5. Incompossibility, individuality, liberty
1. Fragment Vingt-quatre propositions, (GPh, VII, 289-91), and the fragment US
verites absolument premieres, (195). Couturat (La logique de Leibniz, 219) and
Gueroult (Dynamique et metaphysique leibniziennes, 170) believe that
incompossibility implies a negation or an opposition that Leibniz was
unable to discern among positive notions like monads: he would thus have
been led to declare that the origin of incompossibility cannot be known. But
it seems to us that for Leibniz the incompossible is an original relation
irreducible to any form of contradiction. It is a difference and not a negation.
That is why in the following pages we are proposing an interpretation based
only on divergence or convergence of series. The reading has the advantage
of being 'Leibnizian.' But why then does Leibniz declare the origin
unknowable? On the one hand, it is because divergence is still not
understood very well in serial theory in the seventeenth century. On the
other and, more generally, at the level of incompossible worlds, we are
reduced to supposing that series diverge but without comprehending why
they do.
2. 'For anything which is noticeable must be made up of parts which are not,'
Nouveaux essais, II, chap. I, § 18 [Remnant/Bennett, 117).
3. Theodice'e, § 413-17. In Figures II (Paris: Seuil, 1966),195 sq., Gerard Genette
provides criteria allowing us to observe how much the text of the The odic&
follows a model of Baroque narrative.
4. Jorge-Luis Borges, 'Le jardin aux sentiers qui bifurquent,' in Fictions (Paris:
Gallimard, 1974).
5. Maurice Leblanc, La vie extravagante de Balthazar (Paris: Livre de Poche, 1979).
6. Letter to Bourget, December 1714 (GPh, III, 572).
7. 'Remarques sur la lettre de M. Arnauld,' Correspondence with Arnauld,
letter of May 13,1686. 'Primary predicates' are obviously not reserved for
Adam, since every individual has his or her own. Are they for everyone in a
finite number? No, because we can always multiply singular points between
two singular points. The question is moot since what counts is that two
individuals do not share the same primitive attributes. On the themes that
we take up later - 'vague Adam,' Adam common to incompossible worlds,
primitive predicates grasped 'sub ratione generalitatis' - see the same text
[Mason, 24-34].
8. For this hypothesis see Gueroult, 'La constitution de la substance chez
Leibniz,' Revue metaphysique et de morale (1947).
-
174
9.
Nouveaux essais, II, 1, § 2; Eclaircissement des difficultes que M. Bayle a trouvees
dans le systime nouveau (GPh, IV, 566). In other writings, Leibniz brings
together the individual with a last species; but he makes it clear that the
comparison holds for only a mathematical and not a physical species. Cf.
Discours de metaphysique. § 9; Letter to Arnauld, GPh, II, 131.
10. On the difference between the two types of species, see the Nouveaux essais,
III, chap. 6, § 14.
11. Nouveaux essais, II, chap. 27, § 4-5.
12. Justification du calcul des infinitesimales par celui de l'algebre ordinaire (GM, IV,
104): how difference or reason of two lengths subsists in a point when these
lengths vanish and when their relation tends toward
0
0
13. "Tis an hard matter to say where the sensible and the rational begin,'
Nouveaux essais, IV, chap. 16, § 12 (Remnant/Bennett, 471). Kant is the one
who claims to denounce the conciliation of indiscernibles and continuity
because a confusion of phenomena with things in themselves would be
implied; it is thus the distinction of the two worlds (such as Kant restores it)
that gives birth to a contradiction; and with Kant we know in fact where the
sensible ends and the intelligible begins, which amounts to stating that the
principles of indiscemibles and the law of continuity are opposed, but in a
Kantian type of system. We often see the distinction among authors who
assume a contradiction: Gueroult (Descartes selon l'ordre des raisons, 1 (Paris:
A ubier, 1953/, 284) and even Philonenko, in 'La loi de continuiti et le principe des
indiscernables,' Revue de metaphysique et de morale (1967), appeal to the ideal
and the real in Leibniz as two worlds. But the two worlds do not exist, and
for Leibniz the break is never a gap or a discontinuity.
14. Principes de la Nature et de la Grace, § 4.
15. De l'origine radicale des chases.
16. Eugen Fink, Le jeu comme symbole du monde (Paris: Minuit, 1966), 238-39.
17. Cf. Gaston Grua, Jurisprudence universelle et theodicle selon Leibniz (Paris: PUF,
1953).
18. Tibor Klaniczay, 'La naissance du Manierisme et du Baroque au point de vue
sociologique,' in Renaissance, Manierisme, Baroque (Paris: Vrin, 1972), 221.
The author paints a picture of the great crisis that brings about the decline of
the Renaissance and of the two attitudes, Mannerism and Baroque, that are
related to this crisis.
19. Cf. the letter to Remond (January 1716), in GPh, III, 668-69, in which
Leibniz rejects each in its turn: chance, for the sake of chess and checkers,
games of position; void, for the purpose of inverted solitaire; the model of
battle, for the sake of a Chinese game of nonbattle, or the Roman game of
175
NOTES
THE FOLD
[Remnant/Bennett, 51]. On movement that is being made, see De la Nature
en elle-meme: 'In the present moment of its movement, the body is not only
Brigands. On nonbattle as a paradigm of current strategy, see Guy Brossolet,
Essai sur la non-bataille (Paris: Bain, 1975), in which the author appeals to
the Baron of Saxony, but in reality proposes very Leibnizian schemes, 'a
modular type of combat based on tight, numerous, but independent cells'
(113).
20. Georges Friedmann, in Leibniz et Spinoza (Paris: Gallimard, 1975), insists on
Leibniz's philosophy as the thinking of universal anxiety: the Best is not a
'vote of confidence in God; on the contrary, Leibniz seems to be defying God
himself' (218).
21. Jacques Brunschwig has underscored this theme of the lawyer: the The'odicee
can be understood 'in a prudent sense (doctrine of God's justice) as it also
can in an audacious sense (justification, or a trial for the justification of
God),' that conforms to the treatise La cause de Dieu plaidie par sa justice: The
business of God, one of the perplexing cases to which as a young man he had
devoted his doctoral thesis,' in the Introduction to La The'odicie (Paris:
Garnier/Flammarion, 1969).
22. 'The smallest parts of the universe are ruled according to the order of the
greatest perfection; the whole would not be,' Essai anagogique (GPh, VII,
272).
23. 'Mannerism' is one of the most pathetic traits of schizophrenia. In two
different ways Blankenburg (in Tanz in der Therapie Schizophrener [Psych.
Psychosom., 1969]), and Evelyn Sznycer ('Droit de suite baroque,' in
Navratil, Schizophre'nie et art [Paris: Complexe, 1978]) compare schizophrenia
to Baroque dances (the German dance, the pavane, the minuet, the running
dance, etc.). Sznycer recalls Freud's theses on the reconstruction of the
world and the schizophrenic's inner modifications. She engages a function
of excess that she calls 'hypercritical.'
24. On the old problem of future contingents as an essential part of the logic of
events, see Schuhl, Le dominateur et les possibles (Paris: PUF, 1960), and Jules
Vuillemin, Necessite ou contingence: L'aporie de Diodore elles systemes philosophiques (Paris: Minuit, 1984). One of the basic propositions is that the
impossible does not proceed from the possible. But Leibniz is able to consider
that the incompossible can proceed from the possible.
25. Correspondence with Clarke, Leibniz's fifth piece of writing, § 14-15;
Nouveaux essais, II, chaps. 20 and 21.
26. Discours de metaphysique, § 30 [Parkinson, 40-41].
27. 'There is an infinity of present and past figures and movements that play in
the efficient cause of my present writing, and there is an infinity of my soul's
minute inclinations and dispositions, both present and past, that play a role
in the final cause,' Monadologie, § 36 [Parkinson, 185].
28. 'Reason counsels us to expect ordinarily that what we find in the future will
conform to a long experience in the past,' Preface to the Nouveaux essais
176
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
what occupies a place equal to itself, but it also comprehends an effort or
drive to change position so that, through a natural force, the following state
will issue from itself in the present' (§ 13).
The'odice'e, § 269-72. And especially Profession de foi du philosophe, ed. Y.
Belaval, in which Leibniz compares damnation to movement that is taking
place: 'Just as what has changed never remains in one place, but always
tends toward a place, and just as they are never damned and powerless, so
then they would desire to cease forever being damnable, that is, to cease
damning themselves over and again forever' (Paris: Vrin, 1970), 85, 95, and
101 (where Beelzebub's beautiful song is written in Latin verse).
Cf. Quevedo's text, quoted by Jean Rousset, La litterature de l'dge baroque en
France (Paris: Corti, 1953), 116-17. Rousset speaks of 'death in movement.'
Letter to Jaquelot (September 1704), GPh, VI, 559.
Bergson, Essai sur les donnees immediates de la conscience (Paris: PUP, Ed. du
centenaire, 1982), 105-20. Readers can take note of the scheme of inflection
that Bergson advances (117).
Monadologie, § 61, and Principes de la Nature et de la Grdce, § 13 [Parkinson,
188-89, 201].
Cf. Bergson, 123-26, and the second schema of inflection.
Discours de metaphysique, § 14 [Parkinson, 26].
Cf. the letter to Bourguet (August 5, 1715), that defines the quantity of
progress by the 'outcome' of the world as being 'the most perfect of all
possible outcomes,' although no condition can be the most perfect.
On the 'official act bearing a later effect,' in sensitive souls called upon to
become reasonable, cf. La cause de Dieu plaidee par sa justice, § 82. On the
return to a sensitive state after death, while waiting for the resurrection:
Considerations sur la doctrine d'un esprit universe!, § 12-14. On the case of the
damned, from the points of view both of the last thought and the
resurrection, Profession de foi du philosophe, pp. 37-93.
In Le systime de Leibniz (I, 233-86) Michel Serres analyzes the physical and
mathematical implications of Leibniz's schemes of progress in detail,
especially through the correspondence with Bourguet. It appears to us that
the damned play an indispensable physical role in these schemes (somewhat
like 'demons').
6. What is an event?
1. [Diadoche means what succeeds, or is in succession. The term derives from
the Diadochi, the Macedonian generals under Alexander the Great who
divided up their leader's empire immediately after his death. - Trans.]
177
THE FOLD
2.
Here we refer to Whitehead's three principal works: The Concept of Nature
(Cambridge: Cambridge University Press, 1920) for extensions and
intensities, the first two components of the event; for the third, prehensions,
we refer to Process and Reality (New York: Macmillan, 1941) and A dventures of
Ideas (New York: Macmillan, 1933). For the totality of Whitehead's
philosophy readers can consult Wahl, hers le concret (Paris: Vrin); Cesselin,
La philosophie organique de W hitehead (Paris: PUF, 1950); Dumoncel,
W hitehead ou le cosmos torrentiel, in A rchives de philosophie (December 1984
and January 1985).
3. Michel Serres has analyzed the process of screening, the grid, or 'cribratio' in
Leibniz. 'There would be two infraconsciences: the deeper would be
structured as any given totality, a pure multiplicity or general possibility, a
haphazard mixture of signs; the shallower would be covered by combinatory
schemas of this multiplicity. It would be already structured like a complete
mathematics, arithmetic, geometry, infinitesimal calculus (I, 111, and also
107-27). Serres shows the profound opposition between this method and
the Cartesian method. There exists an infinity of filters or superimposed
grids, from our senses themselves up to the final filter, beyond which chaos
would exist. The paradigm of the filter is the key to Meditations sur la
connaissance, la vlritl et les idles.
4.
Letter to Bourguet, March 1714: 'When I maintain that chaos does not exist,
I do not at all mean that our globe or other bodies have never been in a state
of outer apparent confusion ... but I do mean that whoever would have
sensitive organs discerning enough to notice the smallest parts of things
would find that everything is organized.... For it is impossible for a creature
to be capable of delving at once into the smallest parcel of matter because
the actual subdivisions go up to infinity' (GPh, III, 565).
5. Dumoncel, 1985,573.
6. Process and Reality constantly appeals to the 'public-private' pair. The origin
of this distinction is found in Discours de metaphysique. § 14 [Parkinson, 2627]; we shall discover the importance of this theme.
7. 'Action belonging to the soul is perception,' letter to Des Bosses (April 1709).
8. Letter to Arnauld, September 1687, GPh, II, 112.
9. Principes de la Nature et de la Grdce, § 17 [Parkinson, 203].
10. The Profession de foi du philosophe will go the furthest in its analysis of
subjective 'satisfaction,' and in the conciliation of 'novelty' with totality
(87-89).
11. 'The event which is the life of nature in the Great Pyramid yesterday and
today is divisible into two parts, namely the Great Pyramid yesterday and
the Great Pyramid to-day. But the object recognizable which is also called
the Great Pyramid is the same object to-day as it was yesterday,' notes
Whitehead in The Concept of Nature (77).
178
NOTES
12. Monadologie, § 71 (and on 'reflexive acts,' § 30).
13. Cf. the conditions of the choir in the Letter to Amauld (April 1687), GPh, II,
95 [Mason, 119].
14. Such was Heidegger's remark: the monad does not need a window because
it is 'already outside, conforming to its own being'; in Les problemes
fondamentaux de la phlnome'nologie (Paris: Gallimard, 1986), 361.
15. See especially the play of divergent series in Gombrowicz's Cosmos (Paris:
Denoel, 1966).
16. On the new monadology in mathematics since Riemann, see Gilles Chatelet,
'Sur une petite phrase de Riemann,' A nalytiques 3 (May 1979).
7. Perception in the folds
1. Letter to Des Bosses (March 1706, October 1706), in which a primal matter
'belongs to' or is 'fixed' in each entelechia. The letters to Des Bosses are
translated with commentary by Christiane Fremont in L'étre et la relation
(Paris: Vrin, 1981); see especially the remarks on the notion of exigency.
2. This is constant in his letters to Amauld (especially in April 1687) [Mason,
113-29].
3. Arnauld, Letter to Leibniz (August 28, 1687) [Mason, 132ff].
4. 'Because the universe being ruled is a perfect order, there must also exist an
order in a representative, that is, in the soul's perceptions.' In the
Monadologie. § 63 [Parkinson, 189].
5. On minute perceptions and little pricklings, see the Nouveaux essais, II, chap.
1, § 9-25; chap. 20, § 6-9; chap. 21, § 29-36 [Remnant/Bennett, 78-86;
163-67; 183-91].
6. Gaetan Clerambault, guided by his love of folds, analyzed the so-called
Lilliputian hallucinations marked by striations, trellises, and interweavings.
The chloralic's mind is 'surrounded by a veil [where] the play of folds gives
an uneven transparency,' in the Oeuvre psychiatrique, 1 (Paris: PUF, 1942),
204-50.
7. For the distinction of a microscopic process and a macroscopic process in
prehension, see Whitehead, Process and Reality, 129.
8. With these terms Gabriel Tarde appeals to and defines 'monadology' in
'Monadologie et sociologie,' in Essais et melanges sociologiques (Lyon: Storck,
1895), 335.
9. On this problem - that includes the example of the sound of the sea - the
principal texts are: Discours de metaphysique, § 33 [Parkinson, 43]; Letter to
Arnauld (April 1687) [Mason, 114ff]; Consideration sur la doctrine d'un Esprit
universel, § 14; Monodologie, § 20-25 [Parkinson, 182-83]; Principes de la
Nature et de la Grcice, § 13 [Parkinson, 201]. Elias Canetti has recently taken
up the theory of pricklings, but he treats it as a simple reception,
179
THE FOLD
accumulation, and propagation of commands coming from without, in Masse
et puissance (Paris: Gallimard, 1966), 321.
10. Nouveaux essais, II, chap. 1, § 10 [Remnant/Bennett, 112].
11. Salomon Manion, V ersuch aber Transzendantalphilosophie (Berlin, 1790), 33.
Kant will state his critique in a letter to Marcus Herz, in which he reproaches
Malmon for restoring infinite understanding. Martial Gueroult has reviewed
the sum of Malmon's work by underscoring the 'differentials of consciousness' and their principal of reciprocal determination, in La philosophic
transcendantale de Salomon Maiinon (Paris: Alcan, 1929), chap. 2.
12. This 'expression, albeit obscure and confused, which the soul possesses of
the future in advance, is the true cause of what will happen to it, and of the
clearer perception that it will have afterwards when obscurity will have
developed,' in a letter to Arnauld (April 30, 1687) [Mason, 114]. See also the
Nouveaux essais. II, chap. 29, § 2 [Remnant/Bennett, 254].
13. On filters or the scale of graduation, and on Leibniz's opposition to Descartes
on this point, see Yvon Belaval, Leibniz critique de Descartes (Paris: Gallimard,
1978), 164-67; Michel Serres, Le systime de Leibniz, I (Paris: Seuil, 1982),
107-26. Belaval's study is a profound analysis of Leibniz's logic of the idea.
14. In the same way Leibniz remarks, 'Bear in mind that we do think of many
things at once, but pay heed only to the thoughts that stand out most
distinctly,' in the Nouveaux essais, II, chap. 1, § II [Remnant/Bennett, 113].
Such thoughts are distinct only because they are relatively the most clear
and the least obscure. Hence Leibniz can write, 'the soul expresses more
distinctly what pertains to its body' (Letter to Arnauld, April 30, 1687)
[Mason, 113]. Or: 'The soul represents the whole universe also in
representing the body that belongs to it in a particular way' (Monadologie,
§ 62) [Parkinson, 189], although the question is only one of clarity.
15. 'For we experience within ourselves a state, in which we remember nothing
and have no distinguishable perception; as when we fall in a swoon, or
when we are overcome by a deep dreamless sleep. ... And this is the state of
bare monads,' Monadologie, § 20-24 [Parkinson, 182]. And the letter to
Hartsoeker (October 30, 1710): 'It is true that there is no soul that sleeps all
the time' (GPh, III, 508).
16. 'In the gigantic world that surrounds the tick, three stimulants shine like
luminous signals in the shadows, and they serve as signposts that would
guide it unflinchingly to its goal,' notes Jacob von Uexkiill, in Mondes
animaux et monde humain (Paris: Gonthier), 24.
17. Principes de la Nature et de la Grdce, § 4 [Parkinson, 196-97].
18. 'Le petit livre de la vie apres la mort' (1836), in Patio V III (Paris: ]'Eclat,
1987), with Claude Rabant's commentary, which especially treats of
Fechner's great crisis of photophobia, his digestive problems and his loss
of ideas (21-24).
180
NOTES
19. Jean Cocteau, La difficulte" d'étre (Paris: Rocher, 1983), 79-80.
20. Henri Michaux, 'Les 22 plis de la vie humaine,' in A illeurs (Paris: Gallimard,
1948), 172. The theme of the fold haunts all of Michaux's work - writing,
drawings, paintings - as demonstrated by the collection La vie dans les plis
(Paris: Gallimard, 1949), or the poem 'Emplie de': 'Emplie de voiles sans fin
de vouloirs obscurs. Emplie de plis, Emplis de nuit. Emplie des ON indefinis,
[Filled endlessly with folds of dark desires. Filled with
des Os de ma vigie
folds, Full of night. Filled with vague folds, folds of my vigil ...].' Leibnizian
memories are frequent in Michaux: fog and giddiness, Lilliputian hallucinations, minute perceptions speeding over a tiny surface, spontaneity: 'une
c'est un cas de spontaneite
vague toute seule une vague a part de ]'ocean
magique [a wave all alone a wave apart from the ocean ... it's a case of
magical spontaneity].' Cocteau's text above (n. 19) itself resonates with those
of Michaux because Cocteau also goes from waking to dream, and from
conscious perception to minute perceptions: 'The folding, through whose
intervention eternity becomes livable and is not done in dream as in life.
Something of this folding is unfolding within.' Finally, Fernando Pessoa has
developed a conception of metaphysical, psychological, and esthetic
perception that is quite original and yet close to Leibniz. It is based on
minute perceptions and 'maritime series'; a remarkable analysis can be found
in Jose Gil, Pessoa et la mitaphysique des sensations (Paris; Difference, 1988).
21. 'Perception and that which depends upon it and cannot be explained
mechanically. ... The explanation of perception must therefore must be
sought in simple substance, and not in a compound or a machine'
Monadologie, § 17 [Parkinson, 181].
22. Thomas de Quincey, The Revolt of the Tartars, in The Collected W ritings, vol. 7
(Edinburgh; Adam and Charles Black, 1890), 411-12.
23. 'I think that for the fundamental examination of things it is useful to explain
all phenomena by the sole perceptions of monads,' Letter to Des Bosses
(June 1712).
24. Cf. Andre Robinet, 'Leibniz: lecture du Treatise de Berkeley,' in Etudes
philosophiques (1983 ) .
25. Letters to Arnauld, November 1686 (GPh, II, 77) and April 1687 (98)
[Mason, 92-94 and 114].
26. The two basic texts are A ddition a !'explication du systhme nouveau (GPh, IV,
575-76) and Nouveaux essais, II, chap. 8 § 13-15 [Remnant/Bennett, 13132].
27. The letters to Varignon (February, April, and June 1702, in GM, IV) display
the complexity of Leibniz's position.
28. Nouveaux essais, II, chap. 27, § 4 [Remnant/Bennett, 231-32]. There is
transformation, envelopment, or development, and, finally, a fluxion of the
body of this soul. On 'the movement of fluids' and stones thrown into water,
181
THE FOLD
29.
30.
NOTES
see the letter to Princess Sophie (February 1706), in GPh, VII, 566-67. For
'conspiring movements,' see the Letters to Hartsoeker, GPh, III.
'Nature takes care to provide [animals] with organs which collect several
rays of light, or several undulations of the air,' Monadologie, § 25 [Parkinson,
183].
Bergson will rediscover this idea of a resemblance through the perceived
quality by consciousness and tiny movements 'contracted' by a receptive
organ (in the resume and conclusion to Matidre et me moire).
'Nature alone effectively receives all the impressions and comprises one of
them, but without the soul the order of impressions that matter has received
could not be sorted out, and impressions would only be confused. ... The
soul is located exactly at the point where the preceding impressions are
distinguished and held,' letter to Princess Sophie (570).
Monadologie, § 25; and the Nouveaux essais, II, chap. 21, § 72 [Remnant/
Bennett, 210-11).
-
31.
32.
8. The two floors
1. [Every, one, and some are in English in the original. - Trans.]
2. Du style philosophique de Nizolius (GPh, IV), § 31, on collective totalities and
distinctive or distributive totalities.
3.
4.
Monadologie, § 61-62 [Parkinson, 188-89].
Effectively God's first free decrees concern the whole world (moral
necessity); but the particular nature of each monad, its clear region, obeys
subaltern maxims (hypothetical necessity; if such is the sum, then the parts
...). Cf. Discours de melaphysique, § 16 [Parkinson, 29], and Remarques sur la
lettre de M. A rnauld (May 1686) [Mason, 39-52]. In this sense hypothetical
necessity is firmly grounded in moral necessity, as is shown by L'origine
radicale des choses [On the Ultimate Origination of Things, Parkinson, 136-44];
and inversely, moral necessity and final causes are everywhere in the
concatenations of hypothetical necessity (Discours de melaphysique, § 19).
5. Hegel shows that the application of infinitesimal calculus implies the
distinction of two parts or moments of the 'object.' He admires Lagrange for
having brought it forward, in Science de la logique, II (Paris: Aubier, 1981),
317-37.
6. Essai anagogique dans le recherche des causes (GPh, VIII). Maurice Janet
analyzes the principal qualities of extremum in La finaliti en mathimatiques et
en physique (Recherches philosophiques. II). The problem of the 'brachystochrone' that Leibniz often studies happens to be a problem of extremum
('minimal descent'). So too is the question of the gothic arch (the best form
of a projectile in a liquid) in Newton's Principia mathematica.
7. After having analyzed Janet's themes, Albert Lautman clearly marks the
182
limit of extrema, or the difference of nature between two kinds of
properties. 'Insofar as properties that make selection possible are properties
of maximum or minimum, they confer the obtained being with an
advantage of simplicity as if it were an appearance of finality, but this
appearance disappears when we realize that what assures the passage to
existence is not the fact that the properties in question are extremal
properties, but that the selection they determine is implied through the
totality of the structure in question. ... The exceptional property that marks
it is no longer a property of extremum, but the property of being the limit of
a convergent series,' in Essai sur les notions de structure et d'existence en
mathe'matiques, chap. 6 (Paris: Hermann, 1938; reprint, Union generale
d'editions 10/18, 1977), 123-25. It is true that in the Origine radicale des
choses [Parkinson, 136-44], Leibniz likens the selection of the best world to a
property of extremum; but it is at the cost of a fiction that consists in
considering space as an empty 'receptivity,' common to all possible worlds,
that must be filled with a maximum number of places. In fact, we have
observed that the distinction of incompossible wholes was not based on
properties of extremum but on serial properties.
8. See Bernard Cache, L'ameublement du territoire (forthcoming), in which the
two levels are clearly distinguished (inflection-extrema, vector of concavityvector of gravity).
9. Raymond Ruyer, especially La conscience et le corps (Paris: PUF, 1950);
Eliments de psychobiologie, Niofinalisme (Paris: PUF, 1952); and La genise des
formes viantes (Paris: Flammarion, 1958).
10. Leibniz announces his agreement with Newton on the law of gravitation
inverse to squares, but thinks that attraction is sufficiently explained with
the special case of fluids and 'their impulsions' (harmonic circulation of
planets whence originates a centripetal force). Here we have an entire
theory of the formation of a vector of gravity, in the Essai sur les causes des
mouvements celestes, GM, VI; and on magnetism, Ed. Dutens, II. On the
alternative of 'attraction-impulsion' (even for Newton), see Koyre, Etudes
newtoniennes (Paris: Gallimard, 1968), 166-97. With a tinge of irony Koyre
underscores the importance of the Essai for a conciliation of Newtonian
gravity with the action of succession 'Leibniz did what Huygens did not
succeeded in achieving ...' (166 and 179).
11. Ruyer, La genise des formes vivantes, 54,68.
12. Leibniz's correspondence with Des Bosses begs this question of the
'realization' of phenomena or of the perceived outside of the souls. On
'Realizing,' see the letter of April 1715.
13. The theme is frequent in Blanchot, especially in L'espace litte'raire (Paris:
Gallimard, 1955), 160-61 [tr. Ann Smock, Literary Space (Lincoln: University
of Nebraska Press, 1988)]. This conception of the event can be compared to a
183
THE FOLD
Chinese or Japanese tradition, such as what Rene de Ceccatty and
Nakamura translate and comment in ShObcigenzO, La reserve visuelle des
evinements dans leur justesse, by D8gen, the thirteenth-century monk (Paris:
Editions de la Difference). [See also La vision immediate: nature, iveil et
tradition selon le Sh6bOgenzii, trans. Bernard Faure (Paris: Le Mail, 1987), or
Kosen Nirhiyama and John Stevens, trans., A Complete English Translation of
Dagen Zenji's ShObagenze 4 vols. (Sendai, Japan: Daihokkaikaku, and Tokyo:
Nakayama Shobo, 1975-83). - Trans.]
14. Leibniz often underlines that the union of the soul and the body, defined by
an 'immediate presence,' cannot be confused with harmony, in the
Thiodicee, discourse § 55; Remarque
sur un endroit des memoires de Trevoux
(GPh, VI, 595-96); Letter to Remond, November 1715 (GPh, III, 658). See
Christiane Fremont's commentary in L'Etre et la relation (Paris: Vrin, 1981),
41. The Systeme nouveau de la Nature (§ 14) [Parkinson, 121] marks the
linkage of the two problems, and the passage from one to the other. Clearly
Malebranche's occasionalism also appeals to incarnation, but as a mystery of
faith. Although he tends to express himself in the same way, Leibniz
sometimes takes up the problem of incarnation as something intelligible and
resolvable, at least at the human level.
15. 'Although I do hold neither that the soul changes the laws of the body, nor
that the body changes the laws of the soul, and that I may have introduced
preestablished harmony in order to avoid this trouble, I am not willing to
admit a true union between the soul and the body that makes a supposition
of it,' Thlodicie, discourse § 55.
16. End of the preface to the Nouveaux essais [Remnant/Bennett, 65-68).
17. Monadologie, § 70 [Parkinson, 190]; letter to Des Bosses (June 1712).
18. Letter to Arnauld, September 1687 (GPh, II, 120) [Mason, 143ff (October 9,
1687]. And: 'But we must not imagine, as some have done who have
misunderstood my view, that each soul has a mass or portion of matter
appropriate or attached to itself forever, and that it consequently possesses
other inferior living things, forever destined to its service,' Monadologie. § 71
[Parkinson, 190].
19. Letter to Lady Masham, June 1704 (GPh, III, 356).
20. In his groundbreaking article 'Monadologie et sociologie,' Gabriel Tarde puts
forth this substitution of having for being, as a true inversion of metaphysics
that issues directly from the monad; in Essais et melanges sociologiques (Lyon:
Storck, 1895). Jean Milet has commented on this theme and proposes
naming 'echology' this discipline that replaces ontology, in Gabriel Tarde et la
philosophie del' histoire (Paris: Vrin), 167-70.
21. Nouveaux essais, II, chap. 27, § 4-6 [Remnant/Bennett, 231]. The theme is
constant in his correspondence with Des Bosses.
22. On this distinction in scholastic theories of the vinculum, see Leonore
184
NOTES
Boehm, Le vinculum substantiale chez Leibniz (Paris: Vrin, 1962), 77-98; see
also the letter to Des Bosses, Apri11715: 'This link will always be tied to the
dominant monad.'
23. Buffon develops a paradoxical idea that is very close to the vinculum: an
'inner mold' is imposed upon variable organic molecules, in Histoire des
animaux, chap. 3. See also Georges Canguilhem, Connaissance de la vie (Paris:
Vrin, 1975), 63-67 and 215-17, on the use of the word 'monad' - according
to Leibniz - in natural history.
24. The vinculum is 'as such naturally, but not essentially, for it requires
monads, but does not basically envelop them, since it can exist without
them and they can exist without it,' in a letter to Des Bosses (May 1716).
25. Letters to Des Bosses (April and August 1715).
26. The theory of the vinculum comes late in Leibniz's work, appearing in the
correspondence with Des Bosses (1706-1716). Two of Belaval's commentaries have especially enlightened its problems, in Leibniz, Initiation a la
philosophie (Paris: Vrin), 244-52; also, Christiane Fremont, L'Etre et la
relation (Paris: Vrin, 1981), 31-42. Fremont shows that the vinculum is
crucial to Leibniz's theory of relation; she renews our knowledge of this
theory.
27. The soul of the insect that is cut in two, up to infinity, or the soul of the goat
in ashes, remains in an area, no matter how small, where they are projected
(letter to Arnauld, April 1687) [Mason, 125ff]; the soul's 'point of view' is in
the body (Nouveaux essais, II, chap. 8, § 13-15) [Remnant/Bennett, 131-32]:
through a relation of projection we are able to locate a pain, for example, in
the body.
28. To be sure, there is strictly speaking neither generation nor corruption of
organisms, but only composition. Leibniz nonetheless retains the category of
generation-corruption in order to have it distinguished from the two other
categories of 'kinesis'; inner change and outer local movement. But if the change
is of a psychical nature, organic composition is as much material as it is
movement. Cf. the letter to Lady Masham (July 1705), 368. Plastic forces are
in themselves 'mechanical.'
29. Letter to Arnauld (October 1687) [Mason, 153]. And his letter to Des Bosses
(May 1716): 'I limit corporal, that is, composite, substance to living beings
alone, that is to say, solely to organic machines.'
30. 'Secondary matter is an aggregate,' letter to Des Bosses (May 1716); it is
'only piled up,' in the Nouveaux essais, IV, chap. 3, § 4. To the contrary, in a
broad sense, see the preceding letter to Arnauld, and De la Nature en elleméme. § 12 ('secondary matter is a complete substance'). On the meanings of
secondary and primary matter, and on the terminology of 'massa' and
'moles,' see Christiane Fremont's remarks (n. 25 above), 103 and 132-33.
31. Raymond Ruyer has marked very well this mixed area, either in Markov's
185
THE FOLD
chains (La genise des formes vivantes, chap. 8), or in atomic phenomena (Neefinalisme, 218-20).
32. As a painter of textures, Caravaggio modulates dark matter with colors and
forms that act as forces. See Francoise Bardon, Caravage ou l'experience de la
matiire (Paris: PUF, 1978), 68-71. See also the comparison with Giordano
Bruno.
33. 'Semi-beings, that are not upheld by a vinculum,' in his Letter to Des Bosses
(August 1715).
34. A ddition a l'explication du Systeme nouveau (GPh, IV, 587); Letter to the Abbe
de Conti (Dutens III, 446).
35. For these inner unities and external determination, see Eclaircissement des
difficulte's de la philosophie premiere et de la notion de substance; De la Nature en
elle-mime ou de la force immanente, § 14.
36. On the need to recast the Aristotelian coupling of power and action, see the
Letter to Des Bosses (February 1706); De la reforme de la philosophie premiere et
de la notion de substance. And on force-disposition-tendency, see the preface
to the Nouveaux essais; II, chap. 1, § 2, and chap. 21, § 1. In the latter passage,
monads of the first species are said to be 'primary acting forces' [Remnant/
Bennett, 170-71]. That is literally true to the extent that they 'have
impenetrability.'
37. In addition to the writings of his youth, the basic text is Leibniz's letter to De
Voider (in response to that of August 1699, GPh, II, 191). Gueroult
demonstrates that the two models of movement, free action and labor, are
united in this respect. 'We obtain a succession of pulsations, each having a
distinct reality in that each time marks a different instant,' and not at all
because of a discontinuity of time, but for the reason that its very continuity
implies the change of what fills it in two instants, no matter how frequent
they are. Cf. Leibniz: Dynamique et metaphysique leibniziennes (Paris: AubierMontaigne, 1978), 148-49.
38. Letter to Jaquelot, March 1703 (GPh, 111, 457); letters to De Voider (June
1703, June 1704). See Gueroult's commentary and his interpretation of
derivative force as 'predicate' (193-94).
39. 'Matter (I mean the secondary or mass) is not one substance, but made of
substances ...' in his Letter to Jaquelot, November 1715; 'Secondary matter
is not a substance, but ... a mass of several substances,' in his letter to
Remond, November 1715 (GPh, 111, p. 657). The Systeme nouveau de la
Nature speaks of 'brute souls' (§ 6) [Parkinson, 118].
40. Discours de metaphysique, § 35-36; Monadologie, § 83-86 [Parkinson, 192-93].
At the end of his letter to Arnauld in April 1687, Leibniz appeals to a 'right of
the bourgeoisie' that must be reserved for true substances [Mason, 127-29].
See Andre Robinet's remarks in A rchitectonique disjonctive (Paris: Vrin, 1986),
51.
186
NOTES
41. Principes de la Nature et de la GrcIce, § 4. The other texts on classes of monads
are notably his letter to Wagner of June 1710 (GPh, VII, 529), and the
Monadologie, § 18 ff. [Parkinson, 181ff].
42. The theme is constant in Leibniz and is especially developed in his polemics
with the physician Stahl (Remarques et exceptions. Dutens II). Leibniz
contends at once against mechanism, that souls exist in Nature; and against
'paganism,' that they do not act outside of themselves or upon bodies. It is
clear that Leibniz is not satisified with a vitalism or an organicism. He sticks
to an animism for which he refuses an exterior efficacity. It is quite different
from a vitalism in the manner of Kant or of Claude Bernard. It breaks with
animism, all the while keeping two levels, the one being mechanical and the
other only regulatory or directive, in a word, 'ideal' without being active.
The difficulty of Kant's solution is that we cannot be sure if the organic or
vital idea is a force, that is, a soul.
43. "Tis an hard matter to say where sensible and rational begin, and ... which
is the lowest species of living things ... and that the only difference is that
between the large and the small, between sensible and insensible,' Nouveaux
essais. IV, chap. 16, § 12 [Remnant/Bennett, 471 and 474].
44. Letter to Des Bosses (April 1715): 'hoc realisans
9. The new harmony
1. Rhingrave means 'breeches of extreme breadth, up to a yard and a half per
leg, with folds so abundant that they absolutely look like a skirt and impede
the eye from seeing where the legs begin to separate,' in Francois Boucher,
Histoire du costume (Paris: Flammarion, 1965), 256-59.
2. See Bresc-Bauteir, Ceysson, Fagiolo dell'Arco, and Souchal, La grande
tradition de la sculpture du X V e au X V II! siècle (Geneva: Skira, 1987). Fagiolo
dell'Arco has excellent remarks on Baroque sculpture, and so does Souchal
for the 'Rococo.' The examples raised here are all reproduced and analyzed
in this book (191, 224, 231, 266, 270).
3. Heinrich WOIfflin, Renaissance et Baroque. trans. Guy Ballange (Paris: Poche,
1987), 73 (and all of chap. 3).
4. Carl Andre's planar sculptures, and also the conception of 'rooms' (in the
sense of the rooms of an apartment) would not only illustrate the passages of
painting and sculpture, or of sculpture and architecture, but also the
extensive unity of minimal art, in which form no longer contains a volume
but embraces a limitless space in all directions. One is struck perhaps by the
properly Leibnizian position to which Tony Smith appeals: a closed car going
along an interstate highway that only the headlights are illuminating, and
on whose windshield asphalt streams past at top speed. It is a monad, with its
privileged zone (if we object that the closure is not in fact absolute, since the
187
NOTES
THE FOLD
asphalt is on the outside, then we must recall that neo-Leibnizianism
requires a condition of capture rather than one of absolute closure; and even
here closure can be considered to be perfect insofar as the asphalt on the
outside has nothing to do with what passes by on the window). A detailed
review of explicitly Baroque themes has to be made in minimal art and then,
too, in constructivism. See the remarkable analysis of the Baroque by
Strzeminski and Kobro, in L'espace uniste, ecrits du constructivisme polonais
(Lausanne: L'Age d'Homme, 1977). And also, in A rtstudio (no.6, Fall 1987),
the articles by Criqui on Tony Smith; Assenmaker on Carl Andre; Celant on
Donald Judd; Marjorie Welish on Sol Lewitt; Gintz on Robert Morris: that
move to a constant confrontation with the Baroque (we can especially refer
to Robert Morris's folds of felt, 121, 131). A special study would also have to
be written on Christo's 'performances,' on his giant wrappings and the folds
of their envelopments.
5. See not only the pyramid of the The'odicie, which covers all possible worlds,
but also the cone of the Nouveaux essais (IV, chap. 16, § 12), which prevails
for the totality of our world: 'Things ascend upwards in degrees of
perfection. 'Tis an hard matter to say where the sensible and the rational
begin.... It is like the way quantity augments or lessens in a "regular" cone'
[Remnant/Bennett, 471].
6. On the formation of an infinite universe that has lost its center, and of the
role that Giordano Bruno plays in its articulation, see Alexandre Koyre From
the Closed W orld to the Infinite Universe (New York: Harper, 1958). Michel
Serres demonstrates that a new unity becomes manifest when the summit of
a cone is placed at the center of a sphere (Le systeme de Leibniz, II, 653-57).
Yves Bonnefoy has studied the complex position of the theater in the theme
of the Baroque: neither illusion nor renewed awareness, but using illusion
in order to produce one's being, to construct a site of hallucinatory Presence,
or 'reconverting nothingness glimpsed in presence,' since God surely made
the world out of nothing. Such is what Bonnefoy calls 'the movement of
interiority,' in Rome 1630 (Paris: Flammarion, 1970).
7. Benjamin, 'Allegory and Trauerspiel,' in The Origins of German Baroque
Drama, trans. John Osborne (London: Verso, 1985). See also Hocquenghem
and Scherer, 'Pourquoi nous sommes allegoriques,' and 'Pourquoi nous
restons baroques,' in Lame atomique (Paris: Albin Michel, 1986).
8. Many seventeenth-century authors (notably Tesauro) attempt to distinguish
devices ('imprese') from emblems. The former would refer to an individual,
while the latter would express a moral truth and gain the privilege of being
developed in cycles. But we all know that the distinction is abstract, and that
personal reference does not disappear. Even if it is blurred, a pertinence is
evident. See especially Cornelia Kemp, 'Cycles d'emblemes dans les eglises
de l'Allemagne du Sud au XVIII e siecle,' and Friedhelm Kemp, 'Figuration et
188
inscription,' in Figures du Baroque (Paris: PUF, 1983). Cornelia Kemp cites an
especially interesting example in the Saint Leonard cycle in Apfeltrach: the
proper name contains a double propositional concept ('leo' + 'nardus') that
inspires the two parts of the cycles of images.
9. Vanuxem, 'Le Baroque au Piemont,' in Renaissance, Manierisme, Baroque
(Paris: Vrin, 1972), 295.
10. 'To reinforce the distinction between essence and definition, bear in mind
that although a thing has only one essence, this can be expressed by several
definitions, just as the same structure or the same town can be represented
by different drawings in perspective depending on the direction from which
it is viewed,' in the Nouveaux essais, III, chap. 3, § 15 [Remnant/ Bennett,
294]. We should recall that if the point of view is said to vary with each
scenography, it does so only by convenience of expression. In truth, point of
view is the condition in which 'scenographies' or drawings in perspective
form a series.
11. 'The ichnographic chart of the Universe, the relation of all-to-one and oneto-all is the systematic theme of Leibnizianism and of this work,' Serres, II,
620.
12. Cf. The'odicee, § 416. Christiane Fremont has shown in what way the story of
Sextus is a 'founding narrative' of the Roman empire, in 'Trois fictions sur le
probleme du mal,' in Rene Girard et le probleme du mal (Paris: Grasset, 1982).
13. Principes de la Nature et de la Grace, § 17 [Parkinson, 203-4].
14. Elements de la piete veritable (Grua, 12). Yvon Belaval, it must be noted, does
not believe that Leibnizian harmony attests to a particularly musical
inspiration, in Etudes Leibniziennes (Paris: Gallimard, 1976), 86. And when he
confronts Leibniz with musical forces, he thinks of a modern 'algorithmic
music' (381), and not of Baroque music of Leibniz's time.
15. Elements de philosophie cachee, J, 35-36. (The text of the Elements de la piell
offers an analogous movement.) Nicolas de Cusa's writing is the Dialogue sur
la pensie, chap. 6: 'There can be only one infinite principle, and that one
alone is infinitely simple,' in Oeuvres choisies, ed. Maurice de Gandillac (Paris:
Aubier-Montaigne, 1941), 274-76.
16. For Nicolas of Cusa, the irrational number is the 'most simple' because it
must itself be odd and even, instead of being composed of an odd and an
even. But, according to Leibniz, it happens that the irrational envelops an
infinite series of rational finite numbers, in the form of inverse numbers:
1 1 1 1
- - - +- - 1 3 5 7
In Nouveaux essais, IV, chap. 3, § 6 [Remnant/Bennett, 376-77]; and also De
la vraie proportion du cercle au carre circonscrit (GM, V, 118-22). Harmony
refers to this type of series.
189
THE FOLD
NOTES
17. On the harmonic triangle of number, see the Histoire et origine du calcul
differentiel (GM, V, 396-406), and the Nouvelle avancee de l'algibre (VII, 175):
the base of the triangle is no longer the succession of natural numbers, but
the series of inverse numbers
1 1 1
1 ' 2' 3'
18.
19.
20.
21.
22.
23.
24.
Serres has studied the characters and laws of the harmonic triangle, and has
demonstrated the extent of its importance in theory of harmony (I, 186-92
and II, 448-77, on the relations with music). For the harmonic circulation of
the planets, and the law of the proposition inverse to squares, by which
Leibniz integrates Newtonian gravitation, see the Essai sur les causes des
mouvement celestes (GM, VI); and Koyre, Etudes newtoniennes (Paris: Gallimard,
1968), 166-9.
'This mutual relationship of different substances ... is one of the strongest
proofs of God's existence, or of a common cause that every effect must always
express according to its point of view and its ability,' in his letter to Amauld
(September 1687), GPh, IL 115 [Mason, 147-48 (9 October 1687)].
Considerations sur la doctrine d'un Esprit universel unique, GPh, VI, 535. [In
French the relation of spirit, breath, or breeze is clearly marked in the
presence of the Latin spiritus (breath) in esprit (spirit, wit, mental capacity,
etc. - Trans.]
Abraham Robinson, Non-Standard A nalysis, Amsterdam: North Holland, 1966.
Letter to Arnauld (April 1687) [Mason, 113].
[The text plays on accord as linkage, entente, agreement, but also on its
meaning, in music, as chord. As in Logique du sens, amphiboly plays
throughout the logic of the discussion. - Trans.]
On the conciliation of the little elements of disquiet with the bonds of
felicity, and the infinite progression that follows, see the Nouveaux essais, II,
chap. 21, § 36 [Remnant/Bennett, 188-90]; Profession de foi du philosophe, ed.
Belaval (Paris: Vrin, 1961), 87. For the 'harmonic' character of felicity, see
31-33.
The minute solicitations of disquiet are not already located in pain or in
suffering, but they can be integrated in pain. See the Nouveaux essais, II,
chap. 20, § 6. Dissonance of pain must be prepared: chap. 21, end of § 36
('So it is all a matter of "Think about it carefully" and "Remember"'
[Remnant/Bennett, 189-90]. On the example of the dog, cf. L 'eclaircissement
des difficulte's que M. Bayle a trouve'es dans le systime nouveau de I'dme et du corps
(GPh, IV, 532).
25. On the active resolution of dissonance, see the Profession de foi, 45, 89, 93.
26. On the situation of the damned, and the way that they are inversely
symmetrical to the 'blessed,' see the Profession de foi, 85.
190
27. Eclaircissement des difficultes (GPh, IV, 549). We should note how Raymond
Ruyer emphasizes the vertical position of the monads or authentic forms.
28. Correspondence with Clarke, fifth writing, § 91. And in the letter to
Wagner, March 1698 (Grua, 395): 'sum monades, non monachae.' Cf.
Andre Robinet, A rchitectonique (Paris: Vrin, 1986), 361.
29. Dynamics 'do not at all imply something more than a simple coordination of
inner spontaneities, that is, preestablished harmony,' notes Gueroult,
Dynamique et melaphysiatte leibniziennes (Paris: Belles Lettres, 1934), 176.
30. Letter to Arnauld (April 1687) [Mason, 119].
31. On the examples of the boat, of pain, and voluntary movement, see the
draft, and then the letter to Arnauld (November 1686) [Mason, 84-85].
Following the case, 'distinct expression' of a substance will be said to 'be
increased' (action) or to 'be diminished' (passion). See the Discours de
metaphysique, § 15.
32. 'My hand moves not because I will it to do so ... but because I could not will
it with success: except at the precise moment that the elasticity is about to
slacken in the requisite way to achieve this result. ... They go with one
another, by virtue of the relationship established above, but each has its
immediate cause in itself,' in a letter to Arnauld (September 1687) [Mason,
149 (October 9, 1687)]. 'And a soul effects no change in the course of
thoughts of another soul. And in general one particular substance has no
physical influence over another,' in the draft of a letter to Arnauld
(November 1686) [Mason, 87].
33. See Manfred Bukofzer, Histoire de la musique baroque, 1600-1750 (Paris:
Lattes, 1982), 242-44, 390-391. On the appearance of a continuous bass, its
relation with harmony, tonality, and a new counterpoint, see Leo Schrade's
Monteverdi (Lattes), and Pascale Criton's forthcoming study.
34. Uexkiill has made a great, highly Leibnizian review of Nature as a melody:
'Theorie de la signification,' in Mondes animaux et monde humain (Paris:
Gonthier). For 'living tonalities' see 103; and for melodies and motifs: 'The
flower acts on the bee like a sum of counterpoints because its melodies of
development - so rich in motifs - have influenced the morphogenesis of the
bee, and inversely. ... I could affirm that all of nature participates like a
motif in the formation of my physical and spiritual personality, for if such
were not the case, I would not possess organs in order to familiarize myself
with nature' (145-46).
35. Elements de philosophie cachee: The mark of [harmonic] existence is the fact
that the senses conform to each other.' The quotation from Uexkfill above
resembles the commentary of this formula.
36. On most of these points, see Bukofzer, especially chap. 1, and the
comparative review of the Renaissance and the Baroque (24). Rameau's
Observation sur notre instinct pour la musique et sur son principe of 1754 (recently
191
THE FOLD
reprinted by Slatkine) might be considered as the manifesto of the Baroque
and - with its emphasis on the expressive value of accords - the primacy of
harmony. Jean-Jacques Rousseau's position, which is frequently misunderstood, is quite interesting because it is resolutely and willfully retrograde.
For Rousseau decadence does not begin with harmony of accords and their
pretension of being 'expressive,' but already with polyphony and counterpoint. Rousseau feels that we must return to monody as pure melody alone,
that is, a pure line of vocal inflection that rightfully precedes polyphony and
harmony. The only natural harmony is unison. Decadence begins when,
under the influence of the barbaric North, voices become 'inflexible,' when
they lose their inflections for the sake of firm articulations. See Rousseau,
Essai sur l'origine des langues (Paris: Bibliotheque du graphe, 1979'), chaps. 14
and 19. It can be noted that for Leibniz too (and probably for Rameau),
harmony and melody always presuppose a line of infinite inflection; yet
harmony and melody convey it adequately, and the line cannot exist
without them, the line being in itself 'virtual.'
37. On the evolution of the relation of harmony and melody, and on the
formation of a 'diagonal,' see Pierre Boulez, Relevis d'apprenti (Paris: Seuil,
1967), 281-93. And for point of view over the city, Par volonte et par hasard
(Paris: Seuil, 1975), 106-7. Among the critics of Boulez's Pli selon pli
(London: Universal Editions, 1982), Ivanka Stolanova is especially attached
to the way that Mallarme's texts are folded, in accord with new relations of
text and music, in Geste texte musique (Paris: Union generale d'editions 10/18,
1978). See also Jehanne Dautrey, La voix dans la musique contemporaine
(Wyres: Van den Velde, 1987). The expression 'fold-in' is borrowed from
Gysin and Burroughs, who designate thus a method of textual folding, in
extension with the 'cut-up.' (In the same way Carl Andre defines his
sculptures as cuttings or folds in space.)
Index
absolute forms 51, 55-6
Adam 67, 71-3, 78-84
allegory 143-6
ambiguous signs 22-3
animism 12, 138
antecedence 51
appurtenance, theory of 122-6
architecture 31-3, 37, 75-6, 141-2
Aristotle and Aristotelianism xxi, 49,
56, 60-2
Arnauld, Antoine xiii, 27, 60, 62, 98
arts, the, unity of 141-2
automatism of perception 102
Bacon, Francis xiii
Baer, Jean-Georges 11
Baltrusaitis, Jurgis 38
Beckett, Samuel 125
Belaval, Yvon 128
Benjamin, Walter 143
Bergson, Henri xiii, 14, 80, 82, 133
Berio, Luciano 156
Berkeley, George 108
Bernini, Gian Lorenzo 139-40, 142
Bettencourt, Suzanne 40
binary arithmetic 41
Blanchot, Maurice 50, 120
192
Borges, Jorge Luis 70-1, 92
Boulez, Pierre 15, 38, 93
Boyle, Robert 7
Bruno, Giordano 25
Buci-Glucksmann, Christine 37
Butler, Samuel 89
Cache, Bernard 15-16, 20, 41
Cage, John 156
calculus see differential calculus
capitalism 126
Caravaggio, Michelangelo
Merisi da 35, 131
Cartesianism 7, 60, 71, 97, 102-4, 109
catenary curvature 115
causality, physical and psychic 111
chaos 86-7
Christian, Johann Joseph 140
Clerambault, Gaetan xii, 43, 99, 107
clothing, styles of 139-40
compossibility and incompossibility
57, 67-84, 103
compression of time and space xvii
concertism and concertation 48,
143-5, 152-3, 156
conic sections 22-3, 26
continuity, law of 75
193
INDEX
THE FOLD
contradiction, principle of 65
Corradini, Antonio 140
counterpoint 147, 155-6
Couturat, Louis 52, 65
Coysevox, Antoine 140
cupolas 142-4
Cuvier, Georges 11
Dasein 28
De Voider, Burcher 48
Debussy, Claude 156
derivative forces 104, 131, 134-5, 140
derived beings 51
Derrida, Jacques xiii, xxi
Desargues, Gerard 13, 22, 36
Descartes, Rene xviii, 3, 5-6, 36, 48,
51, 61-4, 103
differential calculus 18-19, 110-11
dissonance 151, 157
Donatello 38
Dubuffet, Jean 40, 42, 158
Einfalt 11
El Greco 33, 38, 140
entelechia 80, 135
epigenesis 10-11
epistemology 63
essences, definition of 49
eternal objects 90
European Economic Community xv
events 87
evil, theory of 151
existensification 119
extremum, law of 118, 141-2
facades 31-2
Fautrier, Jean 40
Fechner, Gustav 105-7, 111
Fichte, Johann Gottlieb 101
fluxion 111-12, 124, 130-2
Focillon, Henri xii, xiv, xix
Fremont, Christiane 128
194
Gasset, Ortega y 50, 64
geometry of perception 109-10
geophilosophy xv-xvii
Germany 36-7
Gestalt theory 107, 117-18
God: attributes of 50; existence
of 51, 58; hate of 81
Gombrowicz, Witold 92
Gothicism xii
Gousjon, Jean 140
Great Pyramid 90
Grenot, Nicole 41-2
Gropius, Walter 39
Guattari, Felix xiv-xvii
Gueroult, Martial 72
habitus 101, 133
hallucinatory perceptions 98, 107,
110
HantaI, Simon 38, 40, 99
harmony 146-57
Hegel, G.W.F. xiii-xiv
Heidegger, Martin 11, 28, 33
Heinzen, Helga 42-3
Helmont, Jan Baptista van 7
Hippolyte, Jean xiii
homothesis, law of 17
Husserl, Edmund 122-5
Huygens, Christian 5
identicals 51-2, 55-8, 65
immanence 25-6
inclusion, types of 55, 58; see also
inflection in relation to inclusion
incompossibility see compossibility and
incompossibility
indiscernibles, principle of 74
individuation 27, 72-4
inflection 15-21, 104, 116; in relation
to inclusion 24-7, 47, 80
inscriptions 144
interiority 80
inverse numbers 147-50
involution 22
irrational numbers 18-19, 59, 74, 147
James, Henry 21, 23
James, William 21, 114
Jeanclos, Georges 42
Joyce, James 92
Kafka, Franz xiii
Kandinsky, Wassily 15
Kant, Immanuel 21, 37, 51, 55, 76,
78, 102, 136, 138
Klee, Paul 15-16, 40
Kleist, Heinrich von 143
Knecht, Herbert 37
Koch, Alexander 16-17
Lanfranc (Giovanni Lan-franco)
142
Le Corbusier 31
Leblanc, Maurice 70-1, 92
liberty, human 78-80, 83
Locke, John 4
Louis VIV 144
Lucretius xiv
139,
macroperception 108
Maimon, Salomon 101-2
Malebranche, Nicholas 12, 56, 67,
121, 133, 155
Mallarme, Stephane xiii, 34-5, 38, 43,
76
Mandelbrot, Benoit 17
mannerism 41, 43, 61, 64, 77-8
materialism 138
mathematics 18-19, 73-4
Mazarin, Cardinal 144
melody 146, 154-7
Melville, Herman xiii
metaschematism 132
Michaux, Henri xii, 38
minute perceptions, theory of
99-104, 107
Monadology (Monadologie) 145
monads, classification of 105-6
motives, objectification and division
of 79
musicology 152
Neo-Leibnizianism 157
Neo-Platonism 25, 33
Newton, Sir Isaac 111-12, 117-18
Nicolas of Cusa 147
Nietzsche, Friedrich xiii, 21, 36, 76,
81, 126
nihilism 76
nomadology xvi
nominalism 73, 114
objectiles 20
occasionalism 155
ontology 51
optimism, principle of 77-8, 85
organic and inorganic matter 7-10,
152
origami 7
Pascal, Blaise 147
painting 141, 145
pantheism 149
perception: geometry of 109-10;
psychology of 105; see also
macroperception; minute
perceptions
perspectivism 21, 23
Philosopher's profession of faith (Profession
de foi du philosophe) 35
plastic forces 8, 11-12, 130-2
Platonism xiv, 33, 42-3, 148; see also
Neo-Platonism
pleonasms 57
Plotinus 26
Pollock, Jackson 30
195
THE FOLD
polyphony 155
predicates 60-1, 79-80, 126-7
preformation, theory of 10-11
prehension 88-92
primary forces 104
prime numbers 52
principles, creation of 66
Proust, Marcel xiv—xv
psychophysics 111
Quincey, Thomas de 107
quincunx system xviii
Rameau, Jean-Philippe 151, 155
Rauschenberg, Robert 30
reason 47-9, 76; see also sufficient
reason
reciprocal numbers 147
Robinson, Abraham 149
Rousset, Jean 32
Russell, Bertrand 61, 114
Ruyer, Raymond 116-18
scenographies 22
sculpture 141-3
secondary matter 112, 130-1
series, law of 20
Serres, Michel 22, 145
similitude, principle of 65
singularity 104
Smith, Tony 157
soul, the: creation of motives and
inclinations of 79-80;
progress of 83-5; in relation to the
body 12-13
Spinoza, Baruch xiii—xiv, 51, 121
spontaneity (Leibniz) 151, 154
Stockhausen, Karlheinz 156, 158
Stoic philosophy 60-3, 79
196
subaltern maxims 115, 118
substance, theory of 62-3
sufficient reason, principle of 53-4,
57, 65, 153
syllogisms 56
Tarde, Gabriel 125
Tesauro, Emmanuel 145
texturology 131
theodicy 78
Theodicy (Thiodicie) 69
Thomson, D'Arcy 118
Thorn, Rene 16
Tintoretto 32-3, 85
tonality 157
topology 127
totalization process 100
trompe l'oeil effects 31, 42, 142
Ts'ui Pen 70-1
Uccello, Paolo 38
'universal spirit' doctrine 26
universalism 73
Urfee, Honore d' 71
utopia xviii
vice-diction 67-8
vinculum function 126-34, 137,
154-5
Wagner, Richard 156
Weyl, Hermann 54
Whitehead, Alfred North xii—xiii, 21,
61, 83, 86-92, 135
Wittgenstein, Ludwig 86
WOlfflin, Heinrich 4, 32, 36, 141
Zurburan, Juan de 139
Zweifalt 11, 33, 137