Notes on Deleuze’s The Fold: Leibniz and the Baroque

Part One: The Fold

That last chapter fucked me up.

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Deleuze G (2020) The Fold: Leibniz and the Baroque (Conley T trans), University of Minnesota Press, Minneapolis, USA.

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Chapter One: The Pleats of Matter

‘The Baroque’ refers to the function of producing folds to infinity. There are two types of folds, corresponding to two floors in a house, each of which go on infinitely: the first is matter, the second the soul

On the bottom floor, of matter, the matter is collected by a fold separating matter from soul, and organised by a fold that places the more soul-like matter above the less soul-like matter. Similarly, the soul is never entirely divorced from matter, and is organised in the same way

Something can be composed of one thing but folded in many ways, and this would still be multiple

The two levels of folds (the floors of the house) are connected, in a limited manner of course, so there’s something of a gradation (higher and lower souls, higher and lower matter). The bottom floor has windows (the five senses), whereas the upper floor has no windows. That is, the soul can receive information about the world only if matter does (through the senses) and communicates it to the soul

The folds of matter cause those of the soul to vibrate

The way Leibniz discusses this varies in specifics, but the above is faithful (according to Deleuze, at least)

Wölfflin has observed that the Baroque (architecture, presumably) is characterised by four traits. Firstly, a tendency to expand horizontally (seen in the pediment, stairs, and lower floors). Secondly, the treating of matter as an aggregate, the avoidance of corners and edges. Thirdly, the tendency to make shapes conform to a fluid, curving, vortical motion. Fourthly, the characterisation of matter as somewhat fluid and of fluids as a collection of matter

Leibniz’s understanding of the universe is of a tangential line whose curvature is lengthened by “the fluidity of matter, the elasticity of bodies, and motivating spirit as a mechanism” (2020:4). A force compresses the universe, turning each bit of matter into a vortical shape (itself dividing into smaller bits of matter similarly shaped, etc.), and so matter is a series of caverns completely filled with their own caverns. Parts of distinct matter can be inseparable, according to the pressures and forces that determine their hardness and curvilinear movement, and so bodies are (to varying degrees) elastic

Matter is composed not of particles but of infinite folds (so matter is always an aggregate), the corollary of an elastic force; unfolding “follows the fold up to the following fold” (2020:6)

The formation of life remains mysterious if matter is a collection of points, but if it is an infinity of states (folds folding over one another) then this becomes more likely to occur, for a reason left unstated

Because motion is possible, there must evidently be a motivating force at play in matter: “to the extent that folding is not opposed to unfolding, such is also the case in the pairs tension-release and contraction-dilation” (2020:7)

The lower floor also contains organic matter, separated from inorganic matter since the organic has an internal fold, shaped by plastic forces which also initially preform the internal fold of organic matter: all organs come from prior organs

Mechanisms are composed of parts that are not machines; organs are composed of parts that are machines, which are composed of parts that are machines, and so on. Since these organic machines proceed infinitely inwards, they tend towards internal individuation (the limit they never reach). This internal individuation (which individuates matter by giving it an interior) can only be explained by discussing souls, at the material level all that is explained is internal space

“Folding no longer simply means tension-release, contraction-dilation, but enveloping-developing, involution-evolution” (2020:8). To grow is to unfold, to withdraw or die is to fold. Since an animal contains the cells that will form its offspring, and these cells themselves will form an offspring that contains similar cells, an animal contains all of its descendants in (increasingly) folded forms in itself

Elastic and plastic forces both affect matter, but we can’t pass from one force to the other. The universe is not alive, but it is composed of infinite living creatures. Organisms are irreducibly individual, and their descendants are irreducibly plural

Leibniz and his contemporaries may have meant that an animal literally contains an infinite amount of smaller animals, but we can easily adjust the idea to apply to modern biology, provided we allow for these descendants to be virtual rather than actual

The lower floor includes organisms, since all of the above is material

Plastic forces apply to matter, but only after it has received the unification imparted to it by a soul; therefore, souls are also everywhere in matter

When the human organism unfolds, that human’s soul develops (that is, gains a greater unity) and is raised to reason, sentience, etc. The act of locating a soul at a given point in matter can only be done by such a raised soul, which has thereby already been raised to the second floor of the allegorical house

“[I]f 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” (2020:12)

The souls of animals exist on the second floor, but can be found in matter

The mechanical forces are purely physical, and (assuming a straight line) determine the motion of matter; souls are in the body, yet elsewhere, and (assuming a curve) determine the unity of matter which the mechanical forces require

“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 between-two-folds seems to move about everywhere” (2020:13)

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Chapter Two: The Folds in the Soul

Inflection (the changing of a curved line from convex to concave or the other way around) is a singularity, an atom, which takes place within a system of coordinates but is nevertheless prior to them

The inflection experiences three transformations, and this is one of the things that really requires you to look at the diagrams, it’s damn near impossible to describe in words. Firstly, its vector changes, going from an initial ogive to an inverted ogive, turning at the point of return. Secondly, internal spaces (defined by “variables or singularities of potential” (2020:16)) are projected onto external spaces. Thirdly, each point along it is variable, admits of no tangents but only of further potential folds (hence, we move from fold to fold, not point to point). In this third kind, the other two are rejected and the curve moves vortically

In Leibniz’s account of irrational numbers and differential calculus, the variability of a given value becomes infinite. These are the moments where what was once a straight line becomes curved, or shoots off curves, etc. This determines a circle (again, see the diagrams), the arc of which is a fold. Leibniz posits the idea of a family of curves, each of which has a single variable that expresses singular, infinite variability. Such a curve isn’t taken from a line or a point, but touches possible lines or points. This is the fold

This objectile, as Deleuze calls the ‘point’ in this conception, is a pure function, which retains no consistent form or content, but only fluctuation. It modulates, the object is an event

The ‘point’ is to the line as the object is to the subject. Since the object has undergone a significant shift, so must the subject. It is no longer a series of points on a line (experiences on a subject). Instead, the meeting of varying tangents in one place is what constitutes the subject, its point of view, and this is perspectivism. The subject has become superject, and this is the Baroque, apparently

“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 [...] 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” (2020:20)

Such points of view, though plural, need not be discontinuous

The point of view, in perspectivism, is such that it structures everything else around itself; without a point of view, nothing would be structured, and so truth would be impossible

Inflection, therefore, has given way to inclusion (and that which is included must inhere). The purpose or final cause of the fold is inherence

“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.” (2020:22)

We move from inflection to inclusion, from the virtual to the real

There are three kinds of points (singularities), the physical point of inflection, the mathematical point of position, and the metaphysical point of inclusion. The physical point, which is of course a fold, exists on the line of inflection. The mathematical point is the point of view, the point where multiple lines of curvature connect or overlap. The mathematical point is thus in the body, and so is the projection of the metaphysical point, of the soul

“Explication-implication-complication form the triad of the fold, following the variations of the relation of the One-Multiple” (2020:24)

The monad, infinite and singular, allows a perspective. Different perspectives perceive largely the same things, but the relations they draw between these things are different

The monad, Leibniz says, perceives the entire world, but it perceives closer things in more detail, more clearly. This is already enough to show an infinite number of souls

God creates the world in which all monads exist, but he creates it in order to give it to all the monads he creates. The monad contains the whole world in itself, but cannot see the reason for this, which lies outside the world. God creates the world and places it in the subject in order to affirm that the world is for the subject

“[T]he soul is the expression of the world (actuality), but because the world is what the soul expresses (virtuality)” (2020:26)

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Chapter Three: What Is Baroque?

The monad has some presentation of the world, but it is not one that comes through a window. A painting or a film would be projections, models, etc., and so would all be windows to the outside. The monad’s presentation of the world is through tables alone, on which lines and numbers are placed

Baroque architecture, an essential comparison here, aimed to eliminate the visible window. It wanted to have windows placed such that they illuminated the room, but remained completely imperceptible to the inhabitants

The monad’s opposite is the façade, since the monad is pure inferiority and the façade is pure exteriority. Baroque architecture seeks a total separation of the inside from the outside, but done in a way that makes each one draw attention to the other. The harmony between the two occurs because of the division into two separate floors. Of course, the idea of multiple floors has been in metaphysics since Plato, but only in the Baroque does it become specifically two floors

“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” (2020:30)

Mallarmé presents the fold sometimes as “the sensitive side of the fan, [...] sensitivity itself, stirring up the dust through which it is visible, and exposing its own inanity” (2020:30), the physical fold referring to an open fan and indicating its own inadequacy for explaining phenomena. Other times, he shows the fold as related to the closed fan, the soul, which goes beyond itself by means of inclusion

The fold is in the soul, in such a way that the soul virtually contains all possible folds, internally. It acts internally, and the external thing is a circumstantial occurrence with a correlative in the should (that is, the worlds are not separated, instead the external expresses one internal possibility). “[T]he book, the fold of the Event, the unity that creates being, a multiplicity that makes for inclusion, a collectivity having become consistent” (2020:31)

The internal is that which is read, the external is seen, but they are never totally separate, the two mix in what are called emblems

Baroque painters used dark backgrounds, often dark red or brown, rather than the traditional white canvas. From this darkness they drew light by means of shadows; the opposition between light and dark, clarity and obscurity, is transformed into a relativity. Light in the soul is released only by reason, but inevitably fades into shadow

Leibniz knew how to keep his philosophy behind the masks required by circumstances

The very concept of the Baroque is unclear, but for us it suffices to say that the concept of the Baroque is the fold, but only when the fold is given infinite freedom, when folds are detached from their materials, while this infinite freedom is still determined

There are six traits of the Baroque in art and of Leibniz in philosophy

First, the fold, which is never finished, which continues infinitely. It affects materials, determines forms, and therefore produces expressions

Second, the inside/outside distinction. The fold separates matter and the soul, the former being external and the latter internal. The line of inflection is a “virtuality that never stops dividing itself” (2020:35), realised in matter and actualised in the soul

Third, the division into two floors, allowing for a harmony. The fold goes between the two, creating further folds in each floor, material matter corresponding to the bottom floor and forms corresponding to the upper floor, they go from matter-form to material-force when their folds are revealed

Fourth, the unfold, which is that in which the fold manifests once it has become Baroque. Even void is full of folds

Fifth, texture, which is the way a material is folded together, rather than its component parts. Texture “does not depend on the parts themselves, but on strata that determine its “cohesion”” (2020:37). Matter becomes a material of expression, which is why Renonciat can make a sculpture of wood that expresses the texture of plastic cloth. These folds in matter are of course determined by folds of the soul, in harmony

Sixth, the need of a paradigm, an example fold that expresses the fold in its generality, that doesn’t hide the form of the fold at all

Formal deduction must distinguish between simple and composite folds, hems, and drapes, before material texture, agglomerations, and conglomerations. We are going to investigate how Baroque this is