Wednesday, January 29, 2025

What is an event?

The form of chapter 6 is very simple.  Deleuze develops an analogy between Leibniz and Whitehead, both of whom conceive of the event as the fundamental building block of reality.  In a sense, we might think of this as Deleuze's attempt to articulate the assumptions necessary for any sort of 'psychic atomism'.  But before we get to the details of what makes an event, we can approach the question by asking what problem the concept is meant to solve.  Deleuze articulates this problem quite clearly.

For it is with Leibniz that there emerges in philosophy the question that will continue to haunt Whitehead and Bergson: not how to attain the eternal, but under what conditions does the objective world permit a subjective production of novelty, that is, a creation? The best of all worlds had no other meaning: it was neither the least abominable nor the least ugly world, but the world in which the Whole [le Tout] left open the possibility of a production of novelty, a liberation of veritable quanta of "private" subjectivity, even at the price of the subtraction of the damned. (F, 105)

We don't often consider how our discussions of qualia or consciousness or mind are related to the concept of novelty or creativity.  But what, after all, would be the point of being conscious if consciousness always felt the same?  What makes consciousness interesting is less the fact that it exists than that it so continuously varies qualitatively.  In fact, its pretty hard to separate these two.  Would a static consciousness merit the term?  And, conversely, doesn't any true change implicate the quality of knowing that change?  Each moment of experience feels unique, and there seems to be no way to stop this variation, which I suppose is equivalent to our sense of the passage of time.  If the universe consisted of nothing but moving particles it would be hard to understand how anything truly new could happen.  There would be movement without any qualitative change.  It would all be simply rearranging deck chairs.  To avoid this, we have to hypothesize that there is something built into the ground floor of reality that allows for the continuous stream of novelty that a 'first person' perspective on the world represents.  It's easiest to imagine this as a sort of hidden dimension that opens orthogonally to the physical universe in a way that adds to it without interrupting it.  This is precisely part of the image of the fractal fold -- a continuous line so curvy that, when taken to its limit, it appears to fill a whole space. 

So how does the event, whether it's Whitehead's actual occasion or Leibniz's monad, address this requirement?  Basically, the theory of the event adds a depth to every individual.  Unlike our normal conception of the smallest physical unit, which is inherently a static surface with no interior, the event is the smallest and simplest unit of change -- an inflection.  And yet, because of its fractal nature, each inflection is also the beginning of a possible inclusion that contains an infinity of other inflections.  The event opens up a novel qualitative dimension precisely because it never stands on its own in an isolated manner, but necessarily leads on to other events in an infinite nexus of connections that trails off into obscurity.  It's the folding-in of inclusion that creates a new "private" dimension that lends a depth to every unity.  Fractal folding is the only way that Everything can still be Open.  

When we state the problem this way it's easier to see what's unique about the event as a solution.  The creativity of the event does not 'emerge' nor does it 'evolve'.  It doesn't arrive on the scene when some fortuitous combination of particles crash into one another.  Despite the best efforts of their proponents, these versions of creativity are inevitably limited and reductive.  The merely lend the magic power of naming to a new configuration of particles without explaining where the magic came from.  The whole model of emergence or holarchy (see ENDNOTE) leads us towards the bad kind of infinity, where we keep adding more and more units in concentric circles without ever actually changing anything or reaching Everything.  Instead, the creativity of the event is a sort of involution rather than an evolution, an unfolding rather than an emergence.  It is built into the ground floor of reality, or better yet plunges through the ground floor to reveal that its apparent solidity is full of openings.  There is a topological distinction between these perspectives -- the event cannot be reduced to a series of concentric circles because the 'higher' levels are folded into or feed back into the 'lower' ones.  As a result, the event is inherently or intrinsically unfinished even though, like the good infinity, it is still bounded in some sense.  Change is inherent and ceaseless in principle in this scheme, not merely a matter of counting to higher and higher numbers.  No new units are created, and yet there is room in Everything for an infinite variety of novelty. 

With that overall picture in mind, we can turn to a few details of the correspondence of Leibniz and Whitehead.

It's no accident then that the four components of Whitehead's "actual occasion" match the four types of subject Deleuze covered in chapter 4.  The only surprise is the way the order of their presentation shifts around.  Extension, Intensity, and Individuality are the more easily understood components of Whitehead's events.  These correspond to Leibniz's definables (a series of relations of wholes and parts), conditionables (a series of relations that tend towards internal limits) and individuals (a series of relations that tend towards and external limit).  We can think of these roughly as the quantity, quality, and personality variables needed to define an event and distinguish it from all others.  These map reasonably well onto our central image of the curve of continuous variation.  The event is an inflection point.  But each inflection point 'extends' itself up to the neighborhood next inflection point in a "prolongation" of singularities.  However, this extensive neighborhood is not uniform or undifferentiated. As we zoom in on the fractal curve, we find it filled with all sorts of folds, which differ in quality depending on our starting point.  In fact, we can keep zooming indefinitely, at which point we notice that the counterpart to each nested set of inflections is a point off the curve that acts as the center of curvature of their world.  This is the individual point of view that, according to Leibniz, contains everything, even though it's always situated in the middle of the curve (if we zoom out).  Not a simple scheme, but by this point I think I understand the basic idea.

However, it's less easy to understand the fourth component of Whitehead's event, the "ingression" of an eternal object, and the way this corresponds to the first 'class' of beings in Leibniz's scheme -- the infinite identities that comprise the attributes of God.  This aspect of the event is meant to account for the sense of repetition or object permanence we have, despite the fact that all the other aspects of the event seem to be enmeshed in a ceaseless flux.  We saw these many years ago as the "footholds" that the world provides, something like the conditions of possibility of experiencing Repetition.

In effect, extensions are ceaselessly displacing themselves, gaining and losing parts that are carried along by movement; things are ceaselessly altered; even prehensions are ceaselessly entering into and leaving variable composites. Events are flows [flux]. What then allows us to say: it is the same river, it is the same thing or the same occasion…? It is the Great Pyramid… A permanence must be incarnated in the flows [flux], and must be grasped in a prehension. The Great Pyramid signifies two things: a passage of Nature or a flow, which loses and gains molecules at every moment, but also an eternal object which remains the same throughout these moments. While prehensions are always actual (a prehension is a potential only in relation to another actual prehension), eternal objects are pure Possibilities that are realized in the flows, but also pure Virtualities that are actualized in prehensions. (F, 106)

The eternal objects seem to correspond to the unconscious background assumptions that accompany any conscious experience.  Things like the fact that the experience is happening here, and now, and to me, and consists of a determinate form, and so on.  These unconscious accompaniments stretch off into the distance just like the monad stretches off into the obscure background that contains the whole world.  This sort of convergence to the horizon line suggests that ultimately all the eternal objects are aspects of a single eternal object that we could call God or Nature or World.  All these self-identities are a stabilization of the world of flux.  They are the common world that each monad individually expresses.

If the eternal objects are the collection of stable footholds that the world affords, it is still true that they cannot stand on their own.  Eternal objects always remain virtual, never themselves actual, and so are in some sense parasitic on the actual occasions or monads.  This is part of the paradox of the event, and the core of what makes a 'spiritual' form of atomism distinct from its physical counterpart.  The event is completely individuated and differentiated, yet completely connected to everything else.  Like a quantum wave function that spreads out as we try to pin it down, the events is not a simple form we can outline, but a chiaroscuro drawing that inherently combines the distinct and obscure -- the more distinct, the more obscure (F, 43).   Thus connecting up with other events is not an accidental misfortune that may or may not befall an event, but part of its core definition.  Which is to return to the book's starting point -- the event is a fractal concept, folded up so that it confuses the distinction between inside and outside.  In short, the event always going to infinity, and we might even say that all the events go to the same infinity. 

So far, we spoken as if Leibniz and Whitehead had interchangeable notions of the event.  But our observation that events all occupy the same world brings us to the important difference between the two philosophers.  For Leibniz, all the events converge on a single world, the best world, and all the eternal objects together define a single comprehensive concept of God.  This condition of convergence is why every monad can enclose the same world.  For Whitehead, by contrast, the events are all related, and any event can in principle connect up with any other, but they don't necessarily converge on a single world.  In other words: for Leibniz there is a single curve, infinitely folded, but ultimately closed, topologically equivalent to an infinitely large circle, whereas for Whitehead, the single curve branches and diverges and becomes a proliferating rhizome.  As Deleuze says, "It is a world of captures instead of closures." (F, 108). 

Deleuze provides a perfect metaphor for the difference between these two by invoking the "Baroque concert" at the heart of Leibniz's philosophy.

There is a concert this evening. It is the event. Sonorous vibrations are extended, periodic movements flow through [parcourent] extension with their harmonics or sub- multiples. The sounds have internal properties: height, intensity, and timbre. The sonorous sources, whether instrumental or vocal, are not content simply to emit the sounds: each perceives its own sounds, and perceives the others in perceiving its own. These are active perceptions, which are expressed through each other, or again prehensions that are prehended through each other. "At first the piano complained alone, like a bird deserted by its mate; the violin heard and answered it, as if from a neighboring tree. It was like the beginning of the world…." The sonorous sources are monads or prehensions that are filled with a joy of themselves, an intense satisfaction, insofar as they are filled with their perceptions and pass from one perception to another. And the notes of the scale are eternal objects, pure Virtualities that are actualized in the sources, but also pure Possibilities that are realized in the vibrations or flows. "As if the musicians were not so much playing the little phrase as performing the rites it demanded before it would consent to appear…." But within this ensemble, Leibniz adds the conditions of a Baroque concert: if we suppose that the concert is divided into two sonorous sources, we presume that each hears only its own perceptions, but that it accords with those of the other even better than if it had perceived them, because of the vertical rules of harmony that are enveloped in their respective spontaneity. These are the accords or chords [accords] that replace the horizontal connections. (F, 107)

The monads all play the same tune without needing to listen to one another because they are all reading off the 'best' score, composed by God.  The monad has no windows, but only because God assures that it doesn't need them, and guarantees that its full expression of itself will harmonize perfectly with that of every other monad.  The concert stays in tune even though the musician's cannot hear one another.  By contrast, Whitehead's concert has no score.  All the musicians listen to one another and respond to one another continuously, without any guarantee that they will harmonize.  Thus, Whitehead's 'monad' also has no windows because it has no need of them -- it is continuously open to all the others, flush with the ever-evolving real.

Friday, January 24, 2025

The Worst Possible World Except For All The Rest

The emphasis of chapter 5 shifts from the subject to the world.  Since the whole world is contained within each subject, there is a sense in which these are the ultimately the same thing.  Nevertheless, a single possible world still has many subjects, and there are many possible worlds.  So it's a mistake to think that the monadic subject and the world are identical.  This scheme immediately presents a question.  Why is it that there only seems to be one actual world?  In other words, what's special about this world and these subjects?

Leibniz answer to this question is well known -- this is the best possible world, and all the things that happen in it are therefore 'for the best'.  But as Halpern observed, this apparently sunny optimism hides a dark premise.  The Best world is not an Ideal world nor a Necessary world.  In fact, it's not even a Good one in the sense in which Plato defined this as a descent from a moral and metaphysical Ideal.  Leibniz defends God's choice of this world in the same way that Churchill defended democracy. 

How strange is Leibniz's optimism.  Once again, it is not that the miseries of the world are lacking—the Best flourishes only on the ruins of the Platonic Good. If this world exists, it is not because it is the best, but rather the inverse: it is the best because it is, because this is the world that is. The philosopher is not yet the Inquirer he will become with empiricism, still less a Judge, as he will become with Kant (the tribunal of Reason). He is a Lawyer or an Attorney, God's attorney: he defends God's Cause, in accordance with the word that Leibniz invented: "theodicy." Of course, the justification of God in the face of evil has always been a commonplace of philosophy. But the Baroque is a long period of crisis, when the ordinary consolations are no longer holding. What takes place is a collapse of the world, such that the attorney has to rebuild the world—the same world exactly—but now on another stage, and related to new principles capable of justifying it (hence the role of jurisprudence). To the enormity of the crisis there must correspond an exasperation of the justification: the world must be the best world, not only in its totality, but in its every detail or in each of its cases. (F, 92)

Here Deleuze isolates the problem that Leibniz's metaphysics is meant to solve.  By the time of the Baroque, people are beginning to lose faith in the wisdom of God.  The world starts to seem too complex and disparate, to be moving too quickly, for it to correspond to some static divine blueprint.  Deleuze suggests that this is the beginning of a disillusionment with the Ideal that leads towards Nietzschean nihilism (perhaps we should add a step 2.5 to "How the 'True World' Finally Became a Fable: History of an Error"?). Leibniz, though, tries to halt the progression before it gathers momentum.   So he proposes to replace the immediate clarity and comprehensibility of the divine plan with a faith that, while the details may be counterintuitive and stretch off to infinity, there is a principle at work behind each and every one of them.

But what happened, in this long history of "nihilism," before the world lost its principles? Closer to us, it was necessary for human reason to collapse, as the last refuge of principles, the Kantian refuge: it dies through "neurosis." But even earlier, a psychotic episode was necessary, the crisis and collapse of all theological Reason. This is where the Baroque assumes its position: Is there a way of saving the theological ideal, at a moment when it is embattled on all sides, and when the world cannot stop accumulating "proofs" against it, violences and miseries, at a time when the earth will soon tremble…? The Baroque solution is the following: we will multiply principles—we can always pull out a new one from our sleeve—and consequently we will change its use. We will no longer ask what giveable object corresponds to this or that luminous principle, but rather what hidden principle corresponds to this given object, that is to say, this or that "perplexing case." Principles as such will be put to a reflective use: a case being given, we will invent its principle: this is a transformation of Law into a universal Jurisprudence. (F, 91)

Say what you want about the tenets of National Socialism, at least it's an ethos.  The best possible world, this world, may indeed be pretty bad, but Leibniz rescues it with his faith in the principle of optimization.  If we keep this fundamental problem in mind, the pieces of Leibniz's metaphysics begin to fit together.  Since we can't actually find another world to compare it to, the operational definition of 'the best' world becomes one of continuity and convergence of disparates.  Surely a world where the pieces didn't match or some were missing would be sub-optimal.  But so would one that consisted entirely of hexagons.  That is, we seek precisely the Baroque marriage of unity and variety as evidence of the best.

How can we construct a single convergent world out of completely disparate monads?  Or, if we begin from the other direction, how can we partition a given world into separate monads which each include it in its entirety?  Deleuze broached this topic back in chapter 2, when he discussed the "torsion" of the fold between the world and the soul.  In some curious way, these two each come 'before' the other.  The world only exists in the monads which include it, but the monads are fabricated by God expressly for this world.  Now we see that there is a principle of optimization or resonance that governs the stabilizing feedback loop between these two.  If we relax this principle, we can imagine an infinity of possible worlds each with an infinity of monads, but without any guarantee that any of these worlds reach a point of closure that would allow each to be included in its infinite set of compatible monads.  In other words, for a possible world to come into actual existence, we have to be able to fold it up in an infinity of different shapes.  But for each of these shapes to be as they are, they have to be able to be unfolded into a single compatible world.  We can imagine possible shapes different from the ones we find in this world.  But in doing so, at the same time we would also need to imagine an entirely different world, a completely different 'sheet' that we could then fold into a whole different set of shapes to go with it.  In short, you cannot change just one thing because of how tightly interwoven everything is.  Somehow you have to independently specify both the whole structure and all its details, but then they have to miraculously match.  There are no stable independent building blocks, and there is no final blueprint.  How does God even get started with a problem like this?

Deleuze has a unique interpretation of how Leibniz goes about solving this problem, and it brings us back to what Simondon called the pre-individual, or what Deleuze in other places calls the transcendental field.  The idea is basically that before there are monads and before there is even a world (in some sense) there is a "pure emission of singularities" (F, 83).  These are the events of the world, the inflections or bifurcations that occur at each moment.  But before they can compose a world or condense into various monads, God has to select the 'best' singularities, that is, the ones that will all converge.  He has to knit together the continuity of the world.  At first it may not seem to make sense to talk about a convergence or a continuity of singularities.  After all, aren't they, you know, singular?  But we need to keep in mind the basic image of the fold -- the infinitely varying curve of the world swings back and forth, and each of its singularities of inflection opens a new a region of the curve included under a certain
point-of-view, a region which extends up to the next inflection point.  That is, a singular point can be prolonged over a series of ordinary points so that it joins up with another singular point.  We saw that this was precisely how the principle of continuity could be reconciled with the principle of indiscernibility.  Now, however, instead of thinking of the continuity of the world as given, we need to consider it as composed.  Imagine if each inflection point could be a bifurcation point, as if the curve could continue in two different directions or along two dimensions. In fact, the curve of possible worlds is constantly bifurcating in this way, threatening us with Borges' infinitely infinite and ever-ramifying garden of forking paths (F, 85).  It's only Leibniz's principle of optimization that guarantees the continuity of the world, and the converge of the singularities into a single curve.  The world isn't pre-planned as an Ideal blueprint in God's head.  He constructs it freely as he goes along.  But he always chooses the best bifurcation at each moment, and so brings only one world into existence with his choices.

The principle of indiscernibles establishes cuts; but the cuts are not lacunae or ruptures of continuity; on the contrary, they divide [répartissent] continuity in such a way that there are no lacunae, that is to say, in the "best" way (hence the irrational number). (F, 89)

This idea that God is engaged in some form of calculation in creating the world leads us back to our departure point.  'The Best' is the outcome of this calculus of optimization.  It's also the reason that Deleuze can cast Leibniz as one of the line of thinkers who see the world as a game.  Of course, Nietzsche imagines a divine game of chance, whereas for Leibniz God plays a game of skill.  But in both these cases there is a freedom of play and variation that opposes the work of logical necessity.

Described from God's perspective, the game of the world sounds kinda static.  In creating the world, God appears to 'win' once and for all by choosing the best world and the best monads.  Does this mean that only God has any freedom in this scheme, and that the individuals are no more than literally pawns?  It certainly seems that the condition of optimization requires all the parts to fit together with a perfect, rigid precision that would leave no room for change or improvisation.  But here we should recall the strange status of the monad -- it is not a piece of the world, but includes the entire world, albeit from a certain point-of-view.  God is able to read off the entire history of the world from the folded up fine print in each monad, while from the monad's point of view, the world unfolds in time, as an infinite series of actions or events.  Nevertheless, it is the same world that only actually exists folded up into the monads or unfolding through them.  This fact allows Deleuze to lend Leibniz's scheme a dynamism that preserves a certain type of individual freedom. 

How does this work though? The key to understanding the freedom of the individual lies in the distinction between predication and attribution that Deleuze introduced in the last chapter.  A monad is not like a 'soul atom' in the sense of having some solid and separable essence that might then undergo various modifications as it bumps into other monads.  Because everything that happens to it is already included within the monad, we might expect Leibniz to argue that the monad is free because it is self determined.  But this formulation could easily involve a subtle assumption about how the free act would be determined by the monad's essential self.  As we've seen, the monad doesn't have any essence apart from the unity of its modifications.  It is the inclusion of inflections, a being necessarily in motion, a verb, not a noun.  So freedom is less a question of internal determination by some stable central core than in acting in way that expresses the entirety of the monad at once.  Instead of being determined by an essential point, freedom consists in following an inclination that leads us to include more and more of ourselves.  The image Deleuze gives us is of inclination or motive as a pendulum of variable amplitude.  This is contrasted to the image of determination as a balance of 'reasons' that needs a central fulcrum to operate.  The pendulum is free when its amplitude can increase to a maximum, that is, where its inclination and its motion reinforce or resonate with one another.

We have to start with the minute inclinations that fold our soul in every direction, at every moment, under the action of a thousand "little springs": uneasiness or disquiet [inquietude]. This is the model of the pendulum, the "Unruhe," [restlessness] which replaces the balance. An action is voluntary when the soul, rather than submitting to the effect of the sums into which these minute solicitations enter, instead gives itself a certain amplitude that makes it fold, in its entirety, in one direction or toward one side.  (F, 94)

In a way, it's almost as if the free act duplicates the relationship of inclusion between the monad and the world -- the free act in the present includes the entire past and future of the monad in the sense that it resonates with everything that leads up to it and follows from it.  Thus it expresses the entirety of the monad.

If inclusion is extended to infinity in the past and future, it is because it concerns first of all the living present that, in each instance, presides over their distribution. It is because my individual notion includes what I am doing in the present moment, what I am in the process of doing, that it also includes everything that pushed [pousée] me to do it, and everything that follows from it, to infinity. This privilege accorded to the present refers precisely to the function of inherence in the monad: it does not include a predicate without giving it the value of a verb, that is, the unity of a movement in process [le movement en train de se faire]. Inherence is the condition of freedom, and not its impediment [empêchement] (F, 95)

God's freedom lies in 'tuning' an infinity of monads so that they each harmoniously express the best possible world.  Individual freedom lies in 'tuning' each present moment so that it expresses the entirety of a monad, the whole sweep of its life.  But if the world is composed of moments of monads, we might wonder whether these two freedoms could ever come into conflict.  Does God see to it that everyone maximizes their freedom at every moment?   This seems impossible because there seem to be cases where my present freedom, my maximum expression, is at the expense of yours.  It's in this context that Deleuze explores Leibniz's theory of damnation. 

However, this possibility of progress, or of the soul's expansion, seems to run up against the total quantity of progress in the world, this quantity being defined by the convergence of all the regions that correspond to the compossible monads. And this would be true if time did not exist—that is, if all existing monads were simultaneously summoned to the elevation that makes them reasonable. But things do not work that way: the souls destined to become reasonable await their hour in the world, and are first of all only sensitive souls who sleep in Adam's seed, bearing only an "official act" [acte scellé] that marks the hour of their future elevation, like a birth certificate [acte de naissance] (F, 99)

Technically, Deleuze separates the idea of freedom from the idea of progress.  So there's no conflict between the freedoms as I have suggested (see pg. 97) but between the progress of one monad towards increasing its amplitude or becoming 'elevated' and the progress of other monads.  The damned regress rather than progress.  But they do this freely.  I'm glossing over this distinction for the sake of brevity.  The point is that good things happening to one soul seem to necessarily imply bad things happening to another.  There can be no saved souls if there are no damned ones, no Christians without heathens.  The precision mechanism that God so skillfully creates -- the best of all possible world -- requires the suffering of the damned.  The unfolding of one soul to its maximum potential requires the folding of another into a hardened mass. The whole game is in motion, and the spontaneous unfolding in places requires a folding in others.  But it is a Baroque mechanism, a Baroque dance (F, 93) where one dancer retreats while the other advances, their varying push and pull perfectly matched, but the opposites still requiring one another.

Leibniz's optimism is founded on the infinity of the damned as the sub-basement [soubassement] of the best of worlds: they liberate an infinite quantity of possible progress, and this is what multiplies their rage, they make possible a world in progress. One cannot think the best of worlds without hearing Beelzebub's cries of hatred, which make the lower level tremble. (F, 100)

It's hard not to read a passage like this from a political perspective.

Friday, January 10, 2025

I Know It's Down There Somewhere ...

Let me just take another look.  Though it's perhaps not obvious at first glance, the dude's request is another expression of faith in the principle of sufficient reason.  Normally, we understand this as the principle that "everything has a reason", and we quickly assimilate it to the modern, mechanistic claim that "everything has a cause".  But, while this latter might be true, it's not what Leibniz has in mind with his principle.  Sure, there are always efficient causes of everything that happens to something.  There is always a chain of colliding billiard balls leading up to and away from every event.  But why, by what reason, do those collisions produce this event?  The principle tells us that there is a reason event X can happen to thing Y, a reason which is not merely contingent and accidental, but somehow included in what it means to be precisely thing Y.  Sufficient reason insists that if we just look down far enough into a subject we can read its entire biography off at once. The mere concept of a subject is sufficient to explain all the things that happen to it as its life unfolds.

It's clear that we're describing the way the monad includes the entire world.  So it might at first seem like the principle of sufficient reason is little more than a restatement of the definition of a monad.  While these two are certainly related, the scheme that Deleuze unfolds in chapter 4 is significantly more complicated than this.  The key issue is that the principle of sufficient reason is not the only important principle in Leibniz's philosophy, nor, despite its centrality, is the monad the only subject.  This is also to say that the way the monad includes the whole world is not the only possible type of inclusion.  In fact, Deleuze discusses 4 types of inclusion, which define 4 types of subject, ruled by 4 different principles, as shown in the following chart.


This chart helps us distinguish the baroque and sometimes seemingly contradictory details of Leibniz's philosophy, but I don't want to get bogged down in it.  Because it also serves to join these ideas into a system.  The overarching point here is that in some sense all these principles are really the same principle, and all these subjects really the same subject, even though each expression of this underlying system is always unique.  Deleuze interprets the continuity across this chart as a "creation of concepts" (F, 80) or we might call it a sort of 'becoming of the concept'.  It's as if we were laying out everything that a concept can do -- it can stretch all the way from God to the most individual thing, while having various adventures along the way.  For Leibniz, the concept becomes a real being in motion, unfolding itself into these different shapes, not a static picture in the head of some hairless ape.

In short, one finds in Leibniz an entire history of the concept that passes through wholes-parts, things and substances, through extensions, intensions, and individuals, and through which the concept itself becomes a subject, in conformity with each level. This is the rupture with the classical conception of the concept as a being of reason: the concept is no longer the essence or logical possibility of its object, but the metaphysical reality of the corresponding subject. (F, 76)

At first, it can be hard to see what's so completely new about this notion of the concept.  I mean, what's the difference between a "logical" and a "metaphysical" being?  One way to appreciate the change is to consider what it means for a concept to have certain 'properties', or as a Deleuze prefers to put it in this chapter, what it means to predicate something of a concept.  

The classical conception of the concept suggests that what we predicate of a thing can be considered its attributes.  I am a writer.  I think.  Ergo, I am a thinking thing.  The subject here is fundamentally a noun.  We conceive of it as a neutral substrate of sorts that underlies whatever attributes it presents.  Some of these attributes may be accidental and others essential, but in either case there is still a distinction between the thing itself and its attributes.  We put the thing itself on one side, and everything that happens to it on the other, similarly to the way we divide motion into the mobile object and its successive possible positions.  In short, the logical concept separates the thing from its power of acting, and operates on a "subject-copula-attribute schema" (F, 74).  This is the only way we can conceive of a neutral and static thing that in principle is without doing anything (there must be some joke about Being and Copulation that Heidegger overlooked).  

By contrast, Leibniz's idea of the concept understands the subject as a verb -- "not 'the tree is green' but 'the tree greens…' "(F, 75)

Leibnizian inclusion rests on a subject-verb-complement schema, which since Antiquity has resisted the schema of attribution: a Baroque grammar in which the predicate is above all relation and event, and not attribute. (F, 74)

Instead of being external attributes of the subject, predicates become internal events, and everything which happens to the subject is already included within it.  As a result, everything the subject does is already an inherent aspect of it, simply waiting to be unfolded, and we need never attribute any new state to it from the outside.  Which is to say that the concept is not a general idea of the thing that remains constant throughout all its changes and which we later make more specific by specifying various attributes.  It is no longer merely the logical identity in the equation I am X, Y or Z, or the greatest common denominator, as it were, of everything that happens to it.  Instead, the concept becomes a real individual thing. It already completely specifies everything that will happen to it and even the entirety of the world in which it will happen, as if it could 'survey' (as Ruyer put it) its entire trajectory.  In short, it becomes a real, almost self-sufficient, metaphysical being, that doesn't need our external help to find its attributes.

Above 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-events. (F, 61)

Since I promised not to go into the details of that complicated chart, I think there's only one more point to touch on in this chapter.  We've seen Deleuze insist that, in Leibniz's world, predication is never attribution, because the concept is (or can at least become) a real individual.  But since this individual stretches to encompass everything, we can no longer look at it as defined by an essence that would underlie and undergo various modifications, or as an essential substance that would take on various shapes and forms.  Instead, Leibniz's individual has to be nothing but the unity of all its fluctuations.  Every event that happens to it is already part of it, which turns its essence into just a run-on string of verbs.  This is the at first counterintuitive consequence of inclusion -- when everything is necessarily included, there no essential core left that is separable from these variations.  What we usually think of as an essential subject passing through a particular state becomes a manner of being that appears within the subject.  Fundamentally, the subject presented is always the same, and each monad includes the same world,  But time allows various aspects of angles to come forwards.  Deleuze calls this Leibniz's "Mannerism".

Classicism requires a solid and constant attribute for substance, whereas Mannerism is. fluid: it replaces the essentiality of the attribute with the spontaneity of manners. (F, 78)

It may sound odd to hear Leibniz call the 'manners' of the subject "spontaneous" when we know that he considers its entire history as contained in its concept.  But if we associate spontaneity with whatever new event rises from within, in contrast to events determined from the outside through contact with something else, then the term makes perfect sense. The monad never actually encounters anything but itself.  It is constructed entirely from the unity of relations between internal events, albeit a unity which always refers back to the whole world the monad must harmonize with or express.  This world is folded up into the monad, each of which clearly unfolds only a particular portion of it at any given spatio-temporal point, making each monad a 'manner of being' of the whole world.

This is the second aspect of Mannerism, without which the first would remain empty. The first is the spontaneity of manners which is opposed to the essentiality of the attribute. The second is the omnipresence of the dark depth [fond] that is opposed to the clarity of form, and without which the manners would have no place from which to emerge. The entire formula of the Mannerism of substances is: "Everything in them is born out of their own depths, through a perfect spontaneity." (F, 79)