On Spinoza (Part 9)

​LECTURES BY GILLES DELEUZE

In order to analyse the different dimensions of individuality, I have tried to develop this theme of the presence of the infinite [lâinfini] in the philosophy of the seventeenth century, and the form under which this infinite presented itself. This theme is very fuzzy [flou] and I would like to draw from it some themes concerning the nature, this conception of the individual, this infinitist conception of the individual. Spinoza provides a perfect expression, as if he pushed those themes that were scattered among other authors of the seventeenth century to the end. In all its dimensions, the individual as Spinoza presents it, I would like to say three things about it. On the one hand, it is relation, on the other hand, it is power [puissance], and finally it is mode. But a very particular mode. A mode that one could call intrinsic mode.

The individual insofar as relation refers us to a whole plane that can be designated by the name of composition [compositio]. All individuals being relations, there is a composition of individuals among themselves, and individuation is inseparable from this movement of composition.

Second point, the individual is power [puissance ö potentiae]. This is the second great concept of individuality. No longer composition that refers to relations, but potentiae. We find the modus intrinsecus quite often in the Middle Ages, in certain traditions, under the name gradus. This is degree. The intrinsic mode or degree.

There is something common to these three themes: it's by virtue of this that the individual is not substance. If it's a relation it's not substance because substance concerns a term and not a relation. The substance is terminus, which is a term. If it's power it's not substance either because, fundamentally, whatever is substance is form. It's the form that is called substantial. And lastly, if it's degree it's not substance either since every degree refers to a quality that it graduates, every degree is degree of a quality. Now what determines a substance is a quality, but the degree of a quality is not substance.

You see that all this revolves around the same intuition of the individual as not being substance. I begin with the first character. The individual is relation. This is perhaps the first time in the history of the individual that an attempt to think relation in the pure state will be sketched out. But what does that mean, relation in the pure state? Is it possible, in some way, to think relation independently of its terms? What does a relation independent of its terms mean? There had already been a rather strong attempt in Nicholas of Cusa. In many of his texts that I find very beautiful, there was an idea that will be taken up again later. It seems to me that in his work it appeared in a fundamental way, that is, every relation is measure, only if every measure, every relation, plunges into the infinite. He dealt often with the measure of weight, with weighing, insofar as the relative measure of two weights refers to an absolute measure, and the absolute measure, itself, always brings the infinite into play. This is the theme that there is an immanence of pure relation and the infinite. One understands by "pure relation" the relation separate from its terms. Thus it's for this reason that it's so difficult to think pure relation independently of its terms. It's not because it's impossible, but because it puts into play a mutual immanence of the infinite and relation.

The intellect has often been defined as the faculty of setting out relations. Precisely in intellectual activity there is a kind of infinite that is implied [impliqué]. At the level of relation the implication of the infinite occurs through intellectual activity. What does that mean? Doubtless it will be necessary to wait until the seventeenth century to find a first statute of relation independent of its terms. This is what many philosophers, including those who made use of mathematical means, had sought since the Renaissance.

This will be brought to a first perfection thanks to the infinitesimal calculus. The infinitesimal calculus puts into play a certain type of relation. Which one? The method of exhaustion was like a kind of prefiguration of the infinitesimal calculus. The relation to which infinitesimal calculus gave a solid statute is what is called a differential relation, and a differential relation is of the type dy/dx =, we'll see what it's equal to.

How does one define this relation dy/dx = ? That which is called dy is an infinitely small quantity, or what is called a vanishing [évanouissante] quantity. A quantity smaller than any given or givable quantity. Whatever quantity of y you are given, dy will be smaller than this value. Thus I can say that dy as a vanishing quantity is strictly equal to zero in relation to y. In the same way dx is strictly equal to zero in relation to x. dx is the vanishing quantity of x. Thus I can write, and mathematicians do write dy/dx = 0/0. This is the differential relation. If I call y a quantity of the abscissa and x a quantity of the ordinate, I would say that dy=0 in relation to the abscissa, dx=0 in relation to the ordinate. Is dy/dx equal to zero? Obviously not. dy is nothing in relation to y, dx is nothing in relation to x, but dy over dx does not cancel out. The relation subsists and the differential relation will present itself as the subsistence of the relation when the terms vanish. They have found the mathematical convention that allows them to treat relations independently of their terms. Now what is this mathematical convention? I summarize. It's the infinitely small. Pure relation thus necessarily implies the infinite under the form of the infinitely small since pure relation will be the differential relation between infinitely small quantities. It's at the level of the differential relation that the reciprocal immanence of the infinite and relation is expressed in the pure state. dy/dx = 0/0 but 0/0 is not 0.
Indeed, what subsists when y and x cancel out under the form dy and dx, what subsists is the relation dy/dx itself, which is not nothing.

Now what does this relation dy/dx designate?
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To what is it equal?

We will say that dy/dx equals z, that is to say it does not involve y or x at all, since it's y and x under the form of vanishing quantities. When you have a relation dy/dx derived from a circle, this relation dy/dx = 0/0 doesn't involve the circle at all but refers to what is called a trigonometric tangent.

One comprehends that dy/dx = z, that is to say the relation that is independent of its terms will designate a third term and will serve in the measurement and in the determination of a third term: the trigonometric tangent. In this sense I can say that the infinite relation, that is to say the relation between the infinitely small, refers to something finite. The mutual immanence of the infinite and relation is in the finite. Its in the finite itself that there is immanence of relation and the infinitely small. In order to gather together these three terms, pure relation, the infinite and the finite, I would say that the differential relation dy/dx tends towards a limit, and this limit is z, that is to say the determination of the trigonometric tangent. We are inside an extraordinarily rich knot of notions. Then afterward the mathematicians will say no, it's barbaric to interpret infinitesimal calculus by the infinitely small, it's not that. Perhaps they're right from a certain point of view, but this is to pose the problem badly. The fact is that the seventeenth century, by way of its interpretation of infinitesimal calculus, finds a means of fusing three key concepts, for mathematics and philosophy at the same time. These three key concepts are the concepts of the infinite, relation and limit. Thus if I extract a formula of the infinite from the seventeenth century, I would say that something finite consists of an infinity [infinité] under a certain relation. This formula can appear totally dull: something finite consists in the infinite under a certain relation, when in fact it is extraordinarily original. It marks an equilibrium point, for seventeenth-century thought, between the infinite and the finite, by way of a new theory of relations. And then when these later sorts consider it as going without saying that in the least finite dimension there is the infinite; when thereafter they speak of the existence of God all the time but this is much more interesting than is believed it doesn't finally involve God, it involves the richness of this implication of concepts: relation, infinite, limit.

How is the individual a relation? You will find, at the level of the individual, a limit. This does not prevent there having been some infinite, this does not prevent there being relations and these relations being composed, the relations of one individual are composed with another; and there is always a limit that marks the finitude of the individual, and there is always an infinite of a certain order that is involved by the relation.
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It's a funny vision of the world. They didn't merely think like that, they saw like that. It was their very own taste, their way of treating things. When they see what microscopes show them, they see a confirmation of it: the microscope is the instrument that gives us a sensible and confused presentiment of this activity of the infinite under any finite relation. And Pascal's text on the infinite, he was a great mathematician as well, but when he needs to let us know how he sees the world, he doesn't need his mathematical knowledge [savoir] at all, the two reinforce each other. Then Pascal can make up his text on the two infinites without any reference to mathematics whatsoever. He says extremely simple but extremely original things. And indeed, the originality lies in this way of fusing three concepts: relation, limit, infinite. This makes a funny world. We no longer think like that. What has changed is a whole system of mathematics as conventions, but that has changed only if you comprehend that modern mathematics also plots its concepts on a set of notions of another, equally original type. [Following a remark] The limit towards which the relation tends is the reason for knowing [connâitre] the relation as independent of its terms, that is to say dx and dy, and the infinite, the infinitely small is the reason for being [raison dâêtre] of relation; indeed, it's the reason for being of dy/dx.

Descartes' formula: the infinite conceived and not comprehended. One does not comprehend the infinite because it is incomprehensible, but one conceives it. This is Descartes' great formula: one can conceive it clearly and distinctly, but comprehending it is something else. Thus one conceives it, there is a reason for knowledge [connaissance] of the infinite. There is a reason for knowing that is distinct from the reason for being. Comprehending would be grasping the reason for being, but we cannot grasp the reason for being of the infinite because to do so we would have to be adequate to God; but our understanding is merely finite. On the other hand, one can conceive the infinite, conceive it clearly and distinctly, thus one has a reason for knowing it.

Practical exercises in philosophy would have to be thought experiments [expériences]. This is a German notion: experiments that one can only do in thought.

Let's pass on to the second point. I've had to invoke the notion of limit. Indeed, in order to account for the immanence of the infinite in relation, I return to the preceding point. The logic of relations [rapports], of relationships [relations] is a fundamental thing for philosophy, and alas, French philosophy has never been very interested in this aspect. But the logic of relations has been one of the great creations of the English and the Americans. But there were two stages. The first stage is Anglo-Saxon, the logic of relations such as it was built up on the basis of Russell at the end of the nineteenth century; now this logic of relations claims to be founded on this: the independence of relation in relation to its terms, but this independence, this autonomy of relation in relation to its terms is founded on finite considerations. They are founded on a finitism. Russell even has an atomist period in order to develop his logic of relations.
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This stage had been prepared by a very different stage. The great classical stage of the theory of relations is not like they say; they say that earlier, people confused the logic of relations and the logic of attribution. They confused two types of judgment: judgments of relation (Pierre is smaller than Paul) and judgments of attribution (Pierre is yellow or white), thus they had no consciousness of relations. It's not like that at all. In so-called classical thought, there is a fundamental realization of the independence of relation in relation to relationships, only this realization passes by way of the infinite. The thought of relation as pure relation can only be made in reference to the infinite. This is one of the highly original moments of the seventeenth century.

I return to my second theme: the individual is power [puissance]. The individual is not form, it is power. Why does this follow? It's what I just said about the differential relation 0/0, which is not equal to zero but tends towards a limit.

When you say that, the tension towards a limit, you rediscover this whole idea of the tendency in the seventeenth century in Spinoza at the level of a Spinozist concept, that of conatus. Each thing tends to persevere in its being. Each thing strives [sâefforce]. In Latin, "strive" is "conor," the effort or tendency, the conatus. The limit is being defined according to an effort, and power is the same tendency or the same effort insofar as it tends towards a limit. If the limit is grasped on the basis of the notion of power, namely tending towards a limit, in terms of the most rudimentary infinitesimal calculus, the polygon that multiplies its sides tends towards a limit, which is the curved line. The limit is precisely the moment when the angular line, by dint of multiplying its sides, tends towards infinity [lâinfini]. It's the tension towards a limit that now implies the infinite. The polygon, as it multiplies its sides to infinity, tends towards the circle.

What change does this bring about in the notion of limit?

The limit was a well-known notion. One did not speak of tending towards a limit. The limit is a key philosophical concept. There is a veritable mutation in the manner of thinking a concept. What was limit? In Greek it's "peras." At the simplest level, the limit is the outlines [contours]. Itâs the time limits [termes]. Surveyors [Géomètres]. The limit is a term, a volume has surfaces for its limits. For example, a cube is limited by six squares. A line segment is limited by two endpoints. Plato has a theory of the limit in the Timeus: the figures and their outlines. And why can this conception of the limit as outline be considered as the basis for what one could call a certain form of idealism? The limit is the outline of the form, whether the form is purely thought or sensible, in any case one will call "limit" the outline of the form, and this is very easily reconciled with an idealism because if the limit is the outline of the form, after all what I can do is what there is between the limits. If I were to put some sand, some bronze or some thought matter, some intelligible matter, between my limits, this will always be a cube or a circle. In other words, essence is the form itself related to its outline. I could speak of the pure circle because there is a pure outline of the circle. I could speak of a pure cube without specifying what it involves. I would name these the idea of the circle, the idea of the cube. Hence the importance of "peras"-outline in Platoâs philosophy in which the idea will be the form related to its intelligible outline.

In other words, in the idea of an outline-limit, Greek philosophy finds a fundamental confirmation for its own proper abstraction. Not that it is more abstract than another philosophy, but it sees the justification of the abstractio, such as it conceives it, namely the abstraction of ideas.
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Henceforth the individual will be the form related to its outline. If I look for something to which such a conception concretely applies, I would say, regarding painting for example, that the form related to its outline is a tactile-optical world. The optical form is related, be it only by the eye, to a tactile outline. Then that can be the finger of pure spirit, the outline inevitably has a kind of tactile reference, and if one speaks of the circle or the cube as a pure idea, to the extent that one defines it by its outline and one relates the intelligible form to its outline, there is a reference however indirect it may be to a tactile determination. It is completely wrong to define the Greek world as the world of light, it's an optical world, but not at all a pure optical world. The word that the Greeks use to speak of the "idea" already sufficiently attests to the optical world that they promote: Eidos. Eidos is a term that refers to visuality, to the visible. The sight of spirit, but this sight of spirit is not purely optical. It is optical-tactile. Why? Because the visible form is related, however indirectly it may be, to the tactile outline. It's not surprising that one of those who reacts against Platonic idealism, in the name of a certain technological inspiration, is Aristotle. But if you consider Aristotle, there the tactile reference of the Greek optical world appears quite evidently in an extremely simple theory which consists in saying that substance, or rather sensible substances are composites of form and matter, and it's the form that's essential. And the form is related to its outline, and the experience constantly invoked by Aristotle is that of the sculptor. Statuary has the greatest importance in this optical world; it's an optical world, but a world of sculpture, that is to say one in which the form is determined according to a tactile outline. Everything happens as if the visible form were unthinkable outside of a tactile mold. That is the Greek equilibrium. It's the Greek tactilo-optical equilibrium.

The eidos is grasped by the soul. The eidos, the pure idea is obviously graspable only by the pure soul. As pure soul we can only speak of it, according to Plato himself, by analogy, seeing that we only experiment with our soul insofar as it is bound to a body, we can only speak of it by analogy. Thus, from the point of view of analogy, I would always have said okay, itâs the pure soul that grasps the pure idea. Nothing corporeal. It's a purely intellectual or spiritual grasp. But does this pure soul that grasps the idea proceed in the manner of an eye, in the manner of, or does it proceed rather in the manner of the sense of touch? Touch which would then be purely spiritual, like the eye which would be purely spiritual. This eye is the third eye. This would be a manner of speaking, but we definitely need the analogy. In Plato we definitely need analogical reasoning. Then all my remarks consist in saying that the pure soul no more has an eye than it has a sense of touch, it is in relation with the ideas. But this does not prevent the philosopher, in order to speak of this apprehension of the idea by the soul, from having to ask himself what is the role of an analogon of the eye and an analogon of touch? An analogue of the eye and an analogue of touch in the grasping of the idea. There are then these two analoga since the idea is constantly•[gap in recording] This was the first conception of the outline-limit. But what happens when, several centuries later, one gets a completely different conception of the limit, and the most varied signs come to us from it?

First example, from the Stoics. They lay into Plato quite violently. The Stoics are not the Greeks, they are at the edge [pourtour] of the Greek world. And this Greek world has changed a lot. There had been the problem of how to develop the Greek world, then Alexander. These Stoics are attacking Plato, there is a new Oriental current. The Stoics tell us that we don't need Plato and his ideas, it's an indefensible conception. The outline of something is what? It's non-being, say the Stoics. The outline of something is the spot where the thing ceases to be. The outline of the square is not at all the spot where the square ends. You see that it's very strong as an objection. They take literally this Platonism that Iâve sketched out quite summarily, namely that the intelligible form is the form related to a spiritual touch [tact], that is to say it's the figure related to the outline. They will say, like Aristotle, that the example of the sculptor is completely artificial. Nature never proceeds by molding. These examples are not relevant, they say. In what cases does nature proceed by way of molds, it would be necessary to count them, itâs certainly only in superficial phenomena that nature proceeds by way of molds. These are phenomena that are called superficial precisely because they affect surfaces, but nature, in depth [profondeur], does not proceed by way of molds. I am pleased to have a child who resembles me; I have not sent out a mold. Notice that biologists, until the eighteenth century, cling to the idea of the mold. They insisted on the spermatozoon analogous to a mold, this is not reasonable. On that point Buffon had great ideas; he said that if one wants to comprehend something of the production of living things, it would be necessary to work oneâs way up to the idea of an internal mold. Buffonâs concept of an "internal mold" could help us. It means what? It's awkward because one could just as well speak of a massive surface. He says that the internal mold is a contradictory concept. There are cases in which one is obliged to think by means of a contradictory concept. The mold, by definition, is external. One does not mold the interior, which is to say that for the living thing, the theme of the mold already does not work. Nevertheless there is a limit to the living thing. The Stoics are in the process of getting hold of something very strong, life does not proceed by molding. Aristotle took artificial examples. And on Plato they let loose even more: the idea of the square, as if it were unimportant that the square was made of wood, or of marble, or of whatever you like. But this matters a lot. When one defines a figure by its outlines, the Stoics say, at that very moment everything that happens inside is no longer important. It's because of this, the Stoics say, that Plato was able to abstract the pure idea. They denounce a kind of sleight-of-hand [tour de passe-passe]. And what the Stoics are saying stops being simple: they are in the process of making themselves a totally different image of the limit. What is their example, opposed to the optical-tactile figure? They will oppose problems of vitality. Where does action stop? At the outline. But that, that holds no interest. The question is not at all where does a form stop, because this is already an abstract and artificial question. The true question is: where does an action stop?

Does everything have an outline? Bateson, who is a genius, has written a short text that is called "[why] does everything have an outline?" Take the expression "outside the subject," that is to say "beyond the subject." Does that mean that the subject has an outline? Perhaps. Otherwise what does "outside the limits" mean? At first sight it has a spatial air. But is it the same space? Do "outside the limits" and "outside the outline" belong to the same space? Does the conversation or my course today have an outline? My reply is yes. One can touch it. Let's return to the Stoics. Their favorite example is: how far does the action of a seed go? A sunflower seed lost in a wall is capable of blowing out that wall. A thing with so small an outline. How far does the sunflower seed go, does that mean how far does its surface go? No, the surface is where the seed ends. In their theory of the utterance [énoncé], they will say that it states exactly what the seed is not. That is to say where the seed is no longer, but about what the seed is it tells us nothing. They will say of Plato that, with his theory of ideas, he tells us very well what things are not, but he tells us nothing about what things are. The Stoics cry out triumphantly: things are bodies.
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Bodies and not ideas. Things are bodies, that meant that things are actions. The limit of something is the limit of its action and not the outline of its figure. Even simpler example: you are walking in a dense forest, you're afraid. At last you succeed and little by little the forest thins out, you are pleased. You reach a spot and you say, "whew, here's the edge." The edge of the forest is a limit. Does this mean that the forest is defined by its outline? It's a limit of what? Is it a limit to the form of the forest? It's a limit to the action of the forest, that is to say that the forest that had so much power arrives at the limit of its power, it can no longer lie over the terrain, it thins out.

The thing that shows that this is not an outline is the fact that we can't even specify the precise moment at which there is no more forest. There was a tendency, and this time the limit is not separable, a kind of tension towards the limit. It's a dynamic limit that is opposed to an outline limit. The thing has no other limit than the limit of its power [puissance] or its action. The thing is thus power and not form. The forest is not defined by a form, it is defined by a power: power to make the trees continue up to the moment at which it can no longer do so. The only question that I have to ask of the forest is: what is your power? That is to say, how far will you go?

That is what the Stoics discover and what authorizes them to say: everything is a body. When they say that everything is a body, they don't mean that everything is a sensible thing, because they do not emerge from the Platonic point of view. If they were to define the sensible thing by form and outline, that would hold no interest. When they say that everything is a body, for example a circle does not extend in space in the same fashion if it is made of wood as it does if it is made of marble. Further, "everything is a body" will signify that a red circle and a blue circle do not extend in space in the same fashion. Thus it's tension.

When they say that all things are bodies, they mean that all things are defined by tonos, the contracted effort that defines the thing. The kind of contraction, the embryonic force that is in the thing, if you don't find it, you don't know [connaissez] the thing. What Spinoza takes up again with the expression "what can a body do?"

Other examples. After the Stoics, at the beginning of Christianity a quite extraordinary type of philosophy developes: the Neo-Platonic school. The prefix "neo" is particularly well founded. Itâs in applying themselves to some extremely important Platonic texts that the Neo-Platonists will completely decenter all of Platonism. So much so that, in a certain sense, one could say that all of it was already in Plato. Only it was as though taken into a set that was not Platoâs. The Enneads have been inherited from Plotinus. Skim through Ennead four, book five. You will see a kind of prodigious course on light. A prodigious text in which Plotinus will try to show that light can be comprehended neither as a function of the emitting body nor as a function of the receiving body. His problem is that light makes up a part of these odd things that, for Plotinus, are going to be the true ideal things. One can no longer say that it begins there and ends there. Where does light begin? Where does light end?

Why couldn't one say the same thing three centuries earlier? Why did this appear in the so-called Alexandrine world? It's a manifesto for a pure optical world. Light has no tactile limit, and nevertheless there is certainly a limit. But this is not a limit such that I could say it begins there and it ends there. I couldn't say that. In other words, light goes as far as its power goes. Plotinus is hostile to the Stoics, he calls himself a Platonist. But he had a premonition of the kind of reversal [retournement] of Platonism that he is in the process of making. It's with Plotinus that a pure optical world begins in philosophy. Idealities will no longer be only optical. They will be luminous, without any tactile reference. Henceforth the limit is of a completely different nature. Light scours the shadows. Does shadow form part of light? Yes, it forms a part of light and you will have a light-shadow gradation that will develop space. They are in the process of finding that deeper than space there is spatialization. Plato didn't know [savait] of that. If you read Plato's texts on light, like the end of book six of the Republic, and set it next to Plotinus 's texts, you see that several centuries had to pass between one text and the other. These nuances are necessary. It's no longer the same world. You know [savez] it for certain before knowing why, that the manner in which Plotinus extracts the texts from Plato develops for himself a theme of pure light. This could not be so in Plato. Once again, Plato's world was not an optical world but a tactile-optical world. The discovery of a pure light, of the sufficiency of light to constitute a world implies that, beneath space, one has discovered spatialization. This is not a Platonic idea, not even in the Timeus. Space grasped as the product of an expansion, that is to say that space is second in relation to expansion and not first. Space is the result of an expansion, that is an idea that, for a classical Greek, would be incomprehensible. Itâs an idea that comes from the Orient. That light could be spatializing: it's not light that is in space, it's light that constitutes space. This is not a Greek idea. Several centuries later a tremendously important art form, Byzantine art, burst forth. It's a problem for art critics to figure out how Byzantine art remains linked to classical Greek art while at the same time, from another point of view, it breaks completely with classical Greek art. If I take the best critic in this regard, Riegl, he says something rigorous, in Greek art you have the priority of the foreground [avant-plan]. The difference between Greek art and Egyptian art is that in Greek art the distinction is made between the foreground and the background [arrière-plan], while in Egyptian art, broadly speaking, the two are on the same plane [plan]. The bas-relief. I summarize quite briefly. Greek art is the Greek temple, it's the advent of the cube. For the Egyptians it was the pyramid, plane surfaces. Wherever you set yourself you are always on a plane surface. It's diabolical because it's a way of hiding the volume. They put the volume in a little cube which is the funerary chamber, and they set up plane surfaces, isosceles triangles, to hide the cube. The Egyptians are ashamed of the cube. The cube is the enemy, the black, the obscure, it's the tactile. The Greeks invent the cube. They make cubical temples, that is to say they move the foreground and the background forward. But, Riegl says, there is a priority of the foreground, and the priority of the foreground is linked to the form because it's the form that has the outline. It's for this reason that he will define the Greek world as a tactile-optical world. With the Byzantines it's quite odd. They nestle [nichent] the mosaics, they move them back. There is no depth in Byzantine art, and for a very simple reason, it's that depth is between the image and me. All of Byzantine depth is the space between the spectator and the mosaic. If you suppress this space it's as if you were to look at a painting outside of every condition of perception, it's unbearable.

The Byzantines mount an enormous forced takeover. They privilege the background, and the whole figure will arise from the background. The whole image will arise from the background. But at that very moment, as if by chance, the formula of the figure or the image is no longer form-outline. Form-outline was for Greek sculpture. And nevertheless there is a limit, there are even outlines, but this is not what acts, the work no longer acts that way, contrarily to Greek statuary in which the outline captures the light. For Byzantine mosaic it's light-color, that is to say that what defines, what marks the limits is no longer form-outline but rather the couple light-color, that is to say that the figure goes on as far as the light that it captures or emits goes, and as far as the color of which it's composed goes.

The effect on the spectator is prodigious, namely that a black eye goes exactly as far as this black shines. Hence the expression of these figures whose faces are consumed by the eyes. In other words there is no longer an outline of the figure, there is an expansion of light-color. The figure will go as far as it acts by light and by color. It's the reversal [renversement] of the Greek world. The Greeks wouldn't have known [su] how or wouldn't have wanted to proceed to this liberation of light and color. With Byzantine art color and light are liberated in relation to space because what they discover is that light and color are spatializing. Thus art must not be an art of space, it must be an art of the spatialization of space. Between Byzantine art and Plotinus slightly earlier texts on light there is an obvious resonance. What is affirmed is the same conception of the limit.
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There is an outline-limit and there is a tension-limit. There is a space-limit and there is a spatialization-limit. 

This is the last time that we will speak of Spinoza. I‚m going to begin with a question that was posed to me last time: how can Spinoza say, at least in one text, that every affection, that any affection is an affection of essence?

Actually, "affection of essence," you feel that it‚s a slightly odd expression. To my knowledge it‚s the only case in which one finds this expression. Which case? A very precise text, which is a recapitulative text at the end of book three of the Ethics. Here Spinoza gives us a series of definitions hors livre. He defines or he gives again definitions which, until then, had either not been given or were scattered. He gives definitions of the affects.

You recall that the affects were a very particular kind of affection: this is what follows from that. We often translate it by the word "feeling" [sentiment]. But there is the French word "affect" which corresponds completely to the Latin word "affectus." This, strictly speaking, is what follows from the affections, the affections being perceptions or representations. But in definition one at the end of book three we read this: "Desire is man‚s very essence, insofar as it is conceived to be determined, from any given affection of it, to do something." This definition consists of quite a long explication and, if one continues, one stumbles upon a sentence that also creates something of a problem, for by affection of essence, "we understand any constitution of that essence, whether it is innate (or acquired)." In the Latin text something is missing: the reason for this parenthesis. In the Dutch translation of the Short Treatise, there is the complete sentence that we expect. Why do we expect this complement, "(or acquired)"? Because it‚s a very standard distinction in the seventeenth century between two types of ideas or affections: ideas that are called innate, and ideas that are called acquired and adventitious.

Innate-acquired is a quite standard couple in the seventeenth century but, on the other hand, the fact is that Spinoza has not used this terminology and it‚s only in this recapitulation that the resumption of the words innate and acquired appears. What is this text in which Spinoza employs terms that he hasn‚t employed up until now and in which he issues the formula "affection of essence"?

If you think about everything we‚ve said up until now, there is a problem because one asks oneself how Spinoza can say that all the affections and all the affects are affections of essence. That means that even a passion is an affection of essence.

At the close of all our analyses, we tended to conclude that what truly belongs to essence are the adequate ideas and the active affects, that is, the ideas of the second kind and the ideas of the third kind. It‚s these that truly belong to essence. But Spinoza seems to say entirely the opposite: not only are all the passions affections of essence, but even among the passions, sadnesses, the worst passions, every affect affects essence!

I would like to try to resolve this problem.

It‚s not a question of discussing one of Spinoza‚s texts, we must take it literally. It teaches us that, be that as it may, every affection is affection of essence. Thus the passions belong to essence no less than the actions; the inadequate ideas [belong] to essence no less than the adequate ideas. And nevertheless there was necessarily a difference. The passions and the inadequate ideas must not belong to essence in the same way that the actions and the adequate ideas belong to it.

How do we get out of this?

Affection of essence. What interests me is the formula "of," in Latin the genitive. In French the genitive is indicated by the particle "de." I think I recall that grammar distinguishes several senses of the genitive. There is a whole variation. When you employ the locution "de" to indicate a genitive, this always means that something belongs to someone. If I make the genitive a locution of belonging, this doesn‚t prevent the belonging from having very different senses. The genitive can indicate that something comes from someone and belongs to her insofar as it comes from someone, or it can indicate that something belongs to someone insofar as this someone undergoes the something.

In other words, the locution "de" does not choose the direction [sens] in which it is inflected, if it‚s a genitive of passion or a genitive of action.

My question is this: I have an inadequate idea, I have a confused proposition out of which comes a passion-affect. In what sense does this belong to my essence? It seems to me that the answer is this: in my natural condition I am condemned to inadequate perceptions. This means that I am composed of an infinity of extensive parts [which are] external to one another. These extensive parts belong to me under a certain relation. But these extensive parts are perpetually submitted to the influence of other parts which act upon them and which don‚t belong to me. If I consider certain parts that belong to me and that make up part of my body, let‚s say my skin; corpuscules of skin that belong to me under such relations: my skin. They are perpetually submitted to the action of other external parts: the set of what acts on my skin, particles of air, particles of sun. I‚m trying to explain at the level of a rudimentary example. The corpuscules of sun, the corpuscules of heat act on my skin. This means that they are under a certain relation that is the relation of the sun. The corpuscules of my skin are under a certain relation that is precisely characteristic of my body, but these particles that have no other law than the law of external determinations act perpetually upon one another.

I would say that the perception that I have of heat is a confused perception, and from it come affects which are themselves passions: "I‚m hot!" At the level of the proposition "I‚m hot!," if I try to distribute the Spinozist categories, I would say: an external body acts on mine. It‚s the sun. That is to say that the parts of the sun act on the parts of my body. All of that is pure external determinism, it‚s like the shocks of particles.
I call perception when I perceive the heat that I experience, the idea of the effect of the sun on my body. It‚s an inadequate perception since it‚s an idea of an effect, I do not know the cause and from it follows a passive affect; either it‚s too hot and I‚m sad, or I feel good, what happiness the sun!

In what sense is this an affection of essence?

It‚s inevitably an affection of essence. At first sight it‚s an affection of the existing body. But finally there is only essence. The existing body is still a figure of essence. The existing body is essence itself, insofar as an infinity of extensive parts, under a certain relation, belongs to it. Under a certain relation! What does that mean, this relation of movement and rest?

You recall, you have essence that is a degree of power [puissance]. To this essence corresponds a certain relation of movement and rest. As long as I exist, this relation of movement and rest is executed by the extensive parts that, from then on, belong to me under this relation.

What does that mean?

In the Ethics there is a quite curious slippage [glissement] of notions, as if Spinoza had a double vocabulary there. And this is included, this would be so only in accordance with the physics of that epoch.

He passes sometimes from a kinetic vocabulary to a dynamic vocabulary. He considers the following two concepts as equivalents: relation of movement and rest, and power [pouvoir] of being affected or aptitude to be affected. One must ask oneself why he treats this kinetic proposition and this dynamic proposition as equivalents. Why is a relation of movement and rest that characterizes me at the same time a power of being affected that belongs to me? There will be two definitions of the body. The kinetic definition will be this: every body is defined by a relation of movement and rest. The dynamic definition is: every body is defined by a certain power of being affected. You must be sensitive to the double kinetic and dynamic register.

One will find a text in which Spinoza says that "a very large number of extensive parts belongs to me. Hence I am affected in an infinity of ways." Having, under a certain relation, an infinity of extensive parts is the power of being affected in an infinity of ways. From then on everything becomes clear.

If you understood the law of extensive parts, they never cease to have causes, to be causes, and to undergo the effect of one upon the others. This is the world of causality or extrinsic, external determinism. There is always a particle that strikes another particle. In other words, you cannot think an infinite set of parts without thinking that they have at each instant an effect upon one another.

What does one call affection? One calls affection the idea of an effect. These extensive parts that belong to me, you can‚t conceive them as having no effect upon one another. They are inseparable from the effect that they have on one another. And there is never an infinite set of extensive parts that would be isolated. There is at least one set of extensive parts that is defined by this: this set belongs to me. It is defined by the relation of movement and rest under which the set belongs to me. But this set is not separable from other sets, equally infinite, that act on it, that have influence on it and which do not belong to me. The particles of my skin are obviously not separable from the particles of air that come to strike them. An affection is nothing other than the idea of the effect. The necessarily confused idea since I have no idea of the cause. It‚s the reception of the effect: I say that I perceive. It‚s thus that Spinoza can pass from the kinetic definition to the dynamic definition, that is, that the relation under which an infinity of extensive parts belongs to me is equally a power of being affected. But then what are my perceptions and my passions, my joys and my sadnesses, my affects? If I continue this sort of parallelism between the kinetic element and the dynamic element, I would say that the extensive parts belong to me insofar as they execute a certain relation of movement and rest that characterizes me. They execute a relation since they define the terms between which the relation applies [joue]. If I speak now in dynamic terms, I would say that the affections and the affects belong to me insofar as they fulfill my power of being affected and at each instant my power of being affected is fulfilled. Compare these completely different moments: instant A: you are out in the rain, you catch it yourself, you have no shelter and you are reduced to protecting your right side with your left side and vice versa. You are sensitive to the beauty of this sentence. It‚s a very kinetic formula. I am forced to make half of myself the shelter for the other side. It‚s a very beautiful formula, it‚s a verse of Dante, in one of the circles of Hell where there‚s a little rain and the bodies are lying in a sort of mud. Dante tries to translate the sort of solitude of these bodies that have no other resource than that of turning over in the mud. Every time they try to protect one side of their body with the other side. Instant B: now you open up. Just now the particles of rain were like little arrows, it was horrible, you were grotesque in your swimsuits. And the sun comes out, instant B. Then your whole body opens up. And now you would like your whole body to be capable of spreading out [étalable], you tend toward the sun. Spinoza says that we must not be fooled, that in the two cases your power of being affected is necessarily fulfilled. Plainly you always have the affections and affects that you deserve according to the circumstances, including the external circumstances; but an affection, an affect belongs to you only to the extent that it actually contributes to fulfilling your power of being affected.

It‚s in this sense that every affection and every affect is affect of essence. Ultimately the affections and the affects can only be affections and affects of essence. Why? They exist for you only as they fulfill a power of being affected which is yours, and this power of being affected is the power of being affected of your essence. At no moment do you have to miss it. When it rains and you are so unhappy, you literally lack nothing. This is Spinoza‚s great idea: you never lack anything. Your power of being affected is fulfilled in every way. In every case, nothing is ever expressed or founded in expressing itself as a lack. It‚s the formula "there is only Being." Every affection, every perception and every feeling, every passion is affection, perception and passion of essence. It‚s not by chance that philosophy constantly employs a word for which it‚s reproached, but what do you want, philosophy needs it, it‚s the sort of locution "insofar as" [en tant que]. If it were necessary to define philosophy by a word, one could say that philosophy is the art of the "insofar as." If you see someone being led by chance to say "insofar as," you can tell yourself that it‚s thought being born. The first man who thought said "insofar as." Why? "Insofar as" is the art of the concept. It‚s the concept. Is it by chance that Spinoza constantly employs the Latin equivalent of "insofar as"? The "insofar as" refers to distinctions in the concept that are not perceptible in things themselves. When you work by way of distinctions in the concept and by way of the concept, you can say: the thing insofar as, that is to say the conceptual aspect of the thing.

So then every affection is affection of essence, yes, but insofar as what? When it‚s a matter of inadequate perceptions and passions, we must add that these are affections of essence insofar as the essence has an infinity of extensive parts that belong to it under such a relation.

Here the power of being affected belongs to essence, plainly it is necessarily fulfilled by affects that come from outside. These affects come from outside, they do not come from the essence, they are nevertheless affects of essence since they fulfill the power of being affected of essence. Remember well that they come from outside, and actually the outside is the law to which the extensive parts acting upon one another are submitted.

When one succeeds in rising to the second and third kinds of knowledge, what happens? Here I have adequate perceptioions and active affects. What does that mean? It‚s the affections of essence. I would even say all the more reason. What difference from the preceding case? This time they do not come from outside, they come from inside. Why? We saw it. A common notion already, all the more reason for an idea of the third kind, an idea of essence, why does this come from inside?

Just now I said that inadequate ideas and passive affects belong to me, they belong to my essence. These are thus affections of essence insofar as this essence actually possesses an infinity of extensive parts that belong to it under a certain relation.

Let‚s now try to find the common notions. A common notion is a perception. It‚s a perception of a common relation, a relation common to me and to another body. It follows from affects, active affects. These affections, perceptions and affects are also affections of essence. They belong to essence. It‚s the same thing, but insofar as what? No longer insofar as essence is conceived as possessing an infinity of extensive parts that belong to it under a certain relation, but insofar as essence is conceived as expressing itself in a relation. Here the extensive parts and the action of the extensive parts are cast off since I am raised to the comprehension of relations that are causes, thus I am raised to another aspect of essence. It‚s no longer essence insofar as it actually possesses an infinity of extensive parts, it‚s essence insofar as it expresses itself in a relation.

And all the more reason if I am raised to ideas of the third kind, these ideas and the active affects that follow from them belong to essence and are affections of essence, this time insofar as essence is in itself [en soi], is in itself [en elle-même], in itself and for itself, is in itself [en soi] and for itself [pour soi] a degree of power [puissance]. I would say broadly that every affection and every affect are affections of essence, only there are two cases, the genitive has two senses?ideas of the second kind and [those] of the third kind are affections of essence, but it would have to be said following a word that will only appear quite a bit later in philosophy, with the Germans for example, these are auto-affections. Ultimately, throughout the common notions and the ideas of the third kind, it‚s essence that is affected by itself.

Spinoza employs the term active affect and there is no great difference between auto-affection and active affect. All the affections are affections of essence, but be careful, affection of essence does not have one and only one sense. It remains for me to draw a sort of conclusion that concerns the Ethics-Ontology relation.

Why does all this constitute an ontology? I have a feeling-idea. There has never been but a single ontology. There is only Spinoza who has managed to pull off an ontology. If one takes ontology in an extremely rigorous sense, I see only one case where a philosophy has realized itself as ontology, and that‚s Spinoza. But then why could this coup only be realized once? Why was it by Spinoza?

The power of being affected of an essence can be as well realized by external affections as by internal affections. Above all we must not think that power of being affected refers more to an interiority that did not make up the kinetic relation. The affects can be absolutely external, this is the case of the passions. The passions are affects that fulfill the power of being affected and that come from outside?book five appears to me to found this notion of auto-affection. Take a text like this one: the love by which I love God (understood in the third kind) is the love by which God loves himself and I love myself. This means that at the level of the third kind, all the essences are internal to one another and internal to the power [puissance] called divine power. There is an interiority of essences and that does not mean that they merge. One arrives at a system of intrinsic distinctions; from this point on only one essence affects me˜and this is the definition of the third kind, an essence affects my essence˜but since all essences are internal to one another, an essence that affects me is a way in which my essence affects itself. Although this is dangerous, I return to my example of the sun. What does "pantheism" mean? How do people who call themselves pantheists live? There are many Englishmen who are pantheists. I‚m thinking of Lawrence. He had a cult of the sun. Light and tuberculosis are the two points common to Lawrence and Spinoza. Lawrence tells us that, broadly speaking, there are at least two ways of being in relation to the sun. There are people on the beach, but they don‚t understand, they don‚t know what the sun is, they live badly. If they were to understand something of the sun, after all, they would come out of it more intelligent and better. But as soon as they put their clothes back on, they are as scabby [teigneux] as before. What do they make of the sun, at this level? They remain in the first kind [?] The "I" in "I like the heat" is an I that expresses relations of extensive parts of the vasoconstrictive and vasodilative type, that expresses itself directly in an external determinism putting the extensive parts in play. In that sense these are particles that act on my particles and the effect of one on the other is a pleasure or a joy. That‚s the sun of the first kind of knowledge, which I translate under the naïve formula "oh the sun, I love that." In fact, these are extrinsic mechanisms of my body that play, and the relations between parts, parts of the sun and parts of my body.

Starting when with the sun, starting when can I begin authentically to say "I"? With the second kind of knowledge, I leave behind the zone of the effect of parts on one another. I have acquired some kind of knowledge of the sun, a practical comprehension of the sun. What does this practical comprehension mean? It means that I get ahead, I know what such a miniscule event linked to the sun means, such a furtive shadow at such a moment, I know what this announces. I no longer record the effects of the sun on my body. I raise myself to a kind of practical comprehension of causes, at the same time that I know how to compose the relations of my body with such and such relation of the sun.

Let‚s take the perception of a painter. Let‚s imagine a nineteenth-century painter who goes out into nature. He has his easel, it‚s a certain relation. There is the sun that does not remain immobile. What is this knowledge of the second kind? He will completely change the position of his easel, he is not going to have the same relation to his canvas depending on whether the sun is high or the sun is about to set. Van Gogh painted on his knees. The sunsets forced him to paint almost lying down so that Van Gogh‚s eye had the lowest horizon line possible. At that moment having an easel no longer means anything. There are letters in which Cézanne speaks of the mistral: how to compose the canvas-easel relation with the relation of wind, and how to compose the relation of the easel with the sinking sun, and how to end up in such a way that I might paint on the ground, that I might paint lying on the ground. I compose relations, and in a certain way I am raised to a certain comprehension of causes, and at that very moment I can begin to say that I love the sun. I am no longer in the effect of particles of sun on my body, I am in another domain, in compositions of relation. And at this very moment I am not far from a proposition that would have appeared to us mad in the first degree, I am not far from being able to say, "the sun, I am something of it." I have a relation of affinity with the sun. This is the second kind of knowledge. Understand that, at the second level, there is a kind of communion with the sun. For Van Gogh it‚s obvious. He begins to enter into a kind of communication with the sun.
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What would the third kind be? Here Lawrence abounds. In abstract terms it would be a mystical union. All kinds of religions have developed mystiques of the sun. This is a step further. Van Gogh has the impression that there is a beyond that he cannot manage to render. What is this yet further that he will not manage to render insofar as he is a painter? Is this what the metaphors of the sun in the mystics are? But these are no longer metaphors if one comprehends it like that, they can say literally that God is the sun. They can say literally that "I am God." Why? Not at all because there is an identification. It‚s that at the level of the third kind one arrives at this mode of intrinsic distinction. It‚s here that there is something irreducibly mystical in Spinoza‚s third kind of knowledge: at the same time the essences are distinct, only they distinguish themselves on the inside from one another. So much so that the rays by which the sun affects me are the rays by which I affect myself, and the rays by which I affect myself are the rays of the sun that affect me. It‚s solar auto-affection. In words this has a grotesque air, but understand that at the level of modes of life it‚s quite different. Lawrence develops these texts on this kind of identity that maintains the internal distinction between his own singular essence, the singular essence of the sun, and the essence of the world.

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