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Deleuze/Spinoza

Cours Vincennes - 24/01/1978

Today we pause in our work on continuous variation to return temporarily, for one session, to the history of philosophy, on a very precise point. It's like a break, at the request of some of you. This very precise point concerns the following: what is an idea and what is an affect in Spinoza? Idea and affect in Spinoza. During March, at the request of some of you, we will also take a break to consider the problem of synthesis and the problem of time in Kant.

For me, this produces a curious effect of returning to history. I would almost like for you to take this bit of history of philosophy as a history tout court. After all, a philosopher is not only someone who invents notions, he also perhaps invents ways of perceiving. I will proceed largely by enumeration. I will begin chiefly with terminological remarks. I assume that the room is relatively mixed. I believe that, of all the philosophers of whom the history of philosophy speaks to us, Spinoza is in a quite exceptional situation: the way he touches those who enter into his books has no equivalent.

It matters little whether you've read him or not, for I'm telling a story. I begin with some terminological cautions. In Spinoza's principal book, which is called the Ethics and which is written in Latin, one finds two words: AFFECTIO and AFFECTUS. Some translators, quite strangely, translate both in the same way. This is a disaster. They translate both terms, affectio and affectus, by “affection.” I call this a disaster because when a philosopher employs two words, it's because in principle he has reason to, especially when French easily gives us two words which correspond rigorously to affectio and affectus, that is “affection” for affectio and “affect” for affectus. Some translators translate affectio as “affection” and affectus as “feeling” [sentiment], which is better than translating both by the same word, but I don't see the necessity of having recourse to the word “feeling” since French offers the word “affect.” Thus when I use the word “affect” it refers to Spinoza's affectus, and when I say the word “affection,” it refers to affectio.

First point: what is an idea? What must an idea be, in order for us to comprehend even Spinoza's simplest propositions? On this point Spinoza is not original, he is going to take the word “idea” in the sense in which everyone has always taken it. What is called an idea, in the sense in which everyone has always taken it in the history of philosophy, is a mode of thought which represents something. A representational mode of thought. For example, the idea of a triangle is the mode of thought which represents the triangle. Still from the terminological point of view, it's quite useful to know that since the Middle Ages this aspect of the idea has been termed its “objective reality.” In texts from the 17th century and earlier, when you encounter the objective reality of the idea this always means the idea envisioned as representation of something. The idea, insofar as it represents something, is said to have an objective reality. It is the relation of the idea to the object that it represents.

Thus we start from a quite simple thing: the idea is a mode of thought defined by its representational character. This already gives us a first point of departure for distinguishing idea and affect (affectus) because we call affect any mode of thought which doesn't represent anything. So what does that mean? Take at random what anybody would call affect or feeling, a hope for example, a pain, a love, this is not representational. There is an idea of the loved thing, to be sure, there is an idea of something hoped for, but hope as such or love as such represents nothing, strictly nothing.

Every mode of thought insofar as it is non-representational will be termed affect. A volition, a will implies, in all rigor, that I will something, and what I will is an object of representation, what I will is given in an idea, but the fact of willing is not an idea, it is an affect because it is a non-representational mode of thought. That works, it's not complicated.

He thereby immediately infers a primacy of the idea over the affect, and this is common to the whole 17th century, so we have not yet entered into what is specific to Spinoza. There is a primacy of the idea over the affect for the very simple reason that in order to love it's necessary to have an idea, however confused it may be, however indeterminate it may be, of what is loved.

In order to will it's necessary to have an idea, however confused or indeterminate it may be, of what is willed. Even when one says “I don't know what I feel,” there is a representation, confused though it may be, of the object. There is a confused idea. There is thus a primacy, which is chronological and logical at the same time, of the idea over the affect, which is to say a primacy of representational modes of thought over non-representational modes. It would be a completely disastrous reversal of meaning if the reader were to transform this logical primacy through reduction. That the affect presupposes the idea above all does not mean that it is reduced to the idea or to a combination of ideas. We must proceed from the following point, that idea and affect are two kinds of modes of thought which differ in nature, which are irreducible to one another but simply taken up in a relation such that affect presupposes an idea, however confused it may be. This is the first point.

Now a second, less superficial way of presenting the idea-affect relation. You will recall that we started from a very simple characteristic of the idea. The idea is a thought insofar as it is representational, a mode of thought insofar as it is representational, and in this sense we will speak of the objective reality of an idea. Yet an idea not only has an objective reality but, following the hallowed terminology, it also has a formal reality. What is the formal reality of the idea? Once we say that the objective reality is the reality of the idea insofar as it represents something, the formal reality of the idea, shall we say, is—but then in one blow it becomes much more complicated and much more interesting—the reality of the idea insofar as it is itself something.

The objective reality of the idea of the triangle is the idea of the triangle insofar as it represents the triangle as thing, but the idea of the triangle is itself something; moreover, insofar as it is something, I can form an idea of this thing, I can always form an idea of the idea. I would say therefore that not only is every idea something—to say that every idea is the idea of something is to say that every idea has an objective reality, it represents something—but I would also say that the idea has a formal reality since it is itself something insofar as it is an idea.

What does this mean, the formal reality of the idea? We will not be able to continue very much further at this level, we are going to have to put this aside. It's necessary just to add that this formal reality of the idea will be what Spinoza very often terms a certain degree of reality or of perfection that the idea has as such. As such, every idea has a certain degree of reality or perfection. Undoubtedly this degree of reality or perfection is connected to the object that it represents, but it is not to be confused with the object: that is, the formal reality of the idea, the thing the idea is or the degree of reality or perfection it possesses in itself, is its intrinsic character. The objective reality of the idea, that is the relation of the idea to the object it represents, is its extrinsic character; the extrinsic character and the intrinsic character may be fundamentally connected, but they are not the same thing. The idea of God and the idea of a frog have different objective realities, that is they do not represent the same thing, but at the same time they do not have the same intrinsic reality, they do not have the same formal reality, that is one of them—you sense this quite well—has a degree of reality infinitely greater than the other's. The idea of God has a formal reality, a degree of reality or intrinsic perfection infinitely greater than the idea of a frog, which is the idea of a finite thing.

If you understood that, you've understood almost everything. There is thus a formal reality of the idea, which is to say the idea is something in itself; this formal reality is its intrinsic character and is the degree of reality or perfection that it envelopes in itself.

Just now, when I defined the idea by its objective reality or its representational character, I opposed the idea immediately to the affect by saying that affect is precisely a mode of thought which has no representational character. Now I come to define the idea by the following: every idea is something, not only is it the idea of something but it is something, that is to say it has a degree of reality which is proper to it. Thus at this second level I must discover a fundamental difference between idea and affect. What happens concretely in life? Two things happen... And here, it's curious how Spinoza employs a geometrical method, you know that the Ethics is presented in the form of propositions, demonstrations, etc.... and yet at the same time, the more mathematical it is, the more extraordinarily concrete.

Everything I am saying and all these commentaries on the idea and the affect refer to books two and three of the Ethics. In books two and three, he makes for us a kind of geometrical portrait of our life which, it seems to me, is very very convincing. This geometrical portrait consists largely in telling us that our ideas succeed each other constantly: one idea chases another, one idea replaces another idea for example, in an instant. A perception is a certain type of idea, we will see why shortly. Just now I had my head turned there, I saw that corner of the room, I turn...it's another idea; I walk down a street where I know people, I say “Hello Pierre” and then I turn and say “Hello Paul.” Or else things change: I look at the sun, and the sun little by little disappears and I find myself in the dark of night; it is thus a series of successions, of coexistences of ideas, successions of ideas. But what also happens? Our everyday life is not made up solely of ideas which succeed each other. Spinoza employs the term “automaton”: we are, he says, spiritual automata, that is to say it is less we who have the ideas than the ideas which are affirmed in us. What also happens, apart from this succession of ideas? There is something else, that is, something in me never ceases to vary. There is a regime of variation which is not the same thing as the succession of ideas themselves.

“Variations” must serve us for what we want to do, the trouble is that he doesn't employ the word... What is this variation? I take up my example again: in the street I run into Pierre, for whom I feel hostility, I pass by and say hello to Pierre, or perhaps I am afraid of him, and then I suddenly see Paul who is very very charming, and I say hello to Paul reassuredly and contentedly. Well. What is it? In part, succession of two ideas, the idea of Pierre and the idea of Paul; but there is something else: a variation also operates in me—on this point, Spinoza's words are very precise and I cite them: (variation) of my force of existing, or another word he employs as a synonym: vis existendi, the force of existing, or potentia agendi, the power [puissance] of acting, and these variations are perpetual.

I would say that for Spinoza there is a continuous variation—and this is what it means to exist—of the force of existing or of the power of acting.

How is this linked to my stupid example, which comes, however, from Spinoza, “Hello Pierre, hello Paul”? When I see Pierre who displeases me, an idea, the idea of Pierre, is given to me; when I see Paul who pleases me, the idea of Paul is given to me. Each one of these ideas in relation to me has a certain degree of reality or perfection. I would say that the idea of Paul, in relation to me, has more intrinsic perfection than the idea of Pierre since the idea of Paul contents me and the idea of Pierre upsets me. When the idea of Paul succeeds the idea of Pierre, it is agreeable to say that my force of existing or my power of acting is increased or improved; when, on the contrary, the situation is reversed, when after having seen someone who made me joyful I then see someone who makes me sad, I say that my power of acting is inhibited or obstructed. At this level we don't even know anymore if we are still working within terminological conventions or if we are already moving into something much more concrete.

I would say that, to the extent that ideas succeed each other in us, each one having its own degree of perfection, its degree of reality or intrinsic perfection, the one who has these ideas, in this case me, never stops passing from one degree of perfection to another. In other words there is a continuous variation in the form of an increase-diminution-increase-diminution of the power of acting or the force of existing of someone according to the ideas which s/he has. Feel how beauty shines through this difficult exercise. This representation of existence already isn't bad, it really is existence in the street, it's necessary to imagine Spinoza strolling about, and he truly lives existence as this kind of continuous variation: to the extent that an idea replaces another, I never cease to pass from one degree of perfection to another, however miniscule the difference, and this kind of melodic line of continuous variation will define affect (affectus) in its correlation with ideas and at the same time in its difference in nature from ideas. We account for this difference in nature and this correlation. It's up to you to say whether it agrees with you or not. We have got an entirely more solid definition of affectus; affectus in Spinoza is variation (he is speaking through my mouth; he didn't say it this way because he died too young...), continuous variation of the force of existing, insofar as this variation is determined by the ideas one has.

Consequently, in a very important text at the end of book three, which bears the title “general definition of affectus,” Spinoza tells us: above all do not believe that affectus as I conceive it depends upon a comparison of ideas. He means that the idea indeed has to be primary in relation to the affect, the idea and the affect are two things which differ in nature, the affect is not reducible to an intellectual comparison of ideas, affect is constituted by the lived transition or lived passage from one degree of perfection to another, insofar as this passage is determined by ideas; but in itself it does not consist in an idea, but rather constitutes affect. When I pass from the idea of Pierre to the idea of Paul, I say that my power of acting is increased; when I pass from the idea of Paul to the idea of Pierre, I say that my power of acting is diminished. Which comes down to saying that when I see Pierre, I am affected with sadness; when I see Paul, I am affected with joy. And on this melodic line of continuous variation constituted by the affect, Spinoza will assign two poles: joy-sadness, which for him will be the fundamental passions. Sadness will be any passion whatsoever which involves a diminution of my power of acting, and joy will be any passion involving an increase in my power of acting. This conception will allow Spinoza to become aware, for example, of a quite fundamental moral and political problem which will be his way of posing the political problem to himself: how does it happen that people who have power [pouvoir], in whatever domain, need to affect us in a sad way? The sad passions as necessary. Inspiring sad passions is necessary for the exercise of power. And Spinoza says, in the Theological-Political Treatise, that this is a profound point of connection between the despot and the priest—they both need the sadness of their subjects. Here you understand well that he does not take sadness in a vague sense, he takes sadness in the rigorous sense he knew to give it: sadness is the affect insofar as it involves the diminution of my power of acting.

When I said, in my first attempt to differentiate idea and affect (that the idea is the mode of thought which represents nothing [?]), that the affect is the mode of thought which represents nothing, I said in technical terms that this is not only a simple nominal definition, nor, if you prefer, only an external or extrinsic one.

In the second attempt, when I say on the other hand that the idea is that which has in itself an intrinsic reality, and the affect is the continuous variation or passage from one degree of reality to another or from one degree of perfection to another, we are no longer in the domain of so-called nominal definitions, here we already acquire a real definition, that is a definition which, at the same time as it defines the thing, also shows the very possibility of this thing. What is important is that you see how, according to Spinoza, we are fabricated as such spiritual automata. As such spiritual automata, within us there is the whole time of ideas which succeed one another, and in according with this succession of ideas, our power of acting or force of existing is increased or diminished in a continuous manner, on a continuous line, and this is what we call affectus, it's what we call existing.

Affectus is thus the continuous variation of someone's force of existing, insofar as this variation is determined by the ideas that s/he has. But once again, “determined” does not mean that the variation is reducible to the ideas that one has, since the idea that I have does not account for its consequence, that is the fact that it increases my power of acting or on the contrary diminishes it in relation to the idea that I had at the time, and it's not a question of comparison, it's a question of a kind of slide, a fall or rise in the power of acting. No problem, no question.

For Spinoza there will be three sorts of ideas. For the moment, we will no longer speak of affectus, of affect, since in effect the affect is determined by the ideas which one has, it's not reducible to the ideas one has, it is determined by the ideas one has; thus what is essential is to see which ideas are the ones which determine the affects, always keeping in mind the fact that the affect is not reducible to the ideas one has, it's absolutely irreducible. It's of another order. The three kinds of ideas that Spinoza distinguishes are affection (affectio) ideas; we'll see that affectio, as opposed to affectus, is a certain kind of idea. There would thus have been in the first place affectio ideas, secondly we arrive at the ideas that Spinoza calls notions, and thirdly, for a small number of us because it's very difficult, we come to have essence ideas. Before everything else there are these three sorts of ideas.

What is an affection (affectio)? I see your faces literally fall... yet this is all rather amusing. At first sight, and to stick to the letter of Spinoza's text, this has nothing to do with an idea, but it has nothing to do with an affect either. Affectus was determined as the continuous variation of the power of acting. An affection is what? In a first determination, an affection is the following: it's a state of a body insofar as it is subject to the action of another body. What does this mean? “I feel the sun on me,” or else “A ray of sunlight falls upon you”; it's an affection of your body. What is an affection of your body? Not the sun, but the action of the sun or the effect of the sun on you. In other words an effect, or the action that one body produces on another, once it's noted that Spinoza, on the basis of reasons from his Physics, does not believe in action at a distance, action always implies a contact, and is even a mixture of bodies. Affectio is a mixture of two bodies, one body which is said to act on another, and the other receives the trace of the first. Every mixture of bodies will be termed an affection. Spinoza infers from this that affectio, being defined as a mixture of bodies, indicates the nature of the modified body, the nature of the affectionate or affected body, the affection indicates the nature of the affected body much more than it does the nature of the affecting body. He analyses his famous example, “I see the sun as a flat disk situated at a distance of three hundred feet.” That's an affectio, or at very least the perception of an affectio. It's clear that my perception of the sun indicates much more fully the constitution of my body, the way in which my body is constituted, than it does the way in which the sun is constituted. I perceive the sun in this fashion by virtue of the state of my visual perceptions. A fly will perceive the sun in another fashion.

In order to preserve the rigor of his terminology, Spinoza will say that an affectio indicates the nature of the modified body rather than the nature of the modifying body, and it envelopes the nature of the modifying body. I would say that the first sort of ideas for Spinoza is every mode of thought which represents an affection of the body...which is to say the mixture of one body with another body, or the trace of another body on my body will be termed an idea of affection. It's in this sense that one could say that it is an affection-idea, the first type of ideas. And this first type of ideas answers to what Spinoza terms the first kind of knowledge [connaissance], the lowest.

Why is it the lowest? It's obvious that it's the lowest because these ideas of affection know [connaissent] things only by their effects: I feel the affection of the sun on me, the trace of the sun on me. It's the effect of the sun on my body. But the causes, that is, that which is my body, that which is the body of the sun, and the relation between these two bodies such that the one produces a particular effect on the other rather than something else, of these things I know [sais] absolutely nothing. Let's take another example: “The sun melts wax and hardens clay.” These points are not nothing. They're ideas of affectio. I see the wax which flows, and right beside it I see the clay which hardens; this is an affection of the wax and an affection of the clay, and I have an idea of these affections, I perceive effects. By virtue of what corporeal constitution does the clay harden under the sun's action? As long as I remain in the perception of affection, I know nothing of it. One could say that affection-ideas are representations of effects without their causes, and it's precisely these that Spinoza calls inadequate ideas. These are ideas of mixture separated from the causes of the mixture.

And in effect, the fact that, at the level of affection-ideas, we have only inadequate and confused ideas is well understood for what are affection-ideas in the order of life? And doubtless, alas, many among us who have not done enough philosophy live only like that. Once, only once, Spinoza employs a Latin word which is quite strange but very important: occursus. Literally this is the encounter. To the extent that I have affection-ideas I live chance encounters: I walk in the street, I see Pierre who does not please me, it's the function of the constitution of his body and his soul and the constitution of my body and my soul. Someone who displeases me, body and soul, what does that mean? I would like to make you understand why Spinoza has had such a strong reputation for materialism even though he never ceases to speak of the mind and the soul, a reputation for atheism even though he never ceases to speak of God, it's quite curious. One sees quite well why people have said that this is purely materialist. When I say “This one does not please me,” that means, literally, that the effect of his body on mine, the effect of his soul on mine affects me disagreeably, it is the mixture of bodies or mixture of souls. There is a noxious mixture or a good mixture, as much at the level of the body as at that of the soul.

It's exactly like this: “I don't like cheese.” What does that mean, “I don't like cheese”? That means that it mixes with my body in a manner by which I am modified disagreeably, it cannot mean anything else. Thus there isn't any reason to make up differences between spiritual sympathies and bodily relations. In “I don't like cheese” there is also an affair of the soul, but in “Pierre or Paul does not please me” there is also an affair of the body, all this is tantamount to the same thing. To put it simply, why is this a confused idea, this affection-idea, this mixture—it is inevitably confused and inadequate since I don't know absolutely, at this level, by virtue of what and how the body or the soul of Pierre is constituted, in what way it does not agree with mine, or in what way his body does not agree with mine. I can merely say that it does not agree with me, but by virtue of what constitution of the two bodies, of the affecting body and the affected body, of the body which acts and the body which is subjected, I can at this level know nothing. As Spinoza says, these are consequences separated from their premises or, if you prefer, it is a knowledge [connaissance] of effects independent of the knowledge of causes. Thus they are chance encounters. What can happen in chance encounters?

But what is a body? I'm not going to develop that, that may be the object of a special course. The theory of what a body or even a soul is, which comes down to the same thing, is found in book two of the Ethics. For Spinoza, the individuality of a body is defined by the following: it's when a certain composite or complex relation (I insist on that point, quite composite, very complex) of movement and rest is preserved through all the changes which affect the parts of the body. It's the permanence of a relation of movement and rest through all the changes which affect all the parts, taken to infinity, of the body under consideration. You understand that a body is necessarily composite to infinity. My eye, for example, my eye and the relative constancy of my eye are defined by a certain relation of movement and rest through all the modifications of the diverse parts of my eye; but my eye itself, which already has an infinity of parts, is one part among the parts of my body, the eye in its turn is a part of the face and the face, in its turn, is a part of my body, etc....thus you have all sorts of relations which will be combined with one another to form an individuality of such and such degree. But at each one of these levels or degrees, individuality will be defined by a certain relation composed of movement and rest.

What can happen if my body is made this way, a certain relation of movement and rest which subsumes an infinity of parts? Two things can happen: I eat something that I like, or else another example, I eat something and collapse, poisoned. Literally speaking, in the one case I had a good encounter and in the other I had a bad one. All this is in the category of occursus. When I have a bad encounter, this means that the body which is mixed with mine destroys my constituent relation, or tends to destroy one of my subordinate relations. For example, I eat something and get a stomach ache which does not kill me; this has destroyed or inhibited, compromised one of my sub-relations, one of the relations that compose me. Then I eat something and I die. This has decomposed my composite relation, it has decomposed the complex relation which defined my individuality. It hasn't simply destroyed one of my subordinate relations which composed one of my sub-individualities, it has destroyed the characteristic relation of my body. And the opposite happens when I eat something that agrees with me.

Spinoza asks, what is evil? We find this in his correspondence, in the letters he sent to a young Dutchman who was as evil as can be. This Dutchman didn't like Spinoza and attacked him constantly, demanding of him, “Tell me what you think evil is.” You know that at that time, letters were very important and philosophers sent many of them. Spinoza, who is very very good-natured, believes at first that this is a young man who wants to be taught and, little by little, he comes to understand that this is not the case at all, that the Dutchman wants his skin. From letter to letter, the good Christian Blyenberg's anger swells and he ends by saying to Spinoza, “But you are the devil!” Spinoza says that evil is not difficult, evil is a bad encounter. Encountering a body which mixes badly with your own. Mixing badly means mixing in conditions such that one of your subordinate or constituent relations is either threatened, compromised or even destroyed.

More and more gay, wanting to show that he is right, Spinoza analyzes the example of Adam in his own way. In the conditions in which we live, we seem absolutely condemned to have only one sort of idea, affection-ideas. By means of what miracle could one move away from these actions of bodies that do not wait for us in order to exist, how could one rise to a knowledge [connaissance] of causes? For the moment we see clearly that all that is given to us is ideas of affection, ideas of mixture. For the moment we see clearly that since birth we have been condemned to chance encounters, so things aren't going well. What does this imply? It already implies a fanatical reaction against Descartes since Spinoza will affirm strongly, in book two, that we can only know [connaÓtre] ourselves and we can only know external bodies by the affections that the external bodies produce on our own. For those who can recall a little Descartes, this is the basic anti-cartesian proposition since it excludes every apprehension of the thinking thing by itself, that is it excludes all possibility of the cogito. I only ever know the mixtures of bodies and I only know myself by way of the action of other bodies on me and by way of mixtures.

This is not only anti-cartesianism but also anti-Christianity, and why? Because one of the fundamental points of theology is the immediate perfection of the first created man, which is what's called in theology the theory of Adamic perfection. Before he sinned, Adam was created as perfect as he could be, so then the story of his sin is precisely the story of the Fall, but the Fall presupposes an Adam who is perfect insofar as he is a created thing. Spinoza finds this idea very amusing. His idea is that this isn't possible; supposing that one is given the idea of a first man, one can only be given this idea as that of the most powerless being, the most imperfect there could be since the first man can only exist in chance encounters and in the action of other bodies on his own. Thus, in supposing that Adam exists, he exists in a mode of absolute imperfection and inadequacy, he exists in the mode of a little baby who is given over to chance encounters, unless he is in a protected milieu—but I've said too much. What would that be, a protected milieu?

Evil is a bad encounter, which means what? Spinoza, in his correspondence with the Dutchman, tells him, “You always relate to me the example of God who forbade Adam from eating the apple, and you cite this as the example of a moral law. The first prohibition.” Spinoza tells him, “But this is not at all what happens,” and then Spinoza relates the entire story of Adam in the form of a poisoning and an intoxication. What happened in reality? God never forbade whatever it might be to Adam, He granted him a revelation. Adam foresaw the noxious effect that the body of the apple would have on the constitution of his own body. In other words the apple is a poison for Adam. The body of the apple exists under such a characteristic relation, such is its constitution, that it can only act on Adam's body by decomposing the relation of Adam's body. And if he was wrong not to listen to God, this is not in the sense that he disobeyed in this matter, but that he didn't comprehend anything. This situation also exists among animals, certain of which have an instinct that turns them away from what is poisonous to them, but there are others which don't have this instinct. When I have an encounter such that the relation of the body which modifies me, which acts on me, is combined with my own relation, with the characteristic relation of my own body, what happens? I would say that my power of acting is increased; at least it is increased with regard to this particular relation. When on the contrary I have an encounter such that the characteristic relation of the body which modifies me compromises or destroys one of my relations, or my characteristic relation, I would say that my power of acting is diminished or even destroyed. We rediscover here our two fundamental affects or affectus: sadness and joy. To recapitulate everything at this level, as a function of ideas of affection which I have, there are two sorts of ideas of affection: the idea of an effect which benefits or favors my own characteristic relation, and second, the idea of an effect which compromises or destroys my own characteristic relation. To these two types of ideas of affection will correspond the two movements of variation in the affectus, the two poles of variation: in one case my power of acting is increased and I undergo [Èprouve] an affectus of joy, and in the other case my power of acting is diminished and I undergo an affectus of sadness.

Spinoza will engender all the passions, in their details, on the basis of these two fundamental affects: joy as an increase in the power of acting, sadness as a diminution or destruction of the power of acting. This comes down to saying that each thing, body or soul, is defined by a certain characteristic, complex relation, but I would also say that each thing, body or soul, is defined by a certain power [pouvoir] of being affected. Everything happens as if each one of us had a certain power of being affected. If you consider beasts, Spinoza will be firm in telling us that what counts among animals is not at all the genera or species; genera and species are absolutely confused notions, abstract ideas. What counts is the question, of what is a body capable? And thereby he sets out one of the most fundamental questions in his whole philosophy (before him there had been Hobbes and others) by saying that the only question is that we don't even know [savons] what a body is capable of, we prattle on about the soul and the mind and we don't know what a body can do. But a body must be defined by the ensemble of relations which compose it, or, what amounts to exactly the same thing, by its power of being affected. As long as you don't know what power a body has to be affected, as long as you learn like that, in chance encounters, you will not have the wise life, you will not have wisdom.

Knowing what you are capable of. This is not at all a moral question, but above all a physical question, as a question to the body and to the soul. A body has something fundamentally hidden: we could speak of the human species, the human genera, but this won't tell us what is capable of affecting our body, what is capable of destroying it. The only question is the power of being affected. What distinguishes a frog from an ape? It's not the specific or generic characteristics, Spinoza says, rather it's the fact that they are not capable of the same affections. Thus it will be necessary to make, for each animal, veritable charts of affects, the affects of which a beast is capable. And likewise for men: the affects of which man is capable. We should notice at this moment that, depending on the culture, depending on the society, men are not all capable of the same affects.

It's well known that one method by which certain governments exterminated the Indians of South America was to have left, on trails the Indians traveled, clothing from influenza victims, clothing gathered in the infirmaries, because the Indians couldn't stand the affect influenza. No need even of machine guns, they dropped like flies. It's the same with us, in the conditions of forest life we risk not living very long. Thus the human genera, species or even race hasn't any importance, Spinoza will say, as long as you haven't made the list of affects of which someone is capable, in the strongest sense of the word “capable,” comprising the maladies of which s/he is capable as well. It's obvious that the racehorse and the draft horse are the same species, two varieties of the same species, yet their affects are very different, their maladies are absolutely different, their capacities of being affected are completely different and, from this point of view, we must say that a draft horse is closer to an ox than to a racehorse. Thus an ethological chart of affects is quite different from a generic or specific determination of animals.

You see that the power of being affected can be fulfilled in two ways. When I am poisoned, my power of being affected is absolutely fulfilled, but it's fulfilled in such a way that my power of acting tends toward zero, which is to say it's inhibited. Inversely, when I undergo joy, that is to say when I encounter a body which combines its relation with my own, my power of being affected is equally fulfilled and my power of acting increases and tends toward...what?

In the case of a bad encounter, all my force of existing (vis existendi) is concentrated, tending toward the following goal: to invest the trace of the body which affected me in order to reject the effect of this body, so much so that my power of acting is diminished accordingly. These are very concrete things: you have a headache and you say, “I can't even read anymore”; this means that your force of existing invests the trace of the migraine so fully, it implies changes in one of your subordinate relations, it invests the trace of your migraine so fully that your power of acting is diminished accordingly. On the contrary, when you say, “I feel really good,” and you are content, you are also content because bodies are mixed with you in proportions and under conditions which are favorable to your relation; at that moment the power of the body which affects you is combined with your own in such a way that your power of acting is increased. So although in the two cases your power of being affected will be completely actualized [effectuÈ], it can be actualized in such a way that the power of acting diminishes to infinity or alternatively the power of acting increases to infinity.

To infinity? Is this true? Evidently not, since at our level the forces of existing, the powers [pouvoirs] of being affected and the powers [puissances] of acting are inevitably finite. Only God has an absolutely infinite power [puissance]. Right, but within certain limits I will not cease to pass via these variations of the power of acting as a function of the ideas I have, I will not cease to follow the line of continuous variation of the affectus as a function of affection-ideas that I have and the encounters that I have, in such a way that, at each instant, my power of being affected is completely actualized, completely fulfilled. Fulfilled, simply, in the mode of sadness or the mode of joy. Of course also both at once, since it's well understood that, in the sub-relations which compose us, a part of ourselves can be composed of sadness and another part of ourselves can be composed of joy. There are local sadnesses and local joys. For example, Spinoza gives the following definition of tickling: a local joy; this does not mean that everything is joy in the tickling, it can be a joy of a nature that implies a coexistant irritation of another nature, an irritation which is sadness: my power of being affected tends to be exceeded [dÈpassÈ]. Nothing that exceeds his/her power of being affected is good for a person. A power of being affected is really an intensity or threshold of intensity.

What Spinoza really wants to do is to define the essence of someone in an intensive fashion as an intensive quantity. As long as you don't know your intensities you risk the bad encounter and you will have to say, it's beautiful, both the excess and the immoderation..no immoderation at all, there's only failure, nothing other than failure. Advice for overdoses. This is precisely the phenomenon of the power of being affected which is exceeded in a total destruction.

Certainly in my generation, on average, we were much more cultured or trained in philosophy, when we used to do it, and on the other hand we had a very striking kind of lack of culture in other domains, in music, painting, cinema.

I have the impression that for many among you the relation has changed, that is to say that you know absolutely nothing, nothing in philosophy and you know, or rather you have a concrete grasp of things like a color, you know what a sound is or what an image is. A philosophy is a kind of synthesizer of concepts, creating a concept is not at all ideological. A concept is a created thing.

What I've defined up to now is solely the increase and diminution of the power of acting, and whether the power of acting increases or diminishes, the corresponding affect (affectus) is always a passion. Whether it be a joy which increases my power of acting or a sadnesss which diminishes my power of acting, in both cases these are passions: joyful passions or sad passions. Yet again Spinoza denounces a plot in the universe of those who are interested in affecting us with sad passions. The priest has need of the sadness of his subjects, he needs these subjects to feel themselves guilty. The auto-affections or active affects assume that we possess our power of acting and that, on such and such a point, we have left the domain of the passions in order to enter the domain of actions. This is what remains for us to see.

How could we leave behind affection-ideas, how could we leave behind the passive affects which consist in increase or diminution of our power of acting, how could we leave behind the world of inadequate ideas once we're told that our condition seems to condemn us strictly to this world. On that score we must read the Ethics as preparing a kind of dramatic turn. It's going to speak to us of active affects where there are no longer passions, where the power of acting is conquered instead of passing by all these continuous variations. Here, there's a very strict point. There's a fundamental difference between Ethics and Morality. Spinoza doesn't make up a morality, for a very simply reason: he never asks what we must do, he always asks what we are capable of, what's in our power, ethics is a problem of power, never a problem of duty. In this sense Spinoza is profoundly immoral. Regarding the moral problem, good and evil, he has a happy nature because he doesn't even comprehend what this means. What he comprehends are good encounters, bad encounters, increases and diminutions of power. Thus he makes an ethics and not at all a morality. This is why he so struck Nietzsche.

We are completely enclosed in this world of affection-ideas and these affective continuous variations of joy and sadness, so sometimes my power of acting increases, okay, sometimes it diminishes; but whether it increases or diminishes I remain within passion because, in both cases, I do not possess it: I'm still separated from my power of acting. So when my power of acting increases, it means that I am then relatively less separated, and inversely, but I am still formally separated from my power of acting, I do not possess it. In other words, I am not the cause of my own affects, and since I'm not the cause of my own affects, they are produced in me by something else: I am therefore passive, I'm in the world of passion.

But there are notion-ideas and essence-ideas. Already at the level of notion-ideas a kind of escape from this world is going to appear. One is completely smothered, enclosed in a world of absolute impotence, even when my power of acting increases it's on a segment of variation, nothing guarantees me that, at the street corner, I'm not going to receive a great blow to the head and that my power of acting is going to fall again.

You recall that an affection-idea is a mixture, that is to say the idea of an effect of a body on mine. A notion-idea no longer concerns the effect of another body on mine, it's an idea which concerns and which has for its object the agreement or disagreement of the characteristic relations between two bodies. If there is such an idea—we don't know yet if there is one, but we can always define something even if it means concluding that it can't exist—it's what we will call a nominal definition. I would say that the nominal definition of the notion is that it's an idea which, instead of representing the effect of a body on another, that is to say the mixture of two bodies, represents the internal agreement or disagreement of the characteristic relations of the two bodies.

An example: if I knew enough about the characteristic relation of the body named arsenic and the characteristic relation of the human body, I could form a notion of the disagreement of these two relations to the point that the arsenic, under its characteristic relation, destroys the characteristic relation of my body. I am poisoned, I die.

You see that the notion, differing from the idea of affection, instead of being the seizure of the extrinsic relation of one body with another or the effect of one body on another, the notion is raised to the comprehension of the cause, that is if the mixture has such and such effect, this is by virtue of the nature of the relation of the two bodies considered and of the manner in which the relation of one of the bodies is combined with the relation of the other body. There is always a composition of relations. When I am poisoned, the body of arsenic has induced the parts of my body to enter into a relation other than the one which characterizes me. At that moment, the parts of my body enter into a new relation induced by the arsenic, which is perfectly combined with the arsenic; the arsenic is happy since it feeds on me. The arsenic undergoes a joyful passion because, as Spinoza says so well, each body has a soul. Thus the arsenic is joyful, but me, evidently I'm not. It has induced the parts of my body to enter into a relation which is combined with its own, the arsenic's. Me, I'm sad, I'm heading toward death. You see that the notion, if one can reach it, is a formidable thing.

We are not far from an analytical geometry. A notion is not at all abstract, it's quite concrete: this body here, that body there. If I had the characteristic relation of the soul and of the body of that which I say displeases me, in relation to my characteristic relation in myself, I would comprehend everything, I would know by causes instead of knowing only by effects separated from their causes. At that moment I would have an adequate idea. Just as if I understood why someone pleases me. I took as an example digestive relations, but we wouldn't have to change a line for amorous relations. It's not at all that Spinoza conceived love like he conceived digestion, he conceived digestion like love as well. Take a couple ý la Strindberg, this kind of decomposition of relations and then they are recombined in order to begin again. What is this continuous variation of the affectus, and how does a certain disagreement agree with certain people? Why can certain people live only in a certain indefinitely repeated domestic quarrel? They emerge from it as if it had been a bath of cool water for them.

You understand the difference between a notion-idea and an affection-idea. A notion-idea is inevitably adequate since it's a knowledge [connaissance] by causes. Spinoza not only uses the term notion here to qualify this second sort of idea, but he also uses the term common notion. The word is quite ambiguous: does it mean common to all minds? Yes and no, it's very meticulous in Spinoza. In any case, don't ever confuse a common notion and an abstraction. He always defines a common notion like this: it's the idea of something which is common to all bodies or to several bodies—at least two—and which is common to the whole and to the part. Therefore there surely are common notions which are common to all minds, but they're common to all minds only to the extent that they are first the idea of something which is common to all bodies. Therefore these are not at all abstract notions. What is common to all bodies? For example, being in movement or at rest. Movement and rest will be objects of notions said to be common to all bodies. Therefore there are common notions which designate something common to all bodies. There are also common notions which designate something common to two bodies or to two souls, for example, someone I love. Once again the common notion is not abstract, it has nothing to do with species or genera, it's actually the statement [ÈnoncÈ] of what is common to several bodies or to all bodies; or, since there's no single body which is not itself made up of several, one can say that there are common things or common notions in each body. Hence we fall back upon the question: how can one leave this situation which condemned us to mixtures?

Here Spinoza's texts are very complicated. One can only conceive this departure in the following manner: broadly speaking, when I am affected in chance encounters, either I am affected with sadness or with joy. When I am affected with sadness, my power of acting diminishes, which is to say that I am further separated from this power. When I am affected with joy, it increases, which is to say that I am less separated from this power. Good. If you consider yourself as affected with sadness, I believe that everything is wretched, there is no longer an exit for one simple reason: nothing in sadness, which diminishes your power of acting, can induce you from within sadness to form a notion common to something which would be common to the bodies which affect you with sadness and to your own. For one very simple reason, that the body which affects you with sadness only affects you with sadness to the extent that it affects you in a relation which does not agree with your own. Spinoza means something very simple, that sadness makes no one intelligent. In sadness one is wretched. It's for this reason that the powers-that-be [pouvoirs] need subjects to be sad. Agony has never been a cultural game of intelligence or vivacity. As long as you have a sad affect, a body acts on yours, a soul acts on yours in conditions and in a relation which do not agree with yours. At that point, nothing in sadness can induce you to form the common notion, that is to say the idea of a something in common between two bodies and two souls. What he's saying is full of wisdom. This is why thinking of death is the most base thing. He is opposed to the whole philosophical tradition which is a meditation on death. His formula is that philosophy is a meditation on life and not on death. Obviously, because death is always a bad encounter.

Another case. You are affected with joy. Your power of acting is increased, this doesn't mean that you possess it yet, but the fact that you are affected with joy signifies and indicates that the body or soul which affects you thus affects you in a relation which is combined with your own and which is combined with your own, and that goes for the formula of love and the digestive formula. In an affect of joy, therefore, the body which affects you is indicated as combining its relation with your own and not as its relation decomposing your own. At that point, something induces you to form a notion of what is common to the body which affects you and to your own body, to the soul which affects you and to your own soul. In this sense joy makes one intelligent. There we feel that it's a curious thing, because, geometrical method or not, we grant him everything, he can demonstrate it; but there is an obvious appeal to a kind of lived experience. There's an obvious appeal to way of perceiving, and even more, to a way of living. It's necessary to already have such a hatred of sad passions, the list of sad passions in Spinoza is infinite, he goes so far as to say that every idea of reward envelopes a sad passion, every idea of security envelopes a sad passion, every idea of pride, guilt. It's one of the most marvelous moments in the Ethics. The affects of joy are like a springboard, they make us pass through something that we would never have been able to pass if there had only been sadnesses. He solicits us to form the idea of what is common to the affecting body and the affected body. This can fail, but it can also succeed and I become intelligent.

Someone who becomes good in Latin at the same time that he becomes a lover...this is seen in the classroom. What's it connected to? How does someone make progress? One never makes progress on a homogeneous line, something here makes us make progress down there, as if a small joy here had released a trigger. Anew, the necessity of a map: what happened there that unblocked this here? A small joy precipitates us into a world of concrete ideas which sweeps out the sad affects or which is in the process of struggling, all of this makes up part of the continuous variation. But at the same time, this joy propels us somehow beyond the continuous variation, it makes us acquire at least the potentiality of a common notion. It's necessary to conceive this very concretely, these are quite local things. If you succeed in forming a common notion, at whatever point you yourself have a relation with such a person or such an animal, you say: I've finally understood something, I am less stupid than yesterday. The “I've understood” that one says is sometimes the moment in which you formed a common notion. You formed it quite locally, it didn't give you all the common notions. Spinoza doesn't think at all like a rationalist, among the rationalists there is the world of reason and there are the ideas. If you have one, obviously you have all of them: you are reasonable. Spinoza thinks that being reasonable, or being wise, is a problem of becoming, which changes in a singular fashion the contents of the concept of reason. It's necessary to know the encounters which agree with you. No one could ever say that it's good for her/him when something exceeds her/his power of being affected. The most beautiful thing is to live on the edges, at the limit of her/his own power of being affected, on the condition that this be the joyful limit since there is the limit of joy and the limit of sadness; but everything which exceeds your power of being affected is ugly. Relatively ugly: what's good for flies is not inevitably good for you... There is no longer any abstract notion, there isn't any formula which is good for man in general. What counts is what your power is for you. Lawrence said a directly Spinozist thing: an intensity which exceeds your power of being affected is bad (posthumous writings). It's inevitable: a blue that is too intense for my eyes will not make me say it's beautiful, it will perhaps be beautiful for someone else. There's good for all, you tell me...Yes, because the powers of being affected are combined.

To assume that there was a power of being affected which defined the power of being affected of the whole universe is quite possible since all relations are combined to infinity, but not in just any order. My relation doesn't combine with that of arsenic, but what can this do? Obviously it does a lot to me, but at this moment the parts of my body enter again into a new relation which is combined with that of the arsenic. It's necessary to know in what order the relations are combined. But if we knew in what order the relations of the whole universe are combined, we could define a power of being affected of the whole universe, which would be the cosmos, the world insofar as it's a body or a soul. At this moment the whole world is only one single body following the order of relations which are combined. At this moment you have, to speak precisely, a universal power of being affected: God, who is the whole universe insofar as He is its cause, has by nature a universal power of being affected. It's useless to say that he's in the process of using the idea of God in a strange manner.

You undergo a joy, you feel that this joy concerns you, that it concerns something important regarding your principal relations, your characteristic relations. Here then it must serve you as a springboard, you form the notion-idea: in what do the body which affects me and my own body agree? In what do the soul which affects me and my own soul agree, from the point of view of the composition of their relations, and no longer from the point of view of their chance encounters. You do the opposite operation from what is generally done. Generally people tend to summarize their unhappinesses, this is where neurosis or depression begins, when we set out to figure the totals; oh shit, there's this and there's that. Spinoza proposes the opposite: instead of summarizing of our sadnesses, taking a local point of departure on a joy on the condition that we feel that it truly concerns us. On that point one forms the common notion, on that point one tries to win locally, to open up this joy. It's the labor of life. One tries to diminish the respective share of sadnesses in relation to the respective share of a joy, and one attempts the following tremendous coup: one is sufficiently assured of common notions which refer to relations of agreement between such and such body and my own, one will attempt then to apply the same method to sadness, but one cannot do it on the basis of sadness, that is to say one will attempt to form common notions by which one will arrive at a comprehension of the vital manner in which such and such body disagrees and no longer agrees. That becomes, no longer a continuous variation, that becomes a bell curve.

You leave joyful passions, the increase in the power of acting; you make use of them to form common notions of a first type, the notion of what there was in common between the body which affected me with joy and my own body, you open up to a maximum your living common notions and you descend once again toward sadness, this time with common notions that you form in order to comprehend in what way such a body disagrees with your own, such a soul disagrees with your own.

At this moment you can already say that you are within the adequate idea since, in effect, you have passed into the knowledge of causes. You can already say that you are within philosophy. One single thing counts, the way of living. One single thing counts, the meditation on life, and far from being a meditation on death it's rather the operation which consists in making death only finally affect the proportion that is relatively the smallest in me, that is, living it as a bad encounter. It's simply well known that, to the extent that a body is tired, the probabilities of bad encounters increase. It's a common notion, a common notion of disagreement. As long as I'm young, death is truly something which comes from outside, it's truly an extrinsic accident, except in the case of an internal malady. There is no common notion, on the other hand it's true that when a body ages, its power of acting diminishes: I can no longer do what I could still do yesterday; this, this fascinates me in aging, this kind of diminution of the power of acting. What is a clown, vitally speaking? It's precisely the type that does not accept aging, he doesn't know how to age quickly enough. It's not necessary to age too quickly because there's also another way of being a clown: acting the old man. The more one ages the less one wants to have bad encounters, but when one is young one leaps into the risk of the bad encounter. The type which, to the extent that his power of acting diminishes as a function of aging, his power of being affected varies, doesn't do it, continues to act the young man, is fascinating. It's very sad. There's a fascinating passage in one of Fitzgerald's novels (the water-ski episode [in Tender is the Night]), there are ten pages of total beauty on not knowing how to age...You know the spectacles which are not uncomfortable for the spectators themselves.

Knowing how to age is arriving at the moment when the common notions must make you comprehend in what way things and other bodies disagree with your own. Then inevitably it will be necessary to find a new grace which will be that of your age, above all not clinging to youth. It's a kind of wisdom. It's not the good health which makes one say “Live life as you please,” it's no longer the will to cling to life. Spinoza knew admirably well how to die, but he knew very well what he was capable of, he knew how to say “Piss off” [merde] to the other philosophers. Leibniz came to him to steal bits of manuscript in order to say afterward that they were his own. There are very curious stories about this, he was a dangerous man, Leibniz. I end by saying that at this second level, one attains the notion-idea where relations are combined, and once again this is not abstract since I've tried to say that it's an extraordinarily vital enterprise. One has left the passions behind. One has acquired formal possession of the power of acting. The formation of notions, which are not abstract ideas, which are literally rules of life, gives me possession of the power of acting. The common notions are the second kind of knowledge [connaissance]. In order to understand the third it's necessary already to understand the second. Only Spinoza has entered into the third kind. Above the common notions... You've noticed that while the common notions are not abstract, they are collective, they always refer to a multiplicity, but they're no less individual for that. They are the ways in which such and such bodies agree, at the limit they are the ways in which all bodies agree, but at that moment it's the whole world which is an individuality. Thus the common notions are always individual.

Beyond even the compositions of relations, beyond the internal agreements which define the common notions, there are the singular essences. What's the difference? It would be necessary to say that, at the limit, the relation and relations which characterize me express my singular essence, but nevertheless it's not the same thing. Why? Because the relation which characterizes me...what I'm saying here is not entirely in the text, but it's practically there... The common notions or the relations which characterize me still concern the extensive parts of my body. My body is composed of an infinity of parts extended to the infinite, and these parts enter into such and such relations which correspond to my essence but are not confused with my essence, for the relations which characterize me are still rules under which are associated, in movement and at rest, the extended parts of my body. Whereas the singular essence is a degree of power [puissance], that is to say these are my thresholds of intensity. Between the lowest and the highest, between my birth and my death, these are my intensive thresholds. What Spinoza calls singular essence, it seems to me, is an intensive quality, as if each one of us were defined by a kind of complex of intensities which refers to her/his essence, and also of relations which regulate the extended parts, the extensive parts. So that, when I have knowledge [connaissance] of notions, that is to say of relations of movement and rest which regulate the agreement or disagreement of bodies from the point of view of their extended parts, from the point of view of their extension, I don't yet have full possession of my essence to the extent that it is intensity. And God, what's that? When Spinoza defines God as absolutely infinite power [puissance], he expresses himself well. All the terms that he explicitly employs: degree, which in Latin is gradus, refers to a long tradition in medieval philosophy. Gradus is the intensive quantity, in opposition to or differing from the extensive parts. Thus it would be necessary to conceive the singular essence of each one as this kind of intensity, or limit of intensity. It's singular because, whether it be our community of genera or species, we are all human for example, yet none of us has the same thresho ...

Cours Vincennes - 25/11/1980

It's quite curious to what extent philosophy, up to the end of the 17th century, ultimately speaks to us, all the time, of God. And after all, Spinoza, excommunicated Jew, is not the last to speak to us of God. And the first book of his great work The Ethics is called “Of God.” And from all of them, whether it's Descartes, Malebranche, Leibniz, we get the impression that the boundary between philosophy and theology is extremely vague.

Why is philosophy so compromised with God? And right up to the revolutionary coup of the 18th century philosophers. Is it a dishonest compromise [compromission] or something a little purer? We could say that thought, until the end of the 17th century, must take considerable account of the demands of the Church, thus it's clearly forced to take many religious themes into account. But one feels quite strongly that this is much too easy; we could just as well say that, until this era, thought's lot is somewhat linked to that of a religious feeling.

I'm going back to an analogy with painting because it's true that painting is full of images of God. My question is: is it sufficient to say that this is an inevitable constraint in this era? There are two possible answers. The first is yes, this is an inevitable constraint of the era which refers to the conditions of art in this era. Or to say, a bit more positively, that it's because there's a religious feeling from which the painter, and even more painting, do not escape. The philosopher and philosophy don't escape either. Is this sufficient? Could we not make up another hypothesis, namely that painting in this era has so much need of God that the divine, far from being a constraint for the painter, is the site of his maximum emancipation. In other words, with God, he can do anything whatsoever, he can do what he couldn't do with humans, with creatures. So much so that God is directly invested by painting, by a kind of flow of painting, and at this level painting will find a kind of freedom for itself that it would never have found otherwise. At the limit, the most pious painter and the one who does painting and who, in a certain way, is the most impious, are not opposed to each other because the way painting invests the divine is a way which is nothing but pictorial, where the painter finds nothing but the conditions of his radical emancipation.

I give three examples: “...el Greco...” This creation could only be achieved on the basis of Christian figures. Then it's true that, at a certain level, constraints operated on them, and at another level the artist is the one who?Bergson said this about the living thing [vivant], he said that the living thing is what turns obstacles into means?this would be a good definition of the artist. It's true that there are constraints from the Church which operate on the painter, but there is a transformation of constraints into means of creation. They make use of God in order to achieve a liberation of forms, to push the forms to the point where the forms have nothing to do with an illustration. The forms are unleashed [se déchaînent]. They embark upon a kind of Sabbath, a very pure dance, the lines and colors lose all necessity to be verisimilar [vraisemblables], to be exact, to resemble something. It's the great enfranchisement of lines and colors which is done thanks to this outward show [apparence]: the subordination of painting to the demands of Christianity.

Another example...a creation of the world... The Old Testament sets up for them a kind of liberation of movements, a liberation of forms, lines and colors. So much so that, in a sense, atheism has never been external to religion: atheism is the artistic power [puissance] at work on [travaille] religion. With God, everything is permitted. I have the distinct feeling that for philosophy it's been exactly the same thing, and if philosophers have spoken to us so much of God?and they could well be Christians or believers?this hasn't been lacking an intense sense of jest [rigolade]. It wasn't an incredulous jesting, but a joy arising from the labor they were involved in.

Just as I said that God and Christ offered an extraordinary opportunity for painting to free lines, colors and movements from the constraints of resemblance, so God and the theme of God offered the irreplacable opportunity for philosophy to free the object of creation in philosophy?that is to say concepts?from the constraints that had been imposed on them...the simple representation of things.

The concept is freed at the level of God because it no longer has the task of representing something; at that moment it becomes the sign of a presence. To speak by analogy, it takes on lines, colors, movements that it would never have had without this detour through God. It's true that philosophers are subject to the constraints of theology, but in conditions such that they make this constraint into a means of fantastic creation, that is they will extract from it [lui arracher] a liberation of the concept without anyone even questioning it. Except in the case where a philosopher goes too fast or too far. Is this perhaps the case with Spinoza? From the start, Spinoza was placed in conditions in which what he said to us no longer had anything to represent. That's why what Spinoza is going to name God, in the first book of The Ethics, is going to be the strangest thing in the world. It's going to be the concept insofar as it brings together the set [ensemble] of all these possibilities... Via the philosophical concept of God is made?and it could only have been made at this level?is made the strangest creation of philosophy as a system of concepts.

What painters and philosophers subjected God to represents either painting as passion or philosophy as passion. Painters subjected the body of Christ to a new passion: they condense [ramassent] him, they make him contract... Perspective is freed from every constraint to represent whatever it may be, and it's the same thing for philosophers.

I take the example of Leibniz. Leibniz begins the creation of the world anew. He asks how it is that God creates the world. He goes back to the classical problem: what is the role of God's understanding and God's will in the creation of the world.

Let's suppose that Leibniz tells us the following: God has an understanding, an infinite understanding of course. It does not resemble ours. The word “understanding” itself would be equivocal. It would not have only a single meaning [sens] since the infinite understanding is absolutely not the same thing as our own understanding, which is a finite understanding. What happens in the infinite understanding? Before God creates the world, there was indeed an understanding, but there wasn't anything else, there was no world. No, says Leibniz, but there are possibles. There are possibles in God's understanding, and all these possibles tend toward existence. That's why essence, for Leibniz, is a tendency to exist, a possibility which tends toward existence. All these possibles have weight according to their quantity of perfection. God's understanding becomes like a kind of envelope in which all the possibles descend and collide. All want to pass into existence. But Leibniz tells us that this is not possible, all cannot pass into existence. Why? Because each one on its own could pass into existence, but not all of them form compatible combinations. There are incompatibilities from the point of view of existence. One such possible cannot be compossible with another such possible.

There's the second stage: he is in the process of creating a logical relation of a completely new type: there are not only possibilities, there are also problems of compossibility. Is a possible compossible with another such possible?

So then which set of possibles will pass into existence? Only that set of possibles that, on its own, has the greatest quantity of perfection will pass into existence. The others will be repressed [refoulés].

It's God's will that chooses the best of all possible worlds. It's an extraordinary descent for the creation of the world, and, thanks to this descent, Leibniz creates all sorts of concepts. We cannot even say of these concepts that they are representational since they precede the things to be represented. And Leibniz issues [lance] his famous metaphor: God creates the world like we play chess, it involves choosing the best combination.

And the calculus of chess will dominate the Leibnizian vision of the divine understanding. It's an extraordinary creation of concepts that finds in the theme of God the very condition of its freedom and its liberation. Once again, just as the painter had to make use of God so that lines, colors and movements would no longer be obliged to represent some existing thing, so the philosopher sets up God, in this era, so that concepts would no longer be obliged to represent some prior thing, something given and ready-made. It's not a matter of asking oneself what a concept represents. It's necessary to ask oneself what its place is in a set of other concepts. In the majority of great philosophers, the concepts they create are inseparable, and are taken in veritable sequences. And if you don't understand the sequence of which a concept is part, you cannot understand the concept. I use this term “sequence” because I'm making a kind of parallel [rapprochement] with painting. If it's true that the constituent unity of cinema is the sequence, I believe that, all things being equal, we could also say it about the concept and about philosophy.

At the level of the problem of Being and the One, it's true that philosophers in their endeavor at conceptual creation about the relations of Being and the One are going to re-establish a sequence. In my view, the first great sequences in philosophy, at the level of concepts, are those Plato constructs in the second part of the Parmenides. There are actually two sequences. The second part of the Parmenides is made up of seven hypotheses. These seven hypotheses are divided into two groups: three hypotheses at first, four hypotheses following. These are two sequences.

First time [temps]: let us assume that the One is superior to Being, the One is above Being. Second time: the One is equal to Being.

Third time: the One is inferior to Being, and derived from Being.

You never say that a philosopher contradicts himself; you will ask such-and-such page, in what sequence to put it, at what level of the sequence? And it's obvious that the One about which Plato speaks to us is not the same according to whether it's situated at the level of the first, the second or the third hypothesis.

One of Plato's disciples, Plotinus, speaks to us at a certain level of the One as the radical origin of Being. Here, Being comes out of [sort de] the One. The One makes Being, therefore it is not, it is superior to Being. This will be the language of pure emanation: the One emanates Being. That is to say the One does not come out of itself in order to produce Being, because if it came out of itself it would become Two, but Being comes out of the One. This is the very formula of the emanative cause. But when we establish ourselves at the level of Being, this same Plotinus will speak to us in splendid and lyrical terms of the Being that contains all beings, the Being that comprehends all beings. And he issues a whole series of formulae which will have very great importance for the whole philosophy of the Renaissance. He will say Being complicates all beings. It's an admirable formula. Why does Being complicate all beings? Because each being explicates Being. There will be a linguistic doublet here: complicate, explicate.

Each thing explicates Being, but Being complicates all things, that is, comprehends them in itself. But these pages of Plotinus are no longer about emanation. You tell yourself that the sequence has evolved: he's in the process of speaking to us of an immanent cause. And indeed, Being behaves like an immanent cause in relation to beings, but at the same time the One behaves in relation to Being like an emanative cause. And if we descend even further, we will see in Plotinus, who nevertheless is not Christian, something which closely resembles a creative cause.

In a certain way, if you don't take sequences into account, you will no longer know exactly what he's talking to us about. Unless there were philosophers who destroy sequences because they want to make something else. A conceptual sequence would be the equivalent of shades [nuances] in painting. A concept changes tone or, at the limit, a concept changes timbre. It would have something like timbres, tonalities. Until Spinoza philosophy proceeded essentially by way of sequences. And on this road the shades concerning causality were very important. Is original causality or the first cause emanative, immanent, creative or something else again? So the immanent cause was present at all times in philosophy, but always as a theme that was never pushed to its own limit [jusqu'au bout de soi-même].

Why? Because this was undoubtedly the most dangerous theme. Treating God as an emanative cause can fit because there is still the distinction between cause and effect. But as immanent cause, such that we no longer know very well how to distinguish cause and effect, that is to say treating God and the creature the same, that becomes much more difficult. Immanence was above all danger. So much so that the idea of an immanent cause appears constantly in the history of philosophy, but as [something] held in check, kept at such-and-such a level of the sequence, not having value, and faced with being corrected by other moments of the sequence and the accusation of immanentism was, for every story of heresies, the fundamental accusation: you confuse God and the creature. That's the fatal accusation. Therefore the immanent cause was constantly there, but it didn't manage to gain a status [statut]. It had only a small place in the sequence of concepts.

Spinoza arrives. He was preceded no doubt by all those who had been more or less audacious concerning the immanent cause, that is to say this cause that's quite bizarre in that, not only does it remain in itself in order to produce, but what it produces remains in it. God is in the world, the world is in God. In The Ethics, I think The Ethics is constructed upon an initial great proposition that could be called the speculative or theoretical proposition. Spinoza's speculative proposition is: there is only one single absolutely infinite substance, that is one possessing all attributes, and what are called creatures are not creatures but modes or manners [manières] of being of this substance. Therefore one single substance having all attributes and whose products are the modes, the ways of being. Hence if these are the manners of being of the substance having all attributes, these modes exist in the attributes of the substance. They are contained [pris] in the attributes.

All the consequences immediately appear. There isn't any hierarchy in the attributes of God, of substance. Why? If substance possesses equally all attributes, there is no hierarchy among the attributes, one is not worth more than another. In other words, if thought is an attribute of God and if extension is an attribute of God or of substance, between thought and extension there won't be any hierarchy. All the attributes will have the same value from the moment that they are attributes of substance. We are still in the abstract. This is the speculative figure of immanence.

I draw several conclusions from this. This is what Spinoza will call God. He calls it God because it's absolutely infinite. What does it represent? It's quite curious. Can one live like that? I draw two consequences from this. First consequence: he's the one who dares to do what many had wanted to do, namely to free the immanent cause completely of all subordination to other processes of causality. There is only one cause, and it's immanent. And this influences practice. Spinoza didn't entitle his book Ontology, he's too shrewd for that, he entitles it Ethics. Which is a way of saying that, whatever the importance of my speculative propositions may be, you can only judge them at the level of the ethics that they envelope or imply [impliquer]. He completely frees the immanent cause, with which Jews, Christians, heretics had so often played around up until then, but he does it within very precise sequences of concepts. Spinoza extracts it from a whole sequence and carries out a forced takeover [coup de force] at the level of concepts. There is no longer a sequence. As a result of his extraction [extraire] of immanent cauality from the sequence of great causes, first causes, as a result of his flattening of everything onto an absolutely infinite substance that comprehends all things as its modes, that possesses all attributes and comprehends all things as its modes, he substituted a veritable plane of immanence for the sequence. It's an extraordinary conceptual revolution: in Spinoza everything happens as if on a fixed plane. An extraordinary fixed plane which is not going to be a plane of immobility at all since all things are going to move?and for Spinoza only the movement of things counts?on this fixed plane. He invents a fixed plane.

Spinoza's speculative proposition is this: extract the concept from the state of variations of sequences and project everything onto a fixed plane which is one of immanence. This implies an extraordinary technique.

It's also a certain mode of life, living in a fixed plane. I no longer live according to variable sequences. But then, what would living on a fixed plane be? Spinoza is one who polishes glasses, who abandoned everything, his heritage, his religion, every social success. He does nothing and before he had written anything whatsoever, he is insulted, he is denounced. Spinoza is the atheist, the abominable. He practically can't publish. He writes letters. He didn't want to be a prof. In the Political Treatise he imagines that the teaching profession would be a volunteer activity, and further, that it would be necessary to pay in order to teach. Professors would teach at the risk of their fortunes and their reputations. That would be a true public prof. Spinoza was involved with a large study group, he sends them The Ethics as he writes it, and they explicate for themselves Spinoza's texts, and they write to Spinoza, who replies. These are very intelligent people. This correspondence is essential. He has his little network. He gets out of trouble thanks to the protection of the De Witt brothers, since he is denounced from all sides.

It's as if he invented the fixed plane at the level of concepts. In my view it's the most fundamental attempt to give a status to the univocity of being, an absolutely univocal being. Univocal being is precisely what Spinoza defines as being the substance having all attributes equal, having all things as modes. The modes of substance are beings [l'étant]. The absolutely infinite substance is Being as Being, the attributes all equal to one another are the essence of being, and here you have this kind of plane on which everything falls back and where everything is inscribed.

Never has a philosopher been treated by his readers the way Spinoza has been, thank God. Spinoza was one of the essential authors for German Romanticism, for example. But even these most educated authors tell us a very curious thing. They say at once that The Ethics is the work that presents us with the most systematic totality, it's system pushed to the absolute, it's univocal being, being that is said only in a single sense. It's the extreme point of the system. It's the most absolute totality. And at the same time, when one reads The Ethics, one always gets the feeling that one will never reach a comprehension of the whole [ensemble]. The whole escapes us. We are not quick enough to keep everything together. There is a very beautiful page where Goethe says that he re-read the same thing ten times and he always fails to comprehend the whole, and every time that I read it I comprehend another piece [bout]. He's a philosopher who has a conceptual apparatus that's among the most systematic in all philosophy. And nevertheless, we always get the impression, we readers, that the whole escapes us and we are reduced to being struck by such and such bit. We are really struck by such and such part. At another level he's the philosopher who pushes the system of concepts the furthest, therefore one who demands a very extensive philosophical education [culture]. The start of The Ethics begins with definitions: of substance, of essence, etc... This all refers to Scholasticism, and at the same time there is no other philosopher who can so easily be read without knowing anything at all. And the two [approaches] must be upheld. Go on, then, and comprehend this mystery. Delbos says of Spinoza that he is a great wind that carries us away. That goes well with my story of the fixed plane. Few philosophers have had this quality [mérite] of achieving the status of a great calm wind. And the miserable, the poor sorts who read Spinoza compare it to the gusts that take us away. How do we reconcile the fact that there was an illiterate reading and an illiterate comprehension of Spinoza with this other fact, that Spinoza is one of the philosophers who, once again, composes the most meticulous conceptual apparatus in the world? There's a success at the level of language. The Ethics is a book that Spinoza considers as finished. He does not publish his book because he know that if he publishes it, he'll find himself in prison. Everyone falls upon him, he no longer has a protector. Things go very badly for him. He gives up on publication and, in a sense, this doesn't matter since the study group already had the text. Leibniz knew the text. What is this text made of. It begins with The Ethics demonstrated in a geometric manner. It's the use of the geometric method. Many authors had already employed this method, but generally on a sequence in which a philosophical proposition is demonstrated in the manner of a geometrical proposition, a theorem. Spinoza extracts this from the state of a moment in a sequence and he will make it the complete method of exposition of The Ethics. With the result that The Ethics is divided into five books. It begins with definitions, axioms, propositions or theorems, demonstrations of the theorem, corollary of the theorem, that is to say the propositions that flow [découlent] from the theorem, etc... That's the great wind, it forms a kind of continuous layer [nappe]. Geometric exposition is no longer the expression of a moment in a sequence at all, it can be completely extricated since the geometric method is going to be the process which consists in filling in the fixed plane of absolutely infinite substance. Thus a great calm wind. And in all of this there is a continuous linkage [enchaînement] of concepts, each theorem refers to other theorems, each demonstration refers to other demonstrations.

Cours Vincennes : power (puissance), classical natural right - 09/12/1980

The problems of terminology, of the invention of words.

In order to designate a new concept, sometimes you will take a very common word; it will be even there the best fit. Only implicitly will this very common word take a completely new sense. Sometimes you will take a very special sense of a common word, and you will build up this sense, and sometimes you will need a new word. It is for this reason that, when one reproaches a philosopher for not speaking like everyone else, it doesn’t make any sense. It is sometimes, sometimes, sometimes. Sometimes it is very well to use only common words, sometimes it is necessary to mark the stroke, the moment of the creation of concepts, by an unusual word.

I spoke to you the last time of this great philosopher who was important during the Renaissance, Nicolas of Cusa. Nicolas of Cusa had to create a kind of portmanteau word, he had contaminated two Latin words. Why? It is a good verbal creation. At that moment one spoke Latin, so it passed by way of Latin, he said: The being of things is the Possest‚. it means nothing if you haven’t done Latin, I am going to explain. Possest: it doesn't exist as a word, it is an inexistent word, he created it, this word, the Possest. It is a very pretty word, it is a pretty word for Latin. It is an awful barbarism, this word is awful. But philosophically is beautiful, it is a success. When one creates a word it is necessary that [xxxx xxxx] there are disasters, nothing is determined in advance.

Possest is made of two terms in Latin, posse‚ which is the infinitive of the verb to be able to(pouvoir), and est is the third person of the verb to be (être) in the present indicative, he is‚ (il est). Posse and est, he contaminates the two and it gives Possest. And what is the Possest ? The Possest is precisely the identity of the power (puissance) and of the act by which I define [xxxx xxxx]. So I would not define something by its essence, what it is, I would define it by this barbaric definition, its Possest : what it can do. Literally: what it can actually do.

Power (puissance) or Possest‚ Good. What does this mean? It means that things are powers (puissances). It is not only that they have power, it is that they come down to the power that they have, as much in action as in passion. So if you compare two things, they can‚t be the same thing, but power is a quantity. You will have, thanks to this very special quantity, but you understand the problem that this causes, power is a quantity, okay, but it is not a quantity like length. Is it a quantity like force? Does this mean that the strongest wins? Very doubtful. First of all, it will be necessary to define the quantities that we call forces. They are not quantities as we know them, they are not quantities whose status is simple. I know that they are not qualities, that I know. Power (puissance) is not a quality, but neither are they so-called extensive quantities. Then even if they are intensive quantities, it is a very special quantitative scale, an intensive scale. This would mean: things have more or less intensity, it would be the intensity of the thing which would be, which would replace its essence, which would define the thing in itself, it would be its intensity. You understand perhaps the link to Ontology. The more intense a thing is, [the] more precisely is that intensity its relation to being: the intensity of the thing is its relation with being. Can we say all this? It is going to occupy us for a long time.

Before getting into it, you see which misunderstanding we are trying to avoid.

Question: on intensity and the thing (inaudible).

Gilles: The question is not what we believe, the question is how we try to get by in this world of powers. When I said intensity, if it is not that, it doesn’t do anything since it was already determined, this type of quantity. It is not that. We are here once again to evaluate how it could be important to undertake a discourse on power (puissance)? Given the misunderstandings that we are trying to avoid in every way, it is to understand this as if Spinoza told us, and Nietzsche afterwards, what things will is power. Evidently if the formula power is essence‚ doesn’t even mean, if there is something that this formula doesn't mean, one could translate it by the formula: what each wants is power‚. No what each wants is power‚ is a formula which doesn't have anything to do with this. Firstly it is a triviality, secondly it is a thing which is evidently false, thirdly this is surely not what Spinoza means. It is not what Spinoza means because it is stupid and Spinoza does not want to say silly things. It is not: Ha!, everyone, from stones to men, by way of the animals, they want more and more power (puissance), they want power (pouvoir). No it is not that! We know that it is not that since it doesn't mean that power (puissance) is the object of the will. No. So we know this at least, it is consoling. But I would like to insist, once again I appeal to your feeling of the evaluation of importance, in what the philosophers have said to us. I would like to try to develop why this history is very very important, this conversion where things (?) are no longer defined by a qualitative essence, man as reasonable animal, but are defined by a quantifiable power (puissance). I am far from knowing what this quantifiable power is, but I will just try to arrive there by passing via this kind of dreaming of what is important, practically. Practically, does that change something? Yes, you must already feel that practically it changes a lot of things. If I’m interested in what something can do, in what the thing can do, it is very different from those who are interested in what is the essence of the thing. I don't regard, it is not really the same manner of being in the world. But I would like to try to show it by, precisely, a precise moment in the history of the thought.

Classical Natural Right There I open a parenthesis, but always in this vision: what is this history of power (puissance) and of defining things by power (puissance). I say: there was a very important moment, a very important tradition, where it is very difficult, historically, to get one‚s bearings, if you don't have some schemas and reference marks, some points of recognition. It is a history which concerns natural right, and this history concerning natural right, it is necessary that you understand this: today this appears to us at first glance very out of date, as much juridically as politically. The theories of natural right, in the manuals of law, or in the manuals of sociology, we always see a chapter on natural right, and we treat it as a theory which lasted until Rousseau, including Rousseau, up until the 18th century, but today no one is interested in it, in the problem of natural right. This is not false, but at the same time I would like you to feel that it was too scholarly a vision, it is terrible we bypass things and that is why people are really battered theoretically, we bypass everything that is important in an historic question.

I am saying this, and you are going to see why I am saying it now and how it is really at the heart of the stage where I am. I am saying: for a very long time there has been a theory of natural right, which consists of what? Finally it seems important to me historically because it was the compilation of most of the traditions of Antiquity and the point of confrontation of Christianity with the traditions of Antiquity. In this respect there are two important names in relation to the classical conception of natural right: on the one hand Cicero who recorded in antiquity all the traditions on the subject: Platonic, Aristotelian and Stoic. He gives a kind of presentation of natural right in Antiquity which is going to have an extreme importance. It is in Cicero that the Christian philosophers, the Christian jurists, will take (more than other authors), it is above all in Cicero that this kind of adaptation to Christianity of natural right, notably in Saint Thomas, will be made. So there we will have a kind of historical lineage that I am going to call for convenience, so that you will find it again there, the lineage of classical natural right, Antiquity-Christianity.

Now, what do they call natural right?

On the whole, I would say that, in this whole conception, natural right, that which constitutes natural right is that which conforms to the essence. I would almost say that there are several propositions, in this classical theory of natural right. I would just like you to retain them, because when I return to power‚(puissance) I would like you to have in mind these four propositions. Four basic propositions which are the basis of this conception of classical natural right.

First proposition: a thing is defined by its essence. Natural right is therefore that which conforms to the essence of something. The essence of man is: reasonable animal. This has defined his natural right. What‚s more, in effect, to be reasonable‚ is the law of his nature. The law of nature intervenes here. There is the first proposition; thus preference is given to the essences.

Second proposition, in this classical theory: from now on, you understand, natural right can not refer, and it is striking that for most of the authors of Antiquity it is very much like this, natural right doesn't refer to a state which would be supposed to precede society. The state of nature is not a pre-social state, certainly not, it could not be. The state of nature is the state that conforms to the essence in a good society. What do we call a good society? We will call a good society, a society where man can realise his essence. So the state of nature is not before the social state, the state of nature it is the state that conforms to the essence in the best possible society, that is the most apt to realise the essence. There is the second proposition of classical natural right.

Third proposition of classical natural right, they emanate from it: what is first is duty: we have rights only insofar as we have duties. It is very politically practical, all this. It is duties. Indeed, what is duty? Here, there is a term, there is a concept of Cicero in Latin, which is very difficult to translate and which indicates this idea of functional duty, the duties of function. It is the term officium‚. One of the most important books of Cicero from the point of view of natural right is a book entitled De officiis‚ On the Subject of the functional duties‚.

And why is it this that is first, duty in existence? It is because duty is precisely the conditions under which I can best realise the essence, i.e. to have a life in conformity with the essence, in the best possible society.

Fourth proposition: there follows a practical rule which will have a great political importance. We could summarize it under the title: the competence of the sage. What is the sage? It is somebody who is singularly competent in the research that relates to the essence, and all that follows from it. The sage is the one who knows what the essence is. Thus there is a principle of competence of the sage because it is the sage who tells us what our essence is, what is the best society, i.e. the society most capable of realizing the essence, and what are our functional duties, our officia‚, i.e. under which conditions we can realise the essence. All this is the competence of the sage. And to the question: to what does the classical sage lay claim? One must reply that the classical sage claims to determine what the essence is, and consequently all kinds of practical tasks follow from this. Hence the political claims of the sage. Therefore, if I summarize this classical conception of natural right, as a result you understand why Christianity will be very interested by this ancient conception of natural right. It will integrate it into what it will call natural theology, making it one of its fundamental parts.

The four propositions are immediately reconciled with Christianity. First proposition: things are defined and define their rights according to their essence. Second proposition: the law of nature is not pre-social, it is in the best possible society. It is life in conformity with the essence in the best possible society. Third proposition: what is first are duties over rights, because duties are the conditions under which you realise the essence. Fourth proposition: consequently, there is the competence of somebody superior, whether this is the church, the prince or the sage. There is a knowledge (savoir) of the essences. Thus the man who knows the essences will be capable of telling us at the same time how to conduct ourselves in life. Conducting oneself in life will be answerable to a knowledge, in the name of which I could say if it is good or bad. There will be thus a man of good, in whatever way it is determined, as man of God or man of wisdom, who will have a competence.

Remember these four propositions well.

Imagine a kind of thunder clap, a guy arrives and says: no, no, no, and in a sense it is the very opposite. Only the spirit of contradiction never works. It is necessary to have reasons, even secret ones, it is necessary to have the most important reasons in order to reverse a theory. One day somebody comes along who is going to make a scandal in the domain of thought. It is Hobbes. He had a very bad reputation. Spinoza read him a lot.

Natural Right according to Hobbes And here is what Hobbes tells us: first proposition of Hobbes: it is not that. He says that things are not defined by an essence, they are defined by a power (puissance). Thus natural right is not what is in conformity with the essence of the thing, it is everything that the thing can do. And in the right of something, animal or man, everything that it can do. And in its right everything that it can do. It is at this time that the great propositions of the type, but the large fish eat the small ones start. It is its right of nature. You come across a proposition of this type, you see that it is signed Hobbes, it is in natural right that large fish eat small ones. You risk bypassing it, but you can understand nothing if you say: Ah Good! it is like that. By saying that it is in the natural right of large fish to eat small ones, Hobbes launches a kind of provocation that is enormous since what we‚ve just called natural right was in conformity with the essence, and thus the set of actions that were permitted in the name of the essence. Here, permit‚ takes on a very different sense: Hobbes announces to us that everything that we can do is permitted. Everything that you can do is permitted, this is natural right. It is a simple idea, but it is an idea that is overwhelming. From where is it coming? He calls that natural right. Everyone from time immemorial knew that large fish ate small ones, never has anybody called that natural right, Why? Because we reserved the word natural right for a completely different thing: moral action that conforms to the essence. Hobbes comes along and says: natural right equals power, therefore what you can do is your natural right. In my natural right is everything that I can do.

Second proposition: consequently, the state of nature is distinguished from the social state, and theoretically precedes it. Why? Hobbes hastens to say it: in the social state, there are prohibitions, there are defenses, there are things that I can do but it is defended. That means that it is not natural right, it is social right. It is in your natural right to kill your neighbor, but it is not in your social right. In other words, the natural right which is identical to power (puissance) is necessarily, and refers to, a state which is not the social state. Hence, at that moment, the promotion of the idea that a state of nature is distinguished from the social state. In the state of nature, everything that I can do is permitted. The natural law is that there is nothing to defend from what I can do. The state of nature thus precedes the social state. Already at the level of this second proposition, we understand nothing at all. We believe to have settled all that by saying is there a state of nature; they believed that there was a state of nature, those who said that. Nothing at all, they believe nothing in this respect. They say that logically, the concept of the state of nature is prior to the social state. They do not say that this state existed. If the right of nature is everything that there is in the power (puissance) of a being, we will define the state of nature as being the zone of this power. It is its natural right. It is thus instinct of the social state since the social state comprises and is defined by the defenses that bear upon something that I can do. Much more, if I am defended it is because I can do it. It is in this that you recognize a social defense. Therefore, the state of nature is first compared to the social state from the conceptual point of view. What does this mean? Nobody is born social. Social by agreement, perhaps we become it. And the problem of politics will be: how to make it so that men become social? But nobody is born social. That means that you can only think society as a product of becoming. And right is the operation of becoming social.

And in the same way, nobody is born reasonable. For this reason these authors are so opposed to a Christian theme to which Christianity equally held, namely the theme that is known in Christianity under the name of the Adamic tradition. The Adamic tradition is the tradition according to which Adam was perfect before sin. The first man was perfect and sin makes him lose perfection. This Adamic tradition is philosophically significant: Christian natural right is very well reconciled with the Adamic tradition. Adam, before sin, is man in conformity with the essence, he is reasonable. It is sin, i.e. the adventures of existence, that make him lose the essence, his first perfection. All of this is in conformity with the theory of classical natural right. Just as nobody is born social, nobody is born reasonable. Reasonable is like social, it is a becoming. And the problem of ethics will perhaps be how to make it so that man becomes reasonable, but not at all how to make it so that a man‚s essence, which would be reasonable, is realised. It is very different if you pose the question like this or like that, you go in very different directions. Hobbes‚ second proposition will be: the state of nature is pre-social, i.e. man is not born social, he becomes it.

Third proposition: if what is first is the state of nature, or if what is first is right‚, this is similar since in the state of nature, everything that I can do is my right. Consequently, what is first is right‚. Consequently, duties will only be secondary obligations tending to limit the rights for the becoming social of man. It will be necessary to limit rights so that man becomes social, but what is first is right‚. Duty is relative to right, whereas, in the classical theory of natural right, it is just the opposite, right was just relative to duty. What was first was the officium.

Fourth proposition: if my right is my power, if rights are first in relation to duties, if duties are only the operation by which rights are induced to limit themselves so that men become social, all kinds of questions are put between brackets. Why do they have to become social? Is it interesting to become social? All kinds of questions that did not arise at all.

From the point of view of natural right, Hobbes says, and Spinoza will take all of this up again but from the point of view of natural right, the most reasonable man in the world and the most complete madman are strictly the same. Why is there an absolute equality of the sage and the fool? It is a funny idea. It is a very baroque world. The point of the view of natural right is: my right equals my power, the madman is the one who does what is in his power, exactly as the reasonable man is the one who does what is in his. They are not saying idiotic things, they are not saying that the madman and the reasonable man are similar, they are saying that there is no difference between the reasonable man and the madman from the point of view of natural right. Why? Because each one does everything that he can. The identity of right and power ensures the equality, the identity of all beings on the quantitative scale. Of course, there will be a difference between the reasonable man and the madman, but in the civil state, in the social state, not from the point of view of natural right. They are in the process of wearing down, of undermining the whole principle of the competent sage or the competence of somebody superior. And that, politically, is very important.

Nobody is competent for me. There it is. There is the great idea that will animate the Ethics as the anti-system of Judgement. In a certain manner nobody can do anything for me, but nobody can be competent for me. Feel! What does this mean? It would be necessary to put it all in this sentence nobody is competent for me!‚ They so much wanted to judge in my place. There is also a discovery filled with wonder: Ha, it is fantastic, but nobody can know, nobody can know for me. Is this completely true? In a certain way it is not completely true! Perhaps there are competences. But, feel finally what there could be that is strange in these propositions... Indeed, this whole new theory of natural right, equally powerful natural right , what is first is right, it is not duty, leads to something: there is no competence of the wise, nobody is competent for myself. Consequently if the society is formed, it can only be, in one way or another, by the consent of those which take part in it, and not because the wise one would tell me the best way of realising the essence. Now, evidently, the substitution of a principle of consent for the principle of competence, has a fundamental importance for all of politics. Therefore, you see, what I tried to make is just a table of propositions, four propositions against four propositions, and I am simply saying that, in the propositions of the classical theory of natural right, Cicéro-Saint Thomas, you have the juridical development of a moral vision of the world, and, in the other case, the conception which finds its starting point with Hobbes, you have the development and all the seeds of a juridical conception of Ethics: beings are defined by their power.

If I’ve made this whole long parentheses, it has been to show that the formula beings are defined by their power and not by an essence‚ had political, juridical , consequences which we are just in the process of anticipating. Now, I just add, to finish with this theme, that Spinoza takes up this whole conception of natural Right in Hobbes. He will change things, he will change relatively significant things, he will not have the same political conceptions as those of Hobbes. But on this same point of natural right he declares himself to be draw ing from and to be a disciple of Hobbes. You see that, there, in Hobbes, he found the juridical confirmation of an idea that he himself formed on the other hand , him Spinoza, namely an astonishing confirmation of the idea according to which the essence of things was nothing other than their power, and it is that which is interesting in the idea of natural right. And I add, to be completely honest historically, that never does it emerge like that in one blow, it would be possible to seek, already, in antiquity, a current, but a very partial, very timid current, where a conception like this of natural right equals power would be formed already in antiquity, but it will be stifled . You find it in certain sophists and certain philosophers called Cynics , but its modern explosion will be with Hobbes and Spinoza.

For the moment I have not even explained, I specified what could well be called existing things distinguishing themselves from a quantitative point of view. That means exactly that existing things are not defined by an essence, but by power and they have more or less power. Their right will be the power of each one, the right of each one will be the power of each one, they have more or less power. There is thus a quantitative scale of beings from the point of view of power.

The qualitative polarity of modes of existence It will now be necessary to pass to the second thing, namely the qualitative polarity of modes of existence and to see if the one follows from the others. The ensemble will give us a coherent vision, or will give us the beginnings of a coherent vision of what is called an Ethics.

So you see why you are not beings from the point of view of Spinoza, you are ways of being, which is understood: if each one is defined by what it can do. It is very curious: you are not defined by an essence, or rather your essence is identical to that which you can do, i.e. you are a degree on a scale of powers (puissances). If each one among us is a degree on a scale of power, then you will say to me: there are some who are better, or not. Let’s leave that to the side. For the moment we don’t know. But if it is like this, you don’t have an essence or you only have an essence identical to your power, i.e. you are a degree on this scale. Consequently you are indeed ways of being. The ways of being will be, precisely, this kind of existing thing, existence quantified according to power, according to the degree of power which defines it. You are quantifiers. You are not quantities, or rather you are very special quantities, each one of us is a quantity, but of what type? It is a very very curious vision of the world, very new: to see people as quantities, as packages of power, it is necessary to live it. It is necessary to live it if that says anything to you.

Hence the other question: but at the same time, these same authors, for example Spinoza, will not cease telling us that there are on the whole two modes of existence. And no matter what you do you are led to choose between the two modes of existence. You exist in such a way that you exist sometimes in one such mode, sometimes in another such mode, and the Ethics will be the exposé of these modes of existence. There this is no longer the quantitative scale of power, it is the polarity of distinct modes of existence. How does he pass from the first idea to the second, and what is it he wants to say to us with the second? There are modes of existence which are distinguished as poles of existence. Could you open the windows a little.... You don’t ask what it is worth , to do something or to undergo something is to exist in a certain way. You don’t ask what it is worth , but you ask what mode of existence it implies.

It is what Nietzsche also said with his story of the Eternal return, he said: it is not difficult to know if something is good or not, this question is not very complicated; it is not an affair of morals. He said make the following test, which would only be in your head. Do you see yourselves doing it an infinite number of times. It is a good criterion. You see it is the criterion of the mode of existence. Whatever I do, whatever I say, could I make of it a mode of existence? If I couldn‚t it is ugly, it is evil , it is bad . If I can, then yes! You see that everything changes, it is not morality . In what sense? I say to the alcoholic, for example, I say to him: you like to drink? You want to drink? Good, very well. If you drink, drink in such a way that with each time you drink, you would be ready to drink, redrink, redrink an infinite number of times. Of course at your own rhythm. It is not necessary to rush : at your own rhythm! At that moment there, at least, you agree with yourself. So people are much less shitty to you when they agree with themselves. What it is necessary to fear above all in the life, are the people who do not agree with themselves, this Spinoza said admirably. The venom of neurosis, that’s it! The propagation of neurosis, I propagate to you my evil , it is terrible, terrible, it is above all those who are not in agreement with themselves. They are vampires. Whereas the alcoholic who drinks, on the perpetual mode of: ha, it is the last time, it is the last glass! One more time, or once again. That is a bad mode of existence. If you do something, do it as if you must do it a million times. If you are not able to do it like that, do something else. It is Nietzsche who said this, it is not me, all objections are to be addressed to Nietzsche. That can work, that can not work. I do not know why we are discussing all this, what I said. All that is not an affair of truth, it touches on what it can touch on, it is an affair of the practice of living. There are people who live like that.

What does Spinoza try to say to us? It is very curious, I would say that the whole of part four of the Ethics develops above all the idea of the polar modes of existence. And in what do you recognize it in Spinoza. What do you recognize it in ? For the moment I‚m saying things extremely simply for the moment, what do you recognize it in . You recognize it in a certain tone of Spinoza’s , when he speaks, from time to time, of the strong, he says in Latin: the strong man, or the free man. Or, on the contrary, he says the slave or the impotent. There you recognize a style which belongs to the Ethics. He does not speak about the malicious or the good man. The malicious and the good man is the man related to values according to his essence. But the way in which Spinoza speaks, you feel that it is another tone. It is like for musical instruments. It is necessary to feel the tone of people. It is another tone; he tells you: there is what makes the strong man, there is what you recognize as a strong and free man. Does that mean a sturdy type of man. Of course not! A strong man can be far from strong from a certain point of view, he can even be sick, he can be whatever you want. So, what is this trick of the strong man? It is a way of life, it is a mode of existence that is opposed to the mode of existence which he calls the slave or the impotent. What do they mean, these styles of life? It is a life style (style de vie). There will be a life style: to live as a slave, to live as impotent. And then another type of life. Once again, what is it? Once again this polarity of the modes, under the form, and under the two poles: the strong or the powerful, and the impotent or the slave, that must say something to us.

Let’s continue to go into the night, there, and examine according to the texts what Spinoza calls the slave or the impotent. It is curious. One realizes that what he calls the slave or the impotent, it is there that the resemblances ˜ and I don’t believe I’m forcing the texts ˜ the resemblances to Nietzsche are fundamental, because Nietzsche will not do anything other than to distinguish these two polar modes of existence and to distribute them in very much the same manner. Because we realise with astonishment that what Spinoza calls the impotent ... a mode of existence, what is it? The impotent are the slaves. Good. But what does the slaves mean? Slaves of social conditions? We feel, well, that the answer is no! It is a way of life. There are thus people who are not at all socially slaves, but they live like slaves! Slavery as a way of life and not as social status. Thus there are slaves. But on the same side, the impotent or the slaves, he puts who ? It will become more significant for us: he puts tyrants. Tyrants! And oddly, there will be plenty of stories, the priests. The tyrant, the priest and the slave. Nietzsche will not say more. In his more violent texts, Nietzsche will not say more, Nietzsche will make the trinity: the tyrant, the priest and the slave. It’s Odd that it is already literally so in Spinoza. And what is there in common between a tyrant who has power (pouvoir), a slave who does not have power, and a priest who seems only to have spiritual power. And what is there in common? And how are they impotent since, on the contrary, they seem to be, at least for the tyrant and the priest, men of power. One political power, and the other spiritual power. If we feel, it is that which I call to sort things out by feelings.

We feel that there is quite a common point. And when we read Spinoza, text after text, we are confirmed on this common point. It is almost like a riddle: for Spinoza what is there in common between a tyrant who has political power, a slave, and a priest who exercises a spiritual power? This something in common is what is going to make Spinoza say: but they are impotent; it is that, in a certain way , they need to sadden life! Curious, this idea. Nietzsche will also say things like this: they need to make sadness reign! He feels it, he feels it very deeply: they need to make sadness reign because the power that they have can only be founded on sadness. And Spinoza makes a very strange portrait of the tyrant, by explaining that the tyrant is someone who needs, above all, the sadness of his subjects, because there is no terror that doesn’t have as its basis a kind of collective sadness. The priest, perhaps for completely other reasons, has need of the sadness of man on his own condition. And when he laughs, it is not more reassuring. The tyrant could laugh, and the favourites, the counselors of the tyrant could also laugh too. It is a bad laugh, and why is it a bad laugh? Not because of its quality, Spinoza would not say that, it is precisely a laughter which has for its object only sadness and the communication of sadness. What does this mean? It is bizarre. The priest, according to Spinoza, essentially needs an action motivated by remorse. Introducing remorse. It is a culture of sadness. Whatever the ends, Spinoza will say that at that moment the ends are equal to us. He judges only that: cultivating sadness. The tyrant for his political power needs to cultivate sadness, the priest needs to cultivate sadness as far as Spinoza can see, who has the experience of the Jewish priest, the Catholic priest and the Protestant priest.

Now Nietzsche throws out a grand sentence by saying: I am the first to do a psychology of the priest, he said in some pages which are very comical, and to introduce this topic into philosophy, he will define the operation of the priest precisely by what he will call the bad conscience, that is, this same culture of sadness. He will say that it is saddening life, it is always about saddening life!, somewhere. And, indeed why? Because it involves judging life. Now, you will not judge life.You won’t submit it to judgment. Life is not the object of judgment, life is not able to be judged, the only way in which you could pass judgment on it is first of all to inject it with sadness. And of course we laugh, I mean that the tyrant can laugh, the priest laughs, but, Spinoza said, in a page that I find very beautiful, his laughter is that of the satyr, and the laughter of the satyr is a bad laugh, why? Because it is laughter which communicates sadness; One can mock nature, the laughter of the satyr is when I mock men. I‚m being ironic. The kind of intoxicating irony, I mock men. The satyr is another way of saying that human nature is miserable. Ha see, what misery, human nature! It is the proposition of moral judgment: Ha, what misery is human nature. It could be the object of a sermon or the object of a satyr. And Spinoza, in some very beautiful texts, said: what I’ve just called an Ethics is the opposite of the satyr.

And yet there are some very comical pages in Spinoza’s Ethics, but it is not at all the same laughter. When Spinoza laughs, it is in the mode: Ho, look at this here, of what is he capable! Ho ho, and this, we‚ve never seen that! It could be an atrocious villainy, was it necessary to do it, to go that far. It is never the Satyr‚s laughter, it is never: see how miserable our nature is! It is not the laughter of irony. It is a completely different type of laughter. I would say that it is much more Jewish humor. It is very Spinozist, it is go on, yet another step, I would never have believed that one could have done it! It is a very particular kind of laughter and Spinoza is one of the most cheerful authors in the world. I believe, indeed, that all this that he hates is what religion has conceived as the satyr of human nature. The tyrant, the man of religion, they are satyrs, that is to say that, above all they denounce human nature as miserable since this involves , above all, passing judgment on it. And, consequently, there is a complicity, and this is Spinoza‚s intuition: there is a complicity of the tyrant, the slave, and the priest. Why? Because the slave is the one who feels better the more things go badly. The worse it goes , the happier he is. This is the mode of existence of the slave! For the slave, whatever the situation, it is always necessary that he sees the awful side. The nasty stuff there. There are people who have a genius for this: these are the slaves. It could be a painting, it could be a scene in the street, there are people who have a genius for it. There is a genius of the slave and at the same time, it is the buffoon. The slave and the buffoon. Dostoyevsky wrote some very profound pages on the unity of the slave and the buffoon, and of the tyrant, these are tyrannical types, they cling, they do not let you go. They don't stop shoving your nose into whatever shit. They are not happy, they always have to degrade things. It is not that the things are necessarily high, but it is always necessary that they degrade, it is always too high. They must always find a small disgrace, a disgrace in the disgrace, there they become roses of joy, the more repulsive it is the happier they are. They live only like this; this is the slave!

And it is also the man of remorse and it is also the satyr man, it is all that and it is to this that Spinoza opposes the conception of a strong man a powerful man, whose laughter is not the same. It is a kind of very benevolent laughter, the laughter of the man said to be free or strong. He says : if this is what you want, then go on, it is funny, yes it is funny! It is the opposite of the satyr. It is Ethical laughter!

Cours Vincennes - 12/12/1980

Intervention of Comtesse: (inaudible on the cassette).

Gilles: I feel coming between you and me still a difference. You tend very quickly to stress an authentically Spinozist concept, that of the tendency to persevere in being. The last time, you spoke to me about the conatus, i.e. the tendency to persevere in being, and you asked me: what don't you do it? I responded that for the moment I cannot introduce it because, in my reading, I am stressing other Spinozist concepts, and the tendency to persevere in being, I will derive it from other concepts which are for me the essential concepts, those of power (puissance) and affect. Today, you return to the same theme. There is not even room for a discussion, you would propose another reading, i.e. a differently accentuated reading. As for the problem of the reasonable man and the insane man, I will respond exactly thus: what distinguishes the insane person and the reasonable one according to Spinoza, and conversely at the same time, there is: what doesn't distinguish them? From which point of view can they not be distinguished, from which point of view do they have to be distinguished? I would say, for my reading, that Spinoza‚s response is very rigorous. If I summarize Spinoza‚s response, it seems to me that this summary would be this: from a certain point of view, there is no reason to make a distinction between the reasonable man and the insane person. From another point of view, there is a reason to make a distinction. Firstly, from the point of view of power, there is no reason to introduce a distinction between the reasonable man and the insane man. What does that mean? Does that mean that they have the same power? No, it doesn‚t mean that they have the same power, but it means that each one, as much as there is in him, realises or exercises his power. I.e. each one, as much as there is in him, endeavours [s‚efforce] to persevere in his being. Therefore, from the point of view of power, insofar as each, according to natural right, endeavours to persevere in his being, i.e. exercise his power ˜ you see I always put Œeffort‚ between brackets ˜ it is not that he tries to persevere, in any way, he perseveres in his being as much as there is in him, this is why I do not like the idea of conatus, the idea of effort, which does not translate Spinoza‚s thought because what it calls an effort to persevere in being is the fact that I exercise my power at each moment, as much as there is in me. It is not an effort, but from the point of view of power, therefore, I can not at all say what each one is worth, because each one would have the same power, in effect the power of the insane man is not the same as that of the reasonable one, but what there is in common between the two is that, whatever the power, each exercises his own. Therefore, from this point of view, I would not say that the reasonable man is better than the insane one. I cannot, I have no way of saying that: each has a power, each exercises as much power as there is in him. It is natural right, it is the world of nature. From this point of view, I could not establish any difference in quality between the reasonable man and the insane one.

But from another point of view, I know very well that the reasonable man is Œbetter‚ than the insane one. Better, what does that mean? More powerful, in the Spinozist sense of the word. Therefore, from this second point of view, I must make and I do make a distinction between the reasonable man and the insane one. What is this point of view? My response, according to Spinoza, would be exactly this: from the point of view of power, you have no reason to distinguish the reasonable man and the insane one, but from the other point of view, namely that of the affects, you distinguish the reasonable man and the insane one. From where does this other point of view come? You remember that power is always actual, it is always exercised. It is the affects that exercise them. The affects are the exercises of power, what I experience in action or passion, it is this which exercises my power, at every moment. If the reasonable man and the insane one are distinguished, it is not by means of power, each one realises his power, it is by means of the affects. The affects of the reasonable man are not the same as those of the insane one. Hence the whole problem of reason will be converted by Spinoza into a special case of the more general problem of the affects. Reason indicates a certain type of affect. That is very new. To say that reason is not going to be defined by ideas, of course, it will also be defined by ideas. There is a practical reason that consists in a certain type of affect, in a certain way of being affected. That poses a very practical problem of reason. What does it mean to be reasonable, at that moment? Inevitably reason is an ensemble of affects, for the simple reason that it is precisely the forms under which power is exercised in such and such conditions. Therefore, to the question that has just been posed by Comtesse, my response is relatively strict; in effect, what difference is there between a reasonable man and the insane one? From a certain point of view, none, that is the point of view of power. From another point of view, enormous difference, from the point of view of the affects which exercise power.

Intervention of Comtesse.

Gilles: You note a difference between Spinoza and Hobbes and you are quite right. If I summarize it, the difference is this: for the one as for the other, Spinoza and Hobbes, one is careful to leave the state of nature by a contract. But in the case of Hobbes, it is in effect a contract by which I give up my right of nature. I‚ll specify because it is more complicated: if it is true that I give up my natural right, then on the other hand, the sovereign himself does not also give up his. Therefore, in a certain way, the right of nature is preserved. For Spinoza, on the contrary, in the contract I do not give up my right of nature, and there is Spinoza‚s famous formula given in a letter: I preserve the right of nature even in the civil state. This famous formula of Spinoza clearly means, for any reader of the era, that on this point, I break with Hobbes. In a certain way, he also preserved natural right in the civil state, but only to the advantage of the sovereign. I say that too quickly. Spinoza, on the whole, is a disciple of Hobbes. Why? Because on two general but fundamental points, he entirely follows the Hobbesian revolution, and I believe that Spinoza‚s political philosophy would have been impossible without the kind of intervention that Hobbes had introduced into political philosophy. What is this very, very important double intervention, this extraordinary innovation? It is, first innovation, to have conceived the state of nature and natural right in a way that broke entirely with the Ciceronian tradition. Now, on this point, Spinoza entirely ratifies Hobbes‚ revolution. Second point: consequently, to have substituted the idea of a pact of consent as the foundation of the civil state for the relation of competence such as it was in traditional philosophy, from Plato to Saint Thomas. Now, on these two fundamental points, the civil state can only refer to a pact of consent and not to a relation of competence where there would be a superiority of the sage, and the whole conception, in addition, of the state of nature and of natural right as power and exercise of power, these two fundamental points belong to Hobbes. It is according to these two fundamental points that I would say that the obvious difference that Comtesse has just signaled between Spinoza and Hobbes, presumes and can only be inscribed in one preliminary resemblance, a resemblance by which Spinoza follows the two fundamental principles of Hobbes. This then becomes a balancing of accounts between them, but within these new presuppositions introduced into political philosophy by Hobbes. We will be led to speak about Spinoza‚s political conception this year from the point of view of research that we are doing on Ontology: in what sense can Ontology entail or must it entail a political philosophy? Do not forget that there is a whole political path of Spinoza, I‚m going very quickly. A very fascinating political path because we cannot even read one political book of Spinoza‚s philosophy without understanding what problems it poses, and what political problems he lived through. The Netherlands in the era of Spinoza was not simple and all Spinoza‚s political writings are very connected to this situation. It is not by chance that Spinoza wrote two books on political philosophy, one the Theologico-Political Treatise the other the Political Treatise, and that, between the two, enough things happened such that Spinoza evolved. The Netherlands in that era was torn between two tendencies. There was the tendency of the House of Orange, and then there was the liberal tendency of the De Witt brothers. Now the De Witt brothers, under very obscure conditions, had won at one moment. The House of Orange was not nothing: this put into play the relations of foreign policy, relations with Spain, war or peace. The De Witt brothers were basically pacifists. This put into play the economic structure, the House of Orange supported the large companies, the brothers were very hostile to the large companies. This opposition stirred everything up. Now the De Witt brothers were assassinated in absolutely horrible circumstances. Spinoza felt this as really the last moment in which he could no longer write, this could also happen to him. The De Witt brothers‚ entourage protected Spinoza. This dealt him a blow. The difference in political tone between the Theologico-Political Treatise and the Political Treatise is explained because, between the two, there was the assassination, and Spinoza no longer believed in what he had said before, in the liberal monarchy. His political problem arises in a very beautiful, still very current, way; yes, there is only a political problem that it would be necessary to try to understand, to make ethics into politics. To understand what? To understand why people fight for their slavery. They seem to be so content to be slaves, that they will do anything to remain slaves. How to explain such a thing? It fascinates him. Literally, how to explain that people don't revolt? But at the same time, revolt or revolution, you will never find that in Spinoza. We‚re saying very silly things. At the same time, he made drawings. There is a reproduction of a drawing of his that is a very obscure thing. He had drawn himself in the form of a Neapolitan revolutionary who was well-known in that era. He had included his own head. It is odd. Why does he never speak about revolt or revolution? Is it because he is a moderate? Undoubtedly, he must be a moderate; but let us suppose that he is a moderate. But at that time, even the extremists hesitated to speak of revolution, even the leftists of the era. And Collegians who were against the church, these Catholics were near enough to what we would call today the Catholics of the extreme left. Why isn‚t revolution discussed? There is a silly thing that is said, even in the handbooks of history, that there was no English revolution. Everyone knows perfectly well that there was an English revolution, the formidable revolution of Cromwell. And Cromwell‚s revolution is an almost pure case of a revolution that was betrayed as soon as it was done. The whole of the seventeenth century is full of reflections on how a revolution can not be betrayed. Revolution was always thought by revolutionaries in terms of how it is that such things are always betrayed. Now, the recent example for Spinoza‚s contemporaries is the revolution of Cromwell, who was the most fantastic traitor to the revolution that Cromwell himself had imposed. If you take, well after English Romanticism, it is a fantastic poetic and literary movement, but it is an intense political movement. The whole of English Romanticism is centered on the theme of the betrayed revolution. How to live on when the revolution has been betrayed and seems destined to be betrayed? The model that obsessed the great English Romantics was always Cromwell. Cromwell lived in that era as Stalin did today. Nobody speaks about revolution, not at all because they do not have an equivalent in mind, it is for a very different reason. They won‚t call that revolution because the revolution is Cromwell. Now, at the time of the Theologico-Political Treatise, Spinoza still believed in a liberal monarchy, on the whole. This is no longer true from the Political Treatise. The De Witt brothers were assassinated, compromise is no longer possible. Spinoza gives up publishing the Ethics, he knows that it‚s screwed. At that moment, it seems that Spinoza would have tended much more to think about the chances of a democracy. But the theme of democracy appears much more in the Political Treatise than in the Theologico-Political Treatise, which remained in the perspective of a liberal monarchy. What would a democracy be at the level of the Netherlands? It is what was liquidated with the assassination of the De Witt brothers. Spinoza dies, as if symbolically, when he is at the chapter Œdemocracy‚. We will never know what he would have said. There is a fundamental relation between Ontology and a certain style of politics. What this relation consists of, we don‚t yet know. What does a political philosophy which is placed in an ontological perspective consist of? Is it defined by the problem of the state? Not especially, because the others too. A philosophy of the One will also pass by way of the problem of the state. The real difference does not appear elsewhere between pure ontologies and philosophies of the One. Philosophies of the One are philosophies that fundamentally imply a hierarchy of existing things, hence the principle of consequence, hence the principle of emanation: from the One emanates Being, from Being emanates other things, etc. the hierarchies of the Neo-Platonists. Therefore, the problem of the state, they will encounter it when they encounter themselves? at the level of this problem: the institution of a political hierarchy. Among Neo-Platonists, there are hierarchies everywhere, there is a celestial hierarchy, a terrestrial hierarchy, and what the Neo-Platonists call hypostases are precisely the terms in the institution of a hierarchy. What appears to me striking in a pure ontology is the point at which it repudiates the hierarchies. In effect, if there is no One superior to being, if being is said of everything that is and is said of everything that is in one and the same sense, this is what appeared to me to be the key ontological proposition: there is no unity superior to being and, consequently, being is said of everything that of which it is said, i.e. is said of everything that is, is said of all being [étant], in one and the same sense. It is the world of immanence. This world of ontological immanence is an essentially anti-hierarchical world. Of course, it is necessary to correct: these philosophers of ontology, we will say that evidently a practical hierarchy is needed, ontology does not lead to formulas which would be those of nihilism or non-being, of the type where everything is the same [tout se vaut]. And yet, in certain regards, everything is the same, from the point of view of an ontology, i.e. the point of view of being. All being [étant] exercises as much being [être] as there is in it. That‚s all there is to it. It is anti-hierarchical thought. It is almost a kind of anarchy. There is an anarchy of beings in being. It is the basic intuition of ontology: all beings are the same [se valent]. The stone, the insane, the reasonable, the animal, from a certain point of view, from the point of view of Being [être], they are the same. Each is as much as there is in it, and being is said in one and the same sense of the stone, of the man, of the insane, of the reasonable. It is a very beautiful idea. It is a very savage kind of world. With that, they encounter the political domain, but the way in which they will encounter the political domain depends precisely on this kind of intuition of equal being, of anti-hierarchical being. And the way in which they think the state is no longer the relation of somebody who commands and others who obey. In Hobbes, the political relation is the relation of somebody who commands and of somebody who obeys. This is the pure political relation. From the point of view of an ontology, it is not that. There, Spinoza did not go along with Hobbes at all. The problem of an ontology is, consequently, according to this: being is said of everything that is, this is how to be free. I.e. how to exercise its power under the best conditions. And the state, even more the civil state, i.e. the entire society is thought like this: the ensemble of conditions under which man can exercise his power in the best way. Thus it is not at all a relation of obedience. Obedience will come, moreover, it will have to be justified by what it inscribes in a system where society can mean only one thing, namely the best means for man of exercising his power. Obedience is second compared to this requirement. In a philosophy of the One, obedience is obviously first, i.e. the political relation is the relation of obedience, it is not the relation of the exercise of power. We will find this problem again in Nietzsche: what is equal? What is equal is that each being, whatever it is, in every way exercises all that it can of its power, that, that makes all beings equal. But the powers are not equal. But each endeavours to persevere in its being, i.e. exercise its power. From this point of view, all beings are the same, they are all in being and being is equal. Being is also said of everything that is, but everything that is is not equal, i.e. does not have the same power. But being which is said of everything that is, that, that is equal. With that, it doesn't‚t prevent there being differences between beings. From the point of view of the difference between beings a whole idea of aristocracy can be established, namely there are the better ones. If I try to summarize, understand where we were the last time. We posed a very precise problem, the problem which I have dealt with until now, which is this: what is the status, not of Being [être], but of being [étant], i.e. what is the status of Œwhat is‚ from the point of view of an ontology. What is the status of the being [étant] or of what exists [existant] from the point of view of an ontology? I have tried to show that the two conceptions, that of the quantitative distinction between existing things, and the other point of view, that of the qualitative opposition between modes of existence, far from contradicting themselves, have been interlinked with one another the whole time. This finishes the first category: what is an ontology, and how is it distinguished from philosophies which are not ontologies. Second major category: what is the status of the being [étant] from the point of view of a pure ontology like Spinoza‚s?

Inaudible intervention

Gilles: You say that from the point of view of the hierarchy, what is first is difference and one goes from difference to identity. That is quite right, but I would just add: which type of difference is it about? Response: it is always finally a difference between Being [être] and something superior to being, since the hierarchy is going to be a difference in judgment. Therefore, judgment is done in the name of a superiority of the One over being. We can judge being precisely because there is an authority superior to being. Thus the hierarchy is inscribed as of this difference, since the hierarchy, even its foundation, is the transcendence of the One over being. And what you call difference is exactly this transcendence of the One over being. When you invoke Plato, difference is only first in Plato in a very precise sense, namely the One is more than being. Thus it is a hierarchical difference. Ontology goes from being [être] to beings [étants], i.e. it goes from the same, from what is, and only what is different, it goes therefore from being to the differences, it is not a hierarchical difference. All beings are also in Being. In the Middle Ages, there is a very important school, it was given the name the School of Chartres; and the School of Chartres, they depend mostly on Duns Scotus, and they insist enormously on the Latin term "equality.‰ Equal being. They say all the time that being is fundamentally equal. That doesn‚t mean that existing things, or beings [étants], are equal. But being is equal for all, which means, in a certain way, that all beings are in being. Consequently, whatever the difference you achieve, since there is a non-difference of being, and there are differences between beings, these differences will not be conceived in a hierarchical way. Or, they will be conceived in a hierarchical way very, very secondarily, to catch up with, to reconcile the things. But in the first intuition, the difference is not hierarchical. Whereas in philosophies of the One difference is fundamentally hierarchical. I would say much more: in ontology, the difference between beings is quantitative and qualitative at the same time. Quantitative difference of powers, qualitative difference of modes of existence, but it is not hierarchical. Then, of course, they often speak as if there had been a hierarchy, they will say that the reasonable man is better than the malicious one, but better in what sense and why? It is for reasons of power and exercise of power, not for reasons of hierarchy. I would like to pass to a third rubric which is connected at the second and which would come down to saying that if the Ethics - I defined as the two co-ordinates of the Ethics: the quantitative distinction from the point of view of power, the qualitative opposition from the point of view of the modes of existence. I tried to show last time how we passed perpetually from the one to the other. I would like to begin a third rubric, which is, from the point of view of the Ethics, how does the problem of evil arise. Because, once again, we have seen that this problem arose in an acute way, why? I remind you that I discussed the sense in which, from time immemorial, classical philosophy had set up this paradoxical proposition, by knowing very well that it was a paradox, namely evil is nothing. But precisely, evil is nothing, understand that there are at least two possible manners of speaking. These two manners are not reconciled at all. Because when I say evil is nothing, I could mean firstly one thing: evil is nothing because everything is Good. If I say everything is Good. If you write Good with a capital G, if you write it like that, you can comment on the formula word for word: there is being, good: The One is superior to being, and the superiority of the One over being makes being turn towards the One as being the Good. In other words, Œevil is nothing‚, means: inevitably evil is nothing since it is the Good superior to being which is the cause of being. In other words, the Good makes being. The Good is the One as the reason for being. The One is superior to being. Everything is Good means that it is the good that makes being what is. I am discussing Plato. You understand that Œevil is nothing‚ means that only the Good makes being, and correlatively: makes action. It was the argument of Plato: the malicious one is not voluntarily malicious since what the malicious one wants is the good, it is whatever good. I can thus say that evil is nothing, in the sense that only the Good makes being and makes action, therefore evil is nothing. In a pure Ontology, where there is no One superior to being, I say evil is nothing, there is no evil, there is being. Okay. But that engages me with something completely new, it is that if evil is nothing, then the good is nothing either. It is thus for completely opposite reasons that I can say in both cases that evil is nothing. In one case, I say that evil is nothing because only the Good makes being and makes action, in the other case, I say that evil is nothing because the Good is nothing too, because there is only being. Now we have seen that this negation of the good, like that of evil, did not prevent Spinoza from making an ethics. How is an ethics made if there is neither good nor evil. From the same formula, in the same era, if you take the formula: Œevil is nothing‚, signed by Leibniz, and signed by Spinoza, they both say the same formula, Œevil is nothing‚, but it has two opposite senses. In Leibniz it derives from Plato, and in Spinoza, who makes a pure ontology, it becomes complicated. Hence my problem: what is the status of evil from the point of view of ethics, i.e. from the whole status of beings, of existing things? We will return to the parts where ethics is really practical. We have an exceptional text of Spinoza: it is an exchange of eight letters, four each. A set of eight letters exchanged with a young man called Blyenberg. The sole object of this correspondence is evil. The young Blyenberg asks Spinoza to explain evil ?

(tape inaudible ... and end of the first part)

Cours Vincennes : Ontologie-Ethique - 21/12/1980

On the project of a pure ontology, how is it that Spinoza calls this pure ontology an Ethics? It would be by an accumulation of traits that we realize that it was [a pure ontology], although he calls it an Ethics. We saw the general atmosphere of this link between an Ontology and an Ethics with the suspicion that an ethics is something that has nothing to do with morality. And why do we have a suspicion of the link that makes this pure Ontology take the name of Ethics? We have seen it. Spinoza’s pure Ontology is presented as the absolutely infinite single position. Consequently, the beings (

étants

), this absolutely infinite single substance, is being. Being (

être

) as being. Consequently, the beings (

étants

) will not be Beings (

êtres

), they will be what Spinoza calls modes, the modes of absolutely infinite substance. And a mode is what? It is a manner of being. The beings (

étants

) or what exists (

existants

) are not Beings (

êtres

), there is Being only in the form of absolutely infinite substance. Consequently, we who are beings (

étants

), we who are what exists (

existants

), we will not be Beings (

êtres

), we will be manners of Being (

être

) of this substance. And if I ask myself what is the most immediate sense of the word ethics, in what way is it already other than morality, well, ethics is better known to us today under another name, the word ethology.

When one speaks of an ethology in connection with animals, or in connection with man, what is it a matter of? Ethology in the most rudimentary sense is a practical science, of what? A practical science of the manners of being. The manner of being is precisely the state of beings (étants), of what exists (existants), from the point of view of a pure ontology.

In what way is it already different from a morality? We are trying to compose a kind of landscape which would be the landscape of ontology. We are manners of Being in Being, that is the object of an ethics, i.e. an ethology. In a morality, on the contrary, what is it a matter of? There are two things which are fundamentally welded together. It is a matter of essence and values. A morality recalls us to essence, i.e. our essence, and which is recalled to us by values. It is not the point of view of Being. I do not believe that a morality can be made from the point of view of an ontology. Why? Because morality always implies something superior to Being; what is superior to Being is something which plays the role of the One, of the Good, it is the One superior to Being. Indeed, morality is the enterprise of judging not only all that is, but Being itself. Now one can only judge Being in the name of an authority higher than Being.

In what way, in a morality, is it a matter of essence and values? What is in question in a morality is our essence. What is our essence? In a morality it is always a matter of realising the essence. This implies that the essence is in a state where it is not necessarily realised, that implies that we have an essence. It is not obvious that there is an essence of man. But it is quite necessary for morality to speak and to give us orders in the name of an essence. If we are given orders in the name of an essence, it is because this essence is not realised by itself. It will be said that this essence is in man potentially (en puissance). What is the essence of man is potentially in man, from the point of view of a morality? It is well known, the essence of man is to be a reasonable animal. Aristotle: Man is a reasonable animal. The essence is what the thing is, reasonable animal is the essence of man. Even if man is in essence a reasonable animal, he does not cease to behave in an unreasonable way. How does that happen? It is because the essence of man, as such, is not necessarily realised. Why? Because man is not pure reason, and then there are accidents, he doesn’t cease being diverted. The whole classical conception of man consists in inviting him to agree with his essence because this essence is like a potentiality, which is not necessarily realised, and morality is the process of the realization of the human essence.

Now, how can this essence which is only potential, be realized? By morality. To say that it is to be realized by morality is to say that it must be taken for an end. The essence of man must be taken for an end by existing man. Therefore, to behave in a reasonable way, i.e. to carry out the essence is the task of morality. Now the essence taken as an end is value. Note that the moral vision of the world is made of essence. The essence is only potential, it is necessary to realise the essence, that will be done insofar as the essence is taken for an end, and the values ensure the realization of the essence. It is this ensemble which I would call morality.

In an ethical world, let us try to switch over, there is no longer any of this. What will they say to us in an Ethics? We will find nothing. It is another landscape. Spinoza very often speaks about essence, but for him, essence is never the essence of man. Essence is always a singular determination. There is the essence of this man, and of that man, there is no essence of man. He will himself say that the general essences or the abstract essences of the type the essence of man‚are confused ideas. There is no general idea in an Ethics. There is you, this one, that one, there are singularities. The word essence is quite likely to change sense. When he speaks about essence, what interests him is not the essence, what interests him is existence and what exists.

In other words, what is can only be put in relation to Being at the level of existence, and not at the level of essence.

At this level, there is already an existentialism in Spinoza. It is thus not a matter of an essence of man, in Spinoza, it is not the question of an essence of man that would only be potential and which morality would be assigned to realise, it is about something altogether different. You recognize an ethics in what he, who speaks to you about ethics, tells you of two things in one. He is interested in existing things (existants) in their singularity. Sometimes, he is going to tell you, between what exists there is a distinction, a quantitative difference in existence; what exists can be considered on a kind of quantitative scale according to which they are more or less... More or less what? We are going see. Not at all an essence common to several things, but a quantitative distinction of more and less between existing things, that is Ethics.

In addition, the same discourse of an ethics is pursued by saying that there is also a qualitative opposition between modes of existence. Two criteria of ethics, in other words, the quantitative distinction of existing things, and the qualitative opposition of modes of existence, the qualitative polarization of modes of existence, will be the two ways in which existing things are in being.

These are going to be the links of Ethics with Ontology. Existing things or the beings are in Being from two simultaneous points of view, from the point of view of a qualitative opposition of the modes of existence, and from the point of view of a quantitative scale of existing things. It is completely the world of immanence. Why?

It is the world of immanence because you see at which point it is different from the world of moral values such as I have just defined them, the moral values being precisely this kind of tension between the essence to be realized and the realization of the essence.

I would say that value is exactly the essence taken as an end.

That is the moral world. The completion of the moral world, one can say that it is indeed in Kant that a supposed human essence is taken for an end, in a kind of pure act.

Ethics is not that at all, they are like two absolutely different worlds. What can Spinoza have to say to the others. Nothing.

It would be a matter of showing all that concretely. In a morality, you always have the following operation: you do something, you say something, you judge it yourself. It is the system of judgement. Morality is the system of judgement. Of double judgement, you judge yourself and you are judged. Those who have the taste for morality are those who have the taste for judgement. Judging always implies an authority superior to Being, it always implies something superior to an ontology. It always implies one more than Being, the Good which makes Being and which makes action, it is the Good superior to Being, it is the One. Value expresses this authority superior to Being. Therefore, values are the fundamental element of the system of judgement. Therefore, you are always referred to this authority superior to Being for judging.

In an ethics, it is completely different, you do not judge. In a certain manner, you say: whatever you do, you will only ever have what you deserve. Somebody says or does something, you do not relate it to values. You ask yourself how is that possible? How is this possible in an internal way? In other words, you relate the thing or the statement to the mode of existence that it implies, that it envelops in itself. How must it be in order to say that? Which manner of Being does this imply? You seek the enveloped modes of existence, and not the transcendent values. It is the operation of immanence. (...)

The point of view of an ethics is: of what are you capable, what can you do? Hence a return to this sort of cry of Spinoza’s: what can a body do? We never know in advance what a body can do. We never know how we’re organized and how the modes of existence are enveloped in somebody.

Spinoza explains very well such and such a body, it is never whatever body, it is what you can do, you.

My hypothesis is that the discourse of ethics has two characteristics: it tells us that beings (étants) have a quantitative distinction of more and less, and in addition, it also tells us that the modes of existence have a qualitative polarity, roughly, there are two great modes of existence. What are they?

When it is suggested to us that, between you and me, between two persons, between a person and an animal, between an animal and a thing, there is ethically, that is ontologically, only a quantitative distinction, what quantity is involved? When it is suggested to us that what makes the most profound of our singularities is something quantitative, what does that really mean? Fichte and Schelling developed a very interesting theory of individuation that we sum up under the name quantitative individuation. If things are individuated quantitatively, we vaguely understand. What quantity? It is a matter of defining people, things, animals, anything by what each one can do.

People, things, animals distinguish themselves by what they can do, i.e. they can't do the same thing. What is it that I can do? Never would a moralist define man by what he can do, a moralist defines man by what he is, by what he is by right. So, a moralist defines man as a reasonable animal. It is essence. Spinoza never defines man as a reasonable animal, he defines man by what he can do, body and soul. If I say that reasonable‚ is not the essence of man, but it is something that man can do, it changes so that unreasonable is also something that man can do. To be mad is also a part of the power (pouvoir) of man. At the level of an animal, we see the problem clearly. If you take what is called natural history, it has its foundation in Aristotle. It defines the animal by what the animal is. In its fundamental ambition, it is a matter of what the animal is. What is a vertebrate, what is a fish, and Aristotle’s natural history is full of this search for the essence. In what is called the animal classifications, one will define the animal above all, whenever possible, by its essence, i.e. by what it is. Imagine these sorts who arrive and who proceed completely otherwise: they are interested in what the thing or the animal can do. They are going to make a kind of register of the powers (pouvoirs) of the animal. Those there can fly, this here eats grass, that other eats meat. The alimentary regime, you sense that it is about the modes of existence. An inanimate thing too, what can it do, the diamond, what can it do? That is, of what tests is it capable? What does it support? What does it do? A camel can go without drinking for a long time. It is a passion of the camel. We define things by what they can do, it opens up forms of experimentation. It is a whole exploration of things, it doesn't have anything to do with essence. It is necessary to see people as small packets of power (pouvoir). I am making a kind of description of what people can do.

From the point of view of an ethics, all that exists, all beings (étants) are related to a quantitative scale which is that of power (puissance). They have more or less power. This differentiable quantity is power. The ethical discourse will not cease to speak to us, not of essences, it doesn’t believe in essences, it speaks to us only of power (puissance), that is, the actions and passions of which something is capable. Not what the thing is, but what it is capable of supporting and capable of doing. And if there is no general essence, it is because, at this level of power (puissance), everything is singular. We don‚t know in advance even though the essence tells us what a set of things is. Ethics tells us nothing, it cannot know. One fish cannot do what the next fish can. There will thus be an infinite differentiation of the quantity of power (puissance) according to what exists. Things receive a quantitative distinction because they are related to the scale of power (puissance).

When, well after Spinoza, Nietzsche will launch the concept of will to power (volonté de puissance), I am not saying that he intends to say this, but above all, it means this. And we cannot understand anything in Nietzsche if we believe that it is the operation by which each of us would tend towards power (puissance). Power is not what I want, by definition, it is what I have. I have this or that power and it is this that situates me in the quantitative scale of Beings. Making power the object of the will is a misunderstanding, it is just the opposite. It is according to power that I have, that I want this or that. The will to power means that you will define things, men, animals according to the effective power that they have. Once again, it is the question: What can a body do? This is very different from the moral question: What must you do by virtue of your essence? It is: What can you do, you, by virtue of your power (puissance)? There you have it, therefore, that power (puissance) constitutes the quantitative scale of Beings. It is the quantity of power (puissance) which distinguishes one existing thing (éxistant) from another existing thing (éxistant).

Spinoza very often said that essence is power (

puissance

). Understand the philosophical coup that he is in the process of making.

Cours Vincennes - 13/01/1981

…we find ourselves faced with Blyenbergh’s two objections. The first concerns the point of view of nature in general. It comes down to saying to Spinoza that it’s very nice to explain that every time a body encounters another there are relations that combine and relations that decompose, sometimes to the advantage of one of the two bodies, sometimes to the advantage of the other body. But nature itself combines all the relations at once. Thus in nature in general what doesn’t stop is the fact that all the time there are compositions and decompositions of relations, all the time since, ultimately, the decompositions are like the other side of the compositions. But there is no reason to privilege the composition of relations over the decomposition since the two always go together.

For example: I eat. I compose the relation with the food I absorb. But this is done by decomposing the food’s own relations. Another example: I am poisoned. Arsenic decomposes my relation, okay, but it composes its own relation with the new relations into which the parts of my body enter under the action of the arsenic. Thus there is always composition and decomposition at once. Thus nature, says Blyenbergh, nature such as you conceive it is nothing but an immense chaos.

Under the objection Spinoza wavers.

Spinoza sees no difficulty and his reply is very clear. He says that it is not so for a simple reason: it’s that from the point of view of the whole of nature, one cannot say that there is composition and decomposition at once since, from the point of view of the whole of nature, there are only compositions. There are only compositions of relations. It’s really from the point of view of our understanding [entendement] that we say that such and such relations combine to the detriment of another such relation, which must decompose so that the two others can combine. But it’s because we isolate a part of Nature. From the point of view of the complete whole of Nature, there is never anything but relations that combine with each other. I like this reply very much: the decomposition of relations does not exist from the point of view of the whole of nature since the whole of nature embraces all relations. Thus there are inevitably compositions, and that is all [un point c'est tout].

This very simple, very clear, very beautiful reply sets up another difficulty. It refers to Blyenbergh’s second objection. Let us suppose, at the limit, that he concedes the point on the problem of the whole of nature, so then let’s approach the other aspect, a particular point of view, my particular point of view, that is to say the point of view of a precise and fixed relation. Actually, what I call ME [Moi] is a set of precise and fixed relations which constitute me. From this point of view, and it’s solely from a particular, determinable point of view, you or me, that I can say that there are compositions and decompositions.

I would say that there is composition when my relation is conserved and combined with another, external relation, but I would say that there is decomposition when the external body acts on me in such a manner that one of my relations, or even many of my relations, is destroyed, that is, ceases to be carried out [effectuŽs] by the current parts. Just as from the point of view of nature I was able to say that there are only compositions of relations, as soon as I take a particular determined point of view, I must say that there are decompositions which are not to be confused with compositions. Hence Blyenbergh’s objection, which consists in saying that ultimately what you call vice and virtue is whatever suits [arrange] you. You will call it virtue every time you compose relations, no matter what relations you destroy, and you will call it vice every time that one of your relations is decomposed. In other words you will call virtue whatever is agreeable to you and vice whatever is not agreeable to you. This comes down to saying that food is agreeable to you and poison is not agreeable to you. But when we speak generally of vice and virtue, we appeal to something other than such a criterion of taste, that is, what suits me and what doesn’t suit me. This objection is distinct from the preceding one because it is made in the name of a particular point of view and no longer in the name of the whole of nature. And it is summarized in this line that Blyenbergh constantly repeats: you reduce morality to a matter of taste.

Spinoza is going to throw himself into an endeavor to show that he preserves an objective criterion for the distinction of the good from the bad, or of virtue from vice. He’s going to attempt to show that Spinozism offers us a properly ethical criterion of the good and the bad, of vice and virtue, and that this criterion is not a simple criterion of taste according to what suits me or doesn’t suit me. He is going to try to show that, from a particular point of view, he doesn’t confuse vice and virtue with what suits me. He is going to show it in two texts which, to my knowledge, are Spinoza’s strangest, to the point that the one seems incomprehensible and the other is perhaps comprehensible but seems very bizarre. In the end, everything is resolved in a marvelously lucid way.

The first is in the letters to Blyenbergh (letter 23). He wants to show that not only does he have a criterion for distinguising vice from virtue, but that this criterion applies in cases that appear very complicated, and that further it is a criterion of distinction, not only for distinguishing vice from virtue, but if one comprehends this criterion well, one can make distinctions in cases of crime.

I’ll read this text:

"Nero’s matricide, insofar as it contained anything positive, was not a crime." You see what Spinoza means. Evil isn’t anything. Thus insofar as an act is positive it cannot be a crime, it cannot be evil. Therefore an act as a crime, if it is a crime, it’s not so insofar as it contains something positive, it’s from another point of view. Very well, we can comprehend it abstractly. "Nero killed his mother. Orestes also killed his mother. Orestes was able to accomplish an act which, externally, is the same, and at the same time intended to kill his mother, without deserving the same accusation as Nero." Actually, we treat Orestes in a different way than we treat Nero, even though both of them killed their mothers intentionally. "What, therefore, is Nero’s crime? It consists solely in the fact that, in his act, Nero showed himself to be ungrateful, unmerciful and disobedient." The act is the same, the intention is the same, there is a difference at the level of what? It’s a third determination. Spinoza concludes, "none of these characteristics expresses anything to do with an essence."

Ungrateful, unmerciful, none of these characteristics expresses anything to do with an essence. One doesn’t know what to think. Is this a reply to Blyenbergh? What can one get out of a text of this sort? Ungrateful, unmerciful and disobedient. So then if Nero’s act is bad, it’s not because he killed his mother, it’s not because he intended to kill her, it’s because Nero, in killing his mother, showed himself to be ungrateful, unmerciful and disobedient. Orestes kills his mother but is neither ungrateful nor disobedient. So one keeps searching. One comes across Book IV of The Ethics, and one comes across a text which doesn’t appear to have anything to do with the previous one. One gets the impression that Spinoza has acquired a kind of diabolical humor or has gone mad. Book IV, proposition 59, scholium:

The text of the proposition already does not appear simple. It involves demonstrating, for Spinoza, that all the actions to which we are determined from a feeling which is a passion, we can be determined to do them without it (without the feeling), we can be determined to do them by reason. Everything that we do when pushed by passion, we can do when pushed by pure reason.

Then comes the scholium:

"These things are more clearly explained by an example. The act of beating, insofar as it is considered physically, and insofar as we attend only to the fact that the man raises his arm, closes his fist, and moves his whole arm forcefully up and down, is a virtue, which is conceived from the structure of the human body." He does not cheat with the word virtue, it’s an exercise [effectuation] of the power of the body, it’s what my body can do, it’s one of the things it can do. This makes it part of the potentiae of the human body, of this power [puissance] in action, it’s an act of power, and for that very reason this is what we call virtue. "Therefore, if a man moved by anger or hate (i.e. by a passion) is determined (determined by the passion) to close his fist or move his arm, that, as we have shown in Part II, happens because one and the same action can be associated with any images of things whatever." Spinoza is in the process of telling us something very strange. He is in the process of telling us that he calls the determination of the action association, the link that unites the image of the action with an image of a thing. That is the determination of the action. The determination of the action is the image of a thing to which the image of the act is linked. It’s truly a relation that he himself presents as being a relation of association: one and the same action can be associated with any image of a thing whatever.

The citation from Spinoza continues: "And so we can be determined to one and the same action both from those images of things which we conceive confusedly and from those images of things we conceive clearly and distinctly. It is evident, therefore, that every desire which arises from a feeling which is a passion would be of no use if men could be guided by reason."

That is to say that all the actions that we do determined by passions, we could just as well do determined by pure reason.

What is this introduction of the confused and the distinct? There it is, what I recall from the text and it’s in the text to the letter. He says that an image of action can be associated with images of very different things. Consequently the same action can be associated just as well with images of confused things as with images of clear and distinct things.

So I bring my fist down on my mother’s head. There’s one case. And with the same violence I bring my fist down on the head [membrane] of a bass drum. It’s not the same gesture. But Spinoza suppressed [supprimŽe] this objection. He replied to it in advance. Actually, Spinoza posed the problem in conditions such that this objection could not be valid. In effect, he asks us to consent to an extremely paradoxical analysis of action as follows: between the action and the object on which it bears there is a relation which is a relation of association. Indeed, if, between the action and the object on which it bears, the relation is associative, if it’s a relation of association, then Spinoza is quite right. That is, it’s clearly the same action, whatever the variants might be, which in one case is associated with my mother’s head and in the other case is associated with a bass drum. Thus the objection is suppressed.

What difference is there between these two cases? One senses what Spinoza means and what he means is not nothing. Let’s return to the criterion we’re sure of: what bad is there when I do this thing that is an exercise [effectuation] of the power of my body and which, in this sense, is good? I do that, I simply give someone a blow on the head. What is bad: that I decompose a relation, namely my mother’s head. In beating like that on my mother’s head I destroy the constituent relation of the head: my mother dies or passes out under the blow. In Spinozist terms, I would say that in this case I associate my action with the image of a thing whose relation is directly decomposed by this action. I associate the image of the act with the image of something whose constituent relation is decomposed by this act.

When I bring my fist down on a bass drum? The drumhead is defined how? The tension of the head will also be defined by a certain relation. But in this case here, if the power of a head is to produce harmonics, here I’ve associated my action with the image of something whose relation combines directly with this action. That is, I have drawn harmonics out of the drumhead.

What’s the difference? It’s enormous. In one case I associated my action, once again, the image of a thing whose relation combines directly with the relation of my act, and in the other case, I associated my act with the image of a thing whose relation is immediately and directly decomposed by my act. You grasp the criterion of The Ethics for Spinoza. It’s a very modest criterion, but here, Spinoza gives us a rule. He liked the decompositions of relations very much, he adored the battles of spiders, that made him laugh. Imagine your everyday actions: there are a certain number of them which are characterized as being associated with an image of a thing or being which combines directly with the action, and others which, on the contrary (a type of action), are associated with images of things whose relation is decomposed by the action.

So by convention the actions of direct composition will be called GOOD and the actions of direct decomposition will be called BAD.

We are still floundering among many problems. First problem: what is there in the text of The Ethics that can cast a glimmer of light for us on the text of the letter, the difference between Orestes and Nero. In the letter, it involves two actions which are both crimes. Why is what Nero did something bad, while according to Spinoza one can’t even say that Orestes, in killing his mother, has done something bad? How can one say such a thing? One can say such a thing according to the following: we now have the method of the analysis of action according to Spinoza. Every action will be analyzed along two dimensions: the image of the act as power of the body, what a body can do, and the image of the associated thing, that is to say the object on which the act bears. Between the two there is a relation of association. It’s a logic of action.

Nero kills his mother. In killing his mother, Nero associated his act directly with the image of a being whose relation would be decomposed by this act: he killed his mother. Thus the relation of primary, direct association is between the act and an image of a thing whose relation is decomposed by this act.

Orestes kills his mother because she killed Agamemnon, that is to say because she killed Orestes’ father. In killing his mother, Orestes pursues a sacred vengeance. Spinoza does not say vengeance. According to Spinoza, Orestes associates his act, not with the image of Clytemnestra whose relation will be decomposed by this act, but rather he associates it with the relation of Agamemnon which was decomposed by Clytemnestra. In killing his mother, Orestes recomposes his relation with the relation of his father.

Spinoza is in the process of telling us that, okay, at the level of a particular point of view, you or me, there is always composition and decomposition of relations at once; does that mean that the good and the bad are mixed up and become indiscernible? No, replies Spinoza, because at the level of a logic of the particular point of view there will always be a priority [primat]. Sometimes the composition of relations will be direct and the decomposition indirect, and sometimes, on the contrary, the decomposition willl be direct and the composition indirect. Spinoza tells us: I call good an action that implements [opre] a direct composition of relations even if it implements an indirect decomposition, and I call bad an action that implements a direct decomposition even if it implements an indirect composition. In other words there are two types of actions: actions in which the decomposition comes about as if in consequence and not in principle, because the principle is a composition - and this has value only for my point of view, because from the point of view of nature everything is composition and it’s for that reason that God knows neither evil nor the bad - and inversely there are actions which directly decompose and imply compositions only indirectly. This, then, is the criterion of the good and the bad and it’s with this that it’s necessary to live. Spinoza is an author who, whenever he encounters the problem of a symbolic dimension, continually expunges it, hunts it down, and tries to show that it was a confused idea of the worst imagination. Prophetism is the act by which I receive a sign and by which I emit signs. There is clearly a theory of the sign in Spinoza, which consists in relating the sign to the most confused understanding and imagination in the world, and in the world such as it is, according to Spinoza, the idea of the sign does not exist. There are expressions, there are never signs. When God reveals to Adam that the apple will act as a poison, he reveals to him a composition of relations, he reveals to him a physical truth and he doesn’t send him a sign at all. It’s only to the extent that one comprehends nothing of the substance-mode relation that one invokes signs. Spinoza says a thousand times that God makes no signs, he gives expressions. He does not give a sign which would refer to a signification or a signifier (a crazy notion for Spinoza), he expresses himself, that is to say he reveals his relations. And revealing is neither mystical nor symbolic. Revealing is giving something to comprehend. He gives relations to comprehend in the understanding of God. The apple falls, it’s a revelation of God, it’s a composition of relations… If there is an order of filiations in Spinoza, it’s obviously not a symbolic order, it’s an order that, step by step, makes up Nature, and Nature is an individual, an individual which encompasses all individuals, there is an order of compositions of relations and it’s quite necessary that all the relations be carried out [effectuŽs]. The necessity of Nature is that there will not be relations that are not carried out. Everything possible is necessary, which means that all relations have been or will be carried out.

Spinoza wouldn’t do the Eternal Return, the same relation will not be executed [executŽ] twice. There is an infinity of relations, the whole of Nature is the totality of executions [effectuations] of all possible, and thus necessary, relations. That is identity in Spinoza, the absolute identity of the possible and the necessary. On prophetism, Spinoza says something very simple which will be taken up again by Nietzsche, by all those authors of whom one can say that they are, in this sense, those who have pushed positivism as far as possible. Here, broadly speaking, is the idea that they get: okay, there are laws. These laws are laws of Nature and thus when one speaks of divine revelation there is nothing mysterious. Divine revelation is the exposition of laws. Spinoza calls a law a composition of relations. This is what will be called a law of nature. When one is very restricted one cannot comprehend laws as laws. How does one comprehend them? 2 + 2 = 4 is a composition of relations. You have the relation two plus two, you have the relation four, and you have the relation of identity between the relation two plus two and the relation four. If you comprehend nothing, you hear this law as an order, or as a commandment. The little child at school comprehends the law of nature as a moral law: it is necessary that it be so, and if he says something else he will be punished. It proceeds like that according to our restricted understanding. If we were to grasp the laws as what they are, as physical compositions of relations, compositions of bodies, then notions as strange as command and obedience would remain completely unknown to us. It’s to the extent that we perceive a law that we don’t comprehend that we apprehend it as an order; God forbade absolutely nothing, Spinoza explains on the subject of Adam. He revealed a law to him, namely that the apple combines with a relation that excludes my constituent relation. Therefore it’s a law of nature. It’s exactly like arsenic. Adam comprehends nothing of any of this, and instead of grasping it as a law, he grasps it as one of God’s prohibitions. So when I grasp things under the form command-obedience, instead of grasping them as compositions of relations, at that very moment I start saying that God is like a father, I demand a sign. The prophet is someone who, not grasping the laws of nature, will just ask for the sign that guarantees to him that the order is just.

If I comprehend nothing in the law, I demand on the other hand a sign in order to be sure that what I am ordained to do is really what I am ordained to do. The first reaction of the prophet is: God, give me a sign that it is really you who speaks to me. Later, when the prophet has the sign, he is going to emit signs. This will be the language of signs.

Spinoza is a positivist because he opposes expression to the sign: God expresses, the modes express, the attributes express. Why? In logical language, one would say that the sign is always equivocal, there is an equivocity of the sign, that is to say that the sign signifies, but it signifies in several senses. In contrast, expression is uniquely and completely univocal: there is only one single sense of the expression, and that is the sense following which the relations combine.

According to Spinoza, God proceeds by expression and never by sign. The true language is that of expression. The language of expression is that of the composition of relations to infinity. All that Spinoza will consent to is the fact that, because we are not philosophers, because our understanding is restricted, we always have need of certain signs. Signs are a vital necessity because we comprehend only a very few of the things in the world. That’s the way Spinoza justifies society. Society is the institution [instauration] of the minimum of signs indispensible to life. Of course, there are relations of obedience and command, if one has knowledge [connaissance] there is no need to obey or command. But it happens that one has a very limited knowledge, thus all one can ask of those who command and obey is not to meddle with knowledge. So all obedience and command bearing on knowledge is null and void. Which Spinoza expresses on a very beautiful page of the Theological-Political Treatise, namely that there is only one absolutely inalienable freedom, and that is the freedom of thought. If there is a symbolic domain, it is that of order, command and obedience. It is the domain of signs. The domain of knowledge is the domain of relations, that is to say of univocal expressions.

Cours Vincennes - 20/01/1981

ternity, instantaneity, duration.

affectio

and

affectus

affection and affect.

Duration. Theory of the affects.

Blyenbergh, the Ethics

Sadness and joy. Hate. Power (puissance).

The spheres of belonging.

The unlimited, the infinite.

Bleyenbergh: Composition and decomposition of relations

Spinoza’s example in the letters to Blyenbergh: I am led by a basely sensual appetite or else, the other case: I feel a true love. What are these two cases? It is necessary to try to understand them according to the criteria that Spinoza gives us. A basely sensual appetite, even the mere expression, one feels that it is not good, that it is bad. It is bad in what sense? When I am led by a basely sensual appetite, what does that mean? It means that: within it there is an action, or a tendency to action: for example desire. What happens to the desire when am I led by a basely sensual appetite? It is the desire of. Good. What is this desire? It can only be qualified by its association with an image of a thing, for example I desire a bad woman.

Richard Pinhas: several! [Bursts of general laughter]) or even worse, even worse: several!

Gilles Deleuze : Yes. What does it mean? We saw a bit of it when he suggested the difference between adultery, all that. Forget the ridiculous aspect of the examples, but they are not ridiculous, they are examples! In this case, what he calls basely sensual, basely sensual appetite, the basely sensual consists in this, that the action, in all manners, even for example making love, the action is a virtue! Why? Because it is something that my body can do; don't ever forget the theme of power (puissance). It is in my body’s power. So it is a virtue, and in this sense it is the expression of a power.

But if I remained there with it, I would have no means of distinguishing the basely sensual appetite from the most beautiful of loves. But there it is, when there is basely sensual appetite, why is it? It is because, in fact, I associate my action, or the image of my action, with the image of a thing whose relation is decomposed by this action. In several different ways, in all ways, for example if I am married, in the very example that Spinoza took, I decompose a relation, the relation of the couple. Or if the other person is married, I decompose the relation of the couple. But what’s more, in a basely sensual appetite I decompose all sorts of relations: the basely sensual appetite with its taste for destruction, good we can take everything up again on the decompositions of relations, a kind of fascination of the decomposition of relations, of the destruction of relations. On the contrary in the most beautiful of loves. Notice that there, I don't invoke the mind at all, it would not be Spinozist, according to parallelism. I invoke a love in the case of the most beautiful of loves, a love which is not less bodily than the most basely sensual love. The difference is, simply, that in the most beautiful of loves, my action, the same, exactly the same, my physical action, my bodily action, is associated with an image of the thing whose relation is directly combined, directly composed with the relation of my action. It is in this sense that the two uniting individuals lovingly form an individual which has both of them as parts, Spinoza would say. On the contrary, in the basely sensual love, the one destroys the other, the other destroys the one, that is there is a whole process of decomposition of relations. In short, they make love like they are knocking each other about.

All this is very concrete. So it works.

Only we always come up against this, Spinoza tells us: you don't choose, in the end, the image of the thing with which your action is associated. It engages a whole play of causes and of effects which escape you. Indeed, what is it that makes this basely sensual love take you? You cannot say to yourself: Ha! I could do otherwise. Spinoza is not one of those who believes in a free will. No, it is a whole determinism which associates the images of things with the actions. Then what’s more troubling, the formula: I am as perfect as I can be according to the affections that I have. That is to say that if I am dominated by a basely sensual appetite, I am as perfect as I can be, as perfect as it is possible, as perfect as it is in my power (pouvoir) to be.

And could I say: I am deprived of (manque) a better state? Spinoza seems very firm. In the letters to Blyenbergh he says: I cannot say that I am deprived of a better state, I cannot even say it. Because it doesn't make any sense. To say at the moment when I experience a basely sensual appetite ˜ once again, you will see in the text, if you haven't already seen it, this example which returns ˜ because Blyenbergh clings there to this example. Indeed it is very simple, it is very clear. When I say, at the moment when I experience a basely sensual appetite, when I say: Ha! I am deprived of true love, if I say it, what does that mean to say: I am deprived of something? Literally it doesn't mean anything, absolutely nothing in Spinoza, but nothing! It merely means that my mind compares a state that I have to a state that I don't have, in other words it is not a real relation, it is a comparison of the mind. A pure comparison of the mind. And Spinoza goes so far as to say: you might as well say at that moment there that the stone is deprived of sight. You might as well say at that moment there that the stone is deprived of sight. Indeed, why wouldn‚t I compare the stone to a human organism, and in the name of a same comparison of the mind, I would say: the stone doesn't see, therefore it is deprived of sight. And Spinoza said expressly ˜ I am not looking for the texts because you are reading them, I hope ˜ Spinoza responds expressly to Blyenbergh: it is just as stupid to speak of the stone by saying of it that it is deprived of sight as it would be stupid, at the moment when I experience a basely sensual appetite, to say that I am deprived of a better love.

So then, at this level, we listen to Spinoza, and we tell ourselves that there is something which doesn't work, because in his comparison, I take the two judgments, I say of the stone: it can't see, it is deprived of sight, and I say of someone who experiences a basely sensual appetite that they are deprived of virtue. Are these two propositions, as Spinoza claims, of the same type? It is so apparent that they are not the same, that we can be confident that if Spinoza says to us that they are of the same type, it is because he wants to be provocative. He wants to say to us: I challenge you to tell me the difference between the two propositions. But one feels the difference. Spinoza‚s provocation is going to allow us perhaps to find it. In the two cases, for the two propositions, is the stone (pierre) deprived of sight, or is Pierre ˜ the name this time ˜ deprived of virtue, is the comparison of the mind between two states, a state that I have and a state that I don't have, is the comparison of the mind of the same type? Evidently not! Why? To say that the stone is deprived of sight is, on the whole, to say that nothing in it contains the possibility of seeing. While, when I say: he is deprived of true love, it is not a comparison of the same type, since, this time, I don’t rule out that at other moments this being here has experienced something which resembled true love.

In other words, the question specifies, I will go very slowly, even if you have the impression that all this goes without saying: is a comparison within the same being analogous to a comparison between two beings? Spinoza doesn't back away from the problem, he takes the case of the blind man, and he says to us quietly ˜ but once again, what does he have in mind in saying things like this to us, which are so obviously inaccurate ˜ he says to us: the blind man is deprived of nothing! Why? He is as perfect as he can be according to the affections that he has. He is deprived of (privé de) visual images, to be blind is to be deprived of visual images; that means that he doesn’t see, but neither does the stone see. And he says: there is no difference between the blind man and the stone from this point of view, namely: the one like the other doesn't have visual images. So it is just as stupid, says Spinoza, it is just as stupid to say that the blind man is deprived of sight as it is to say: the stone is deprived of sight. And the blind man, then? He is as perfect as he can be, according to what? You see even so, Spinoza doesn't say to us: according to his power (puissance); he says that the blind man is as perfect as he can be according to the affections of his power, that is according to the images of which he is capable. According to the images of things of which he is capable, which are the true affections of his power. So it would be entirely the same thing as saying: the stone doesn't have sight, and to say: the blind man doesn't have sight.

Pure instantaneity of essence Blyenbergh begins here to understand something. He begins to understand. However, Spinoza Why does he make this kind of provocation? And, Blyenbergh [X] once again it appears to me a typical example of the point at which the commentators are mistaken, it seems to me, by saying that Blyenbergh is stupid, because Blyenbergh doesn't get Spinoza wrong. Blyenbergh answers Spinoza immediately by saying: all that is very pretty but you can only manage it if you insist upon (he didn't say it in this form, but you will see, the text really comes down to the same thing) a kind of pure instantaneity of the essence. It is interesting as an objection, it is a good objection. Blyenbergh retorts: you cannot assimilate the blind man not seeing and the stone not seeing, you can only make such an assimilation if, at the same time, you pose a kind of pure instantaneity of the essence, namely: there belongs to an essence only the present, instantaneous affection that it experiences insofar as it experiences it. The objection here is very very strong. If indeed I am saying: there belongs to my essence only the affection that I experience here and now, then, indeed, I am not deprived of anything. If I am blind I am not deprived of sight, if I am dominated by a basely sensual appetite, I am not deprived of better love. I am not deprived of anything. There belongs to my essence, indeed, only the affection that I experience here and now. And Spinoza answers quietly: yes, that’s the way it is.

This is curious. What is curious? That it is the same man who never stops telling us that the essence is eternal. The singular essences, that is yours, mine, all the essences are eternal. Notice that it is a way of saying that the essence doesn't endure. Now as a matter of fact there are two ways of not enduring, at first sight: the way of eternity or the way of instantaneity. Now it is very curious how slyly he passes from one to the other. He began by telling us: the essences are eternal, and now he tells us: the essences are instantaneous. If you like, it becomes a very bizarre position. To the letter of the text: the essences are eternal, but those things which belongs to the essence are instantaneous; there belongs to my essence only what I experience actually insofar as I experience it actually. And indeed, the formula: I am as perfect as I can be according to the affection which determines my essence‚ implies this strict instantaneity.

That is pretty much the high point of the correspondence, because a very curious thing is going to happen. Spinoza responds to this very violently because he increasingly loses patience with this correspondence. Blyenbergh protests here, he says: but in the end, you cannot define the essence by instantaneity, what does this mean? Then it is a pure instantaneity? Sometimes you have a basely sensual appetite, sometimes you have a better love, and you will say each time that you are as perfect as you can be, there as in a series of flashes! In other words Blyenbergh says to him: you cannot expel the phenomenon of duration. There is a duration, and it is precisely according to this duration that you can become better, there is a becoming, and it is according to this duration that you can become better or worse. When you experience a basely sensual appetite it is not a pure instantaneity which comes over you. It is necessary to take it in terms of duration, that is: you become worse than you were before. And when a better love forms in you, of course you become better. There is an irreducibility of duration. In other words the essence cannot be measured in its instantaneous states.

Now this is curious because Spinoza stops the correspondence. On this point no response from Spinoza. And at just the same time Blyenbergh does something imprudent, that is sensing that he‚s posed an important question to Spinoza, he starts to pose all sorts of questions, he thinks he has caught Spinoza out, and Spinoza tells him to back off. He says to him let go of me a while, leave me in peace‚. He cuts the correspondence short, he stops, he won't answer anymore.

All of this is very dramatic because it can be said: Aha! Then he didn't have anything to respond If he had to respond because the response that Spinoza could have made, and we are certainly forced to conclude that he could have made it, therefore if he didn't make it, it is because he did not want to, the response is all in the Ethics. Therefore just as on certain points the correspondence with Blyenbergh goes farther than the Ethics, on other points, and for a simple reason I think, which is that Spinoza above all doesn't want to give Blyenbergh, for reasons which are his own, he above all doesn't want to give Blyenbergh the idea of what this book is, this book of which everyone is speaking at the time, that Spinoza experiences the need to hide because he feels that he has a lot to fear. He doesn't want to give Blyenbergh, whom he feels to be an enemy, he doesn't want to give him an idea of what the Ethics is. So he stops the correspondence. We can consider in this respect that he has a response that he doesn't want to give. He says to himself: I will still have problems.

The sphere of belonging of essence But it is up to us to try to reconstitute this response. Spinoza knows very well that there is duration. You see that we are now in the process of playing with three terms: eternity, instantaneity, duration. What is instantaneity? We don’t yet know at all what eternity is in Spinoza, but eternity is the modality of essence. It is the modality which belongs to essence. Let’s suppose that the essence is eternal, that is that it is not subject to time. What does this mean? We don’t know.

What is instantaneity? Instantaneity is the modality of affection of essence. Formula: I am always as perfect as I can be according to the affections that I have here and now. Therefore affection is actually an instantaneous cut. In effect it is the species of horizontal relation between an action and an image of a thing. Third dimension, it is as if we were in the process of constituting the three dimensions of what we could call the sphere. Here I take a word, which is not at all Spinozist, but I take a word which allows us to regroup this, a Husserlian word, the sphere of belonging of the essence: the essence is what belongs to it. I believe that Spinoza would say that this sphere of belonging of the essence has three dimensions. There is the essence itself, eternal; there are the affections of the essence here and now which are like so many instants, that is, what affects me at this moment; and then there is what?

It is found, and here, the terminology is important, Spinoza rigorously distinguishes betweenaffectio and affectus. It is complicated because there are a lot of translators who translate affectio by affection‚, all of the translators translate affectio by affection‚ that, that works, but there are lots of translators who translate affectus by feeling. On the one hand this doesn’t say much, in French, the difference between affection and feeling, and on the other hand it is a shame, even a slightly more barbaric word would be better, but it would be better, it seems to me, to translate affectus by affect, since the word exists in French; this retains at least the same root common to affectio and to affect. Therefore Spinoza, if only by his terminology, distinguishes well between the affectio and the affectus, the affection and the affect.

Affection envelops an affect What is it, the affect‚? Spinoza tells us that it is something that the affection envelops. The affection envelops an affect. You recall, the affection is the effect ˜ literally if you want to give it an absolutely rigorous definition ˜ it is the instantaneous effect of an image of a thing on me. For example perceptions are affections. The image of things associated with my action is an affection. The affection envelops, implicates, all of these are the words Spinoza constantly uses. To envelope: it is necessary to really take them as material metaphors, that is that within the affection there is an affect. There is a difference in nature between the affect and the affection. The affect is not something dependent on the affection, it is enveloped by the affection, that’s something else. There is a difference in nature between the affect and the affection. What does my affection, that is the image of the thing and the effect of this image on me, what does it envelop? It envelops a passage or a transition. Only it is necessary to take passage or transition in a very strong sense. Why?

Duration is the passage, the lived transition You see, it means: it is something other than a comparison of mind, here we are no longer in the domain of a comparison of mind. It is not a comparison of the mind in two states, it is a passage or transition enveloped by the affection, by every affection. Every instantaneous affection envelops a passage or transition. Transition, to what? Passage, to what? Once again, not at all a comparison of the mind, I must add in order to go more slowly: a lived passage, a lived transition, which obviously doesn’t mean conscious. Every state implicates a lived passage or transition. Passage from what to what, between what and what? More precisely, so close are the two moments of time, the two instants that I consider instant A and instant A‚, that there is a passage from the preceding (antérieur) state to the current (actuel) state. The passage from the preceding state to the current state differs in nature with the preceding state and with the current state. There is a specificity of the transition, and it is precisely this that we call duration and that Spinoza calls duration. Duration is the lived passage, the lived transition. What is duration? Never anything but the passage from one thing to another, it suffices to add, insofar as it is lived.

When, centuries later, Bergson will make duration into a philosophical concept, it will obviously be with wholly different influences. It will be according to itself above all, it will not be under the influence of Spinoza. Nevertheless, I am just pointing out that the Bergsonian use of duration coincides strictly. When Bergson tries to make us understand what he calls duration‚, he says: you can consider psychic states as close together as you want in time, you can consider the state A and the state A‚ as separated by a minute, but just as well by a second, by a thousandth of a second, that is you can make more and more cuts, increasingly tight, increasingly close to one another. You may well go to the infinite, says Bergson, in your decomposition of time, by establishing cuts with increasing rapidity, but you will only ever reach states. And he adds that the states are always of space. The cuts are always spatial. And you will have brought your cuts together very well, you will let something necessarily escape, it is the passage from one cut to another, however small it may be. Now, what does he call duration, at its simplest? It is the passage from one cut to another, it is the passage from one state to another. The passage from one state to another is not a state, you will tell me that all of this is not strong, but it is a really profound statute of living. For how can we speak of the passage, the passage from one state to another, without making it a state? This is going to pose problems of expression, of style, of movement, it is going to pose all sorts of problems. Yet duration is that, it is the lived passage from one state to another insofar as it is irreducible to one state as to the other, insofar as it is irreducible to any state. This is what happens between two cuts.

In one sense duration is always behind our backs, it is at our backs that it happens. It is between two blinks of the eye. If you want an approximation of duration: I look at someone, I look at someone, duration is neither here nor there. Duration is: what has happened between the two? Even if I would have gone as quickly as I would like, duration goes even more quickly, by definition, as if it was affected by a variable coefficient of speed: as quickly as I go, my duration goes more quickly. However quickly I pass from one state to another, the passage is irreducible to the two states. It is this that every affection envelops. I would say: every affection envelops the passage by which we arrive at it. Or equally well: every affection envelops the passage by which we arrive at it, and by which we leave it, towards another affection, however close the two affections considered are. So in order to make my line complete it would be necessary for me to make a line of three times: A, A,' A"; A is the instantaneous affection, of the present moment, A' is that of a little while ago, A" is what is going to come. Even though I have brought them together as close as possible, there is always something which separates them, namely the phenomenon of passage. This phenomenon of passage, insofar as it is a lived phenomenon, is duration: this is the third member of the essence.

I therefore have a slightly stricter definition of the affect, the affect: what every affection envelops, and which nevertheless is of another nature is the passage, it is the lived passage from the preceding state to the current state, or of the current state to the following state. Good. If you understand all that, for the moment we‚re doing a kind of decomposition of the three dimensions of the essence, of the three members of the essence. The essence belongs to itself under the form of the eternity, the affection belongs to the essence under the form of instantaneity, the affect belongs to the essence under the form of duration.

Affect, increase and decrease of power Now the passage is what? What could a passage be? It is necessary to leave the too spatial idea. Every passage Spinoza tells us, and this is going to be the basis of his theory of affectus, of his theory of the affect, every passage is ˜ here he doesn't say implicates‚, understand that the words are very very important ˜ he will tell us of the affection that it implicates an affect, every affection implicates, envelops, but the enveloped and the enveloping just don't have the same nature. Every affection, that is every determinable state at a single moment, envelops an affect, a passage. But the passage, I don't ask what it envelops, it is enveloped; I ask of what does it consist, what is it? And my response from Spinoza, is it obvious what it is? It is increase and decrease of my power (puissance). It is increase or decrease of my power, even infinitesimally. I take two cases: I am in a dark room ˜ I‚m developing all of this, it is perhaps useless, I don't know, but it is to persuade you that when you read a philosophical text it is necessary that you have the most ordinary situations in your head, the most everyday ones. You are in a dark room, you are as perfect, Spinoza will say: Let’s judge from the point of view of affections, you are as perfect as you can be according to the affections that you have. You don't have any, you don't have visual affections, that’s all. There, that’s all. But you are as perfect as you can be. All of a sudden someone enters and turns on the lights without warning: I am completely dazzled. Notice that I took the worse example for me. Then, no. I‚ll change it, I was wrong. I am in the dark, and someone arrives softly, all that, and turns on a light, this is going to be very complicated this example. You have your two states which could be very close together in time. The state that I call: dark state, and small b, the lighted state. They are very close together. I am saying: there is a passage from one to the other, so fast that it may even be unconscious, all that, to the point that your whole body, in Spinozist terms these are examples of bodies, your whole body has a kind of mobilization of itself, in order to adapt to this new state. The affect is what? It is the passage. The affection is the dark state and the lighted state. Two successive affections, in cuts. The passage is the lived transition from one to the other. Notice that in this case here there is no physical transition, there is a biological transition, it is your body which makes the transition.

Every affection is instantaneous What does this mean? The passage is necessarily an increase of power or a decrease of power. It is necessary to already understand and it is for this reason that all this is so concrete, it is not determined in advance. Suppose that in the dark you were in deep state of meditation. Your whole body was focused on this extreme meditation. You held something. The other brute arrives and turns on the light, if need be you lose an idea that you were going to have. You turn around, you are furious. We hold onto this because we will use the same example again. You hate him, even if not for long, but you hate him, you say to him: „Hey! Listen. In this case the passage to the lighted state will have brought you what? A decrease of power. Evidently if you had looked for your glasses in the dark, there they would have brought you an increase of power. The guy who turned the light on, you say to him: „Thank you very much, I love you. Good.

We’ve already said that, maybe this story of increase and decrease of power is going to play in quite variable directions and contexts. But, on the whole, there are directions. If we stick to you, one could say in general, without taking the context into account, if one increases the affections of which you are capable, there is an increase of power, if one decreases the affections of which you are capable there is a decrease of power. We can say this on the whole even knowing that it is not always like this. What do I mean? I mean something very simple: it is that every affection is instantaneous ˜ Spinoza, you see how he is very very curious, in virtue of his rigor he will say: every affection is instantaneous, and it is this that he responded to Blyenbergh, he didn't want to say more on it. One could not say that he distorted his thought, he only gave one sphere of it, he only gave a tip of it. Every affection is instantaneous, he will always say this, and he will always say: I am as perfect as I can be according to what I have in the instant. It is the sphere of belonging of the instantaneous essence. In this sense, there is neither good nor bad. But in return, the instantaneous state always envelopes an increase or a decrease of power, and in this sense there is good and bad. So much so that, not from the point of view of its state, but from the point of view of its passage, from the point of view of its duration, there is something bad in becoming blind, there is something good in becoming seeing, since it is either decrease of power or else increase of power. And here it is no longer the domain of a comparison of the mind between two states, it is the domain of the lived passage from one state to another, the lived passage in the affect. So much so that it seems to me that we can understand nothing of the Ethics, that is of the theory of the affects, if we don't keep very much in mind the opposition that Spinoza established between the comparisons between two states of the mind, and the lived passages from one state to another, lived passages that can only be lived in the affects. The affects are joy or sadness There remains for us quite a few things to understand. I would not say that the affects signal the decreases or increases of power, I would say that the affects are the decreases and the increases of lived power. Not necessarily conscious once again. It is I believe a very very profound conception of the affect. So Let’s give them names in order to better mark them. The affects which are increases of power we will call joys, the affects which are decreases of power we will call sadnesses. And the affects are either based on joy, or else based on sadness. Hence Spinoza‚s very rigorous definitions: sadness is the affect that corresponds to a decrease of power, of my power, joy is the affect which corresponds to an increase of my power. Sadness is a affect enveloped by an affection. The affection is what? It is an image of a thing which causes me sadness, which gives me sadness. You see, there we find everything, this terminology is very rigorous. I repeat. I don't know anymore what I‚ve said. The affect of sadness is enveloped by an affection, the affection is what, it is the image of a thing which gives me sadness, this image can be very imprecise, very confused, it matters little. There is my question: why does the image of a thing which gives me sadness, why does this image of a thing envelop a decrease of power (puissance) of acting? What is this thing which gives me sadness? We have at least all of the elements to respond to it, now everything is regrouped, if you have followed me everything must regroup harmoniously, very harmoniously. The thing which gives me sadness is the thing whose relations don't agree with mine. That is affection. All things whose relations tend to decompose one of my relations or the totality of my relations affect me with sadness. In terms of affectio you have there a strict correspondence, in terms of affectio, I would say: the thing has relations which are not composed with mine, and which tend to decompose mine. Here I am speaking in terms of affectio. In terms of affects I would say: this thing affects me with sadness, therefore by the same token], in the same way, decreases my power. You see I have the double language of instantaneous affections and of affects of passage. Hence I return as always to my question: why, but why, if one understood why, maybe one would understand everything. What happens? You see that he takes sadness in one sense, they are the two big affective tonalities, not two particular cases. Sadness and joy are the two big affective tonalities, that is affective in the sense of affectus, the affect. We are going to see as two lineages: the lineage based on sadness and the lineage based on joy, that are going to cover the theory of the affects. Why the thing whose relations don't agree with mine, why does it affect me with sadness, that is decrease my power of acting? You see we have a double impression: both that We’ve understood in advance, and then that we‚re missing something in order to understand. What happens, when something is presented having relations which don't compose with mine, it could be a current of air.

I am going back, I am in the dark, in my room, I am alone, I am left in peace. Someone enters and he makes me flinch, he knocks on the door, he knocks on the door and he makes me flinch. I lose an idea. He enters and he starts to speak; I have fewer and fewer ideas ouch, ouch, I am affected with sadness. Yes, I feel sadness, I‚ve been disturbed, damn! Spinoza will say, the lineage of sadness is what? Then on top of it all I hate it! I say to him: „eh, listen, it‚s okay. It could be not very serious, it could be a small hate, he irritates me damn it: hoooo! I cannot have peace, all that, I hate it!

What does it mean, hate? You see, sadness, he said to us: your power of acting is decreased, then you experience sadness insofar as it is decreased, your power of acting, okay. I hate it‚, that means that the thing whose relations don't compose with yours, you strive, this would only be what you have in mind, you strive for its destruction. To hate is to want to destroy what threatens to destroy you. This is what hate means. That is, to want‚ to decompose what threatens to decompose you. So the sadness engenders hate. Notice that it engenders joys too.

Hate engenders joys. So the two lineages, on one hand sadness, on the other hand joy, are not going to be pure lineages. What are the joys of hate? There are joys of hate.

As Spinoza says: if you imagine the being that you hate to be unhappy, your heart experiences a strange joy. One can even engender passions. And Spinoza does this marvelously. There are joys of hate. Are these joys? We can at least say, and this is going to advance us a lot for later, that these joys are strangely compensatory, that is indirect. What is first in hate, when you have feelings of hate, always look for the sadness at base, that is your power of acting was impeded, was decreased. And even if you have, if you have a diabolical heart, even if you have to believe that this heart flourishes in the joys of hate, these joys of hate, as immense as they are, will never get rid of the nasty little sadness of which you are a part; your joys are joys of compensation. The man of hate, the man of resentment, etc., for Spinoza, is the one all of whose joys are poisoned by the initial sadness, because sadness is in these same joys. In the end he can only derive joy from sadness. Sadness that he experiences himself by virtue of the existence of the other, sadness that he imagines inflicting on the other to please himself, all of this is for measly joys, says Spinoza. These are indirect joys. We rediscover our criteria of direct and indirect, all comes together at this level.

So much so that I return to my question: then yes, it is necessary to say it all the same: in what way does an affection, that is the image of something that doesn't agree with my own relations, in what way does this decrease my power of acting? It is both obvious and not. Here is what Spinoza means: suppose that you have a power (puissance), Let’s set it up roughly the same, and there, first case you come up against something whose relations don't compose with yours. Second case, on the contrary you encounter something whose relations compose with your own. Spinoza, in the Ethics, uses the Latin term: occursus, occursus is exactly this case, the encounter. I encounter bodies, my body never stops encountering bodies. The bodies that he encounters sometimes have relations which compose, sometimes have relations which don't compose with his. What happens when I encounter a body whose relation doesn't compose with mine? Well there: I would say ˜ and you will see that in book IV of the Ethics this doctrine is very strong. I cannot say that it is absolutely affirmed, but it is very much suggested ˜ a phenomenon happens which is like a kind of fixation. What does this mean, a fixation? That is, a part of my power is entirely devoted to investing and to isolating the trace, on me, of the object which doesn't agree with me. It is as if I tense my muscles, take once again the example: someone that I don't wish to see enters into the room, I say to myself Uh oh‚, and in me is made something like a kind of investment: a whole part of my power is there in order to ward off the effect on me of the object, of the disagreeable object. I invest the trace of the thing on me. I invest the effect of the thing on me. I invest the trace of the thing on me, I invest the effect of the thing on me. In other words, I try as much as possible to circumscribe the effect, to isolate it, in other words I devote a part of my power to investing the trace of the thing. Why? Evidently in order to subtract it, to put it at a distance, to avert it. Understand that this goes without saying: this quantity of power that I‚ve devoted to investing the trace of the disagreeable thing, this is the amount of my power that is decreased, which is removed from me, which is as it were immobilized.

This is what is meant by: my power decreases. It is not that I have less power, it is that a part of my power is subtracted in this sense that it is necessarily allocated to averting the action of the thing. Everything happens as if a whole part of my power is no longer at my disposal. This is the tonality affective sadness‚: a part of my power serves this unworthy need which consists in warding off the thing, warding off the action of the thing. So much immobilized power. To ward off the thing is to prevent it from destroying my relations, therefore I‚ve toughened my relations; this can be a formidable effort, Spinoza said: „like lost time, like it would have been more valuable to avoid this situation. In this way, a part of my power is fixed, this is what is meant by: a part of my power decreases. Indeed a part of my power is subtracted from me, it is no longer in my possession. It is invested, it is like a kind of hardening, a hardening of power (puissance), to the point that it is almost bad, damn, because of lost time!

On the contrary in joy, it is very curious. The experience of joy as Spinoza presents it, for example I encounter something which agrees, which agrees with my relations. For example music. There are wounding sounds. There are wounding sounds which inspire in me an enormous sadness. What complicates all this is that there are always people who find these wounding sounds, on the contrary, delicious and harmonious. But this is what makes the joy of life, that is the relations of love and hate. Because my hate against the wounding] sound is going to be extended to all those who like this wounding sound. So I go home, I hear these wounding sounds which appear to me as challenges, which really decompose all of my relations, they enter into my head, they enter into my stomach, all that. A whole part of my power is hardened in order to hold at a distance these sounds which penetrate me. I obtain silence and I put on the music that I like; everything changes. The music that I like, what does that mean? It means the resonant relations which are composed with my relations. And suppose that at that very moment my machine breaks. My machine breaks: I experience hate! (Richard: Oh no!) An Objection? (Laughter of Gilles Deleuze) Finally I experience a sadness, a big sadness. Good, I put on music that I like, there, my whole body, and my soul ˜ it goes without saying ˜ composes its relations with the resonant relations. This is what is meant by the music that I like: my power is increased. So for Spinoza, what interests me therein is that, in the experience of joy, there is never the same thing as in sadness, there is not at all an investment ˜ and we‚ll see why ˜ there is not at all an investment of one hardened part which would mean that a certain quantity of power (puissance) is subtracted from my power (pouvoir). There is not, why? Because when the relations are composed, the two things of which the relations are composed, form a superior individual, a third individual which encompasses and takes them as parts. In other words, with regard to the music that I like, everything happens as if the direct composition of relations (you see that we are always in the criteria of the direct) a direct composition of relations is made, in such a way that a third individual is constituted, individual of which me, or the music, are no more than a part. I would say, from now on, that my power (puissance) is in expansion, or that it increases.

If I take these examples, it is in order to persuade you all the same that, when, and this also goes for Nietzsche, that when authors speak of power (puissance), Spinoza of the increase and decrease of power (puissance), Nietzsche of the Will of Power (Volonté de Puissance), which it too, proceeds What Nietzsche calls affect‚ is exactly the same thing as what Spinoza calls affect, it is on this point that Nietzsche is Spinozist, that is, it is the decreases or increases of power (puissance). They have in fact something which doesn't have anything to do with whatever conquest of a power (pouvoir). Without doubt they will say that the only power (pouvoir) is finally power (puissance), that is: to increase one‚s power (puissance) is precisely to compose relations such that the thing and I, which compose the relations, are no more than two sub-individualities of a new individual, a formidable new individual.

I am going back. What distinguishes my basely sensual appetite from my best, most beautiful, love? It is exactly the same! The basely sensual appetite, you know, it‚s all the expressions, we can all make suggestions, it is in order to laugh, therefore we can say anything, the sadness After love, the animal is sad, what is this? This sadness? What does it say to us? Spinoza would never say this. Or then it is not worth the pain, there is no reason, sadness, good There are people who cultivate sadness. Feel, feel what happens to us, this denunciation which is going to run throughout the Ethics, namely: there are people who are so impotent that they are the ones who are dangerous, they are the ones who take power (pouvoir). And they can take power (pouvoir) ˜ so far away are the notions of power (puissance) and of power (pouvoir) ˜ the people of power (pouvoir) are the impotent who can only construct their power (pouvoir) on the sadness of others. They need sadness. They can only reign over slaves, and the slave is precisely the regime of the decrease of power (puissance). There are people who can only reign, who only acquire power (pouvoir) by way of sadness and by instituting a regime of sadness of the type: repent‚, of the type hate someone‚ and if you don't have anyone to hate, hate yourself, etc. Everything that Spinoza diagnoses as a kind of immense culture of sadness, the valorization of sadness, all of which says to you: if you don't pass by way of sadness, you will not flourish. Now for Spinoza this is an abomination. And if he writes an Ethics, it is in order to say: no! No! Everything you want, but not this. Then indeed, good = joy, bad = sadness. But the basely sensual appetite, you see now, and the most beautiful of loves, it is not at all a spiritual thing, but not at all. It is when an encounter works, as one says, when it functions well. It is a functionalism, but a very beautiful functionalism. What does that mean? Ideally it is never like this completely, because there are always local sadnesses, Spinoza is not unaware of that, there are always sadnesses. The question is not if there is or if there isn‚t, the question is the value that you give to them, that is the indulgence that you grant them. The more you grant them indulgence, that is the more you invest your power (puissance) in order to invest the trace of the thing, the more you will lose power (puissance). So in a happy love, in a love of joy, what happens? You compose a maximum of relations with a maximum of relations of the other, bodily, perceptual, all kinds of natures. Of course bodily, yes, why not; but perceptive also: Ah good Let’s listen to some music! In a certain manner one never stops inventing.

When I spoke of a third individual of which the two others are no more than parts, it doesn't at all mean that this third individual preexists, it is always by composing my relations with other relations, and it is under such a profile, under such an aspect that I invent this third individual of which the other and myself are no more than parts, sub-individuals. That’s it: each time that you proceed by composition of relations and composition of composed relations, you increase your power. On the contrary, the basely sensual appetite, it is not because it is sensual that it is bad. It is because, fundamentally, it never stops gambling on the decomposition of relations. It is really this sort of thing: Come on, hurt me, sadden me so that I can sadden you. The spat, etc. Ha, like we are okay with the spat. Ho. Like it is long after, that is, the small joys of compensation. All that is disgusting, but it is foul, it is the measliest life in the world. Ha come on, Let’s make our scene Because it is necessary to hate one another, afterwards we like one another much more. Spinoza vomits, he says: what are these mad people? If they did this, again, for themselves, but they are contagious, they are propagators. They won't let go of you until they have inoculated you with their sadness. What’s more, they treat you as idiots if you tell them that you don't understand, that it is not your thing. They tell you that this is the true life. And the more that they wallow, based on the spat, based on this stupidity, on the anguish of Haaaa, Heu The more that they hold on to you the more that they inoculate you, if they can hold on to you, then they pass it on to you. (Gilles Deleuze looks extremely nauseated).

Claire Parnet: Richard would like you to speak of the appetite

Gilles Deleuze: Of the composition of relations?! (Laughter). I have said everything on the composition of relations. Understand, the misinterpretation would be to believe: look for a third individual of which we would be only the parts. It does not preexist nor does the manner in which relations are decomposed. That preexists in Nature since Nature is everything, but from your point of view it is very complicated. There we are going to see what problems this poses for Spinoza because all this is very concrete all the same, on the ways of living. How to live? You don't know beforehand which are the relations. For example you are not necessarily going to find your own music. I mean: it is not scientific, in what sense? You don't have a scientific knowledge of relations which would allow you to say: „there is the woman or the man who is necessary for me. One goes along feeling one‚s way, one goes along blind. That works, that doesn't work, etc. And how to explain that there are people who only launch into things where they say that it is not going to work? (general laughter). They are the people of sadness, they are the cultivators of sadness, because they think that that is the foundation of existence. Otherwise the long apprenticeship by which, according to a presentiment of my constituent relations, I vaguely apprehend first what agrees with me and what doesn't agree with me. You will tell me that if it is in order to lead to that, it is not strong. Nothing but the formula: above all don't do what doesn't agree with you. It is not Spinoza who said this first, at first, but the proposition means nothing other than : don't do what doesn't agree with you‚ if you take it out of all context. If you take this conception ˜ that I find very grandiose ˜ to its conclusion, the relations which are composed, etc. How is it that someone very concrete is going to lead his existence in such a manner that he is going to acquire a kind of affection, of affect, or of presentiment, of the relations which agree with him, of the relations which don't agree with him, of situations where he must withdraw, of situations where he must engage himself, etc. That is not at all: it is necessary to do this‚, it is no longer at all the domain of morality. It is not necessary to do anything at all, it is necessary to find. It is necessary to find his thing, that is not at all to withdraw, it is necessary to invent the superior individualities into which I can enter as a part, for these individualities do not preexist. All that I meant takes on, I believe, a concrete signification, the two expressions take on a concrete signification. [The essence is eternal.

The eternal essence, degree of power (puissance) The eternal essence, what does it mean? Your essence is eternal, your singular essence, that is your own essence in particular, what does this mean? For the moment we can only give one sense to this formula, namely: you are a degree of power (puissance). You are a degree of power: it is this that Spinoza means when he says, verbatim: I am a part (pars) of the power of God‚, that means, literally: I am a degree of power (puissance). Immediate objection. I am a degree of power, but after all: me as a baby, little kid, adult, old man, it is not the same degree of power, therefore it varies, my degree of power. Okay, Let’s leave that aside. How, why does this degree of power have a latitude. Okay. But I say on the whole: I am a degree of power and it is in this sense that I am eternal. No one has the same degree of power as another. See, we will have need of it later, the fact that it is a quantitative conception of individuation. But it is a special quantity since it is a quantity of power (puissance). A quantity of power we have always called an intensity. It is to this and to this alone that Spinoza assigns the term eternity‚. I am a degree of power of God, that means: I am eternal. Second sphere of belonging: I have instantaneous affections. We saw this, it is the dimension of instantaneity. Following this dimension the relations compose or don't compose. It is the dimension of affectio: composition or decomposition between things.

Third dimension of belonging: the affects. That is: each time that an affection executes my power (puissance), and it executes it as perfectly as it can, as perfectly as is possible. The affection, indeed, that is the belonging to, executes my power; it realises my power, and it realises my power as perfectly as it can, according to the circumstances, according to here and now. It executes my power here and now, according to my relations with things. The third dimension is that each time an affection executes my power, it doesn't do it without my power increasing or decreasing, it is the sphere of the affect. So my power is an eternal degree‚ doesn't prevent it from ceaselessly, in duration, increasing and decreasing. This same power which is eternal in itself, doesn’t stop increasing and decreasing, that is varying in duration. How to understand this, after all? Understanding this, after all, is not difficult. If you reflect, I have just said: the essence is a degree of power, that is: if it is a quantity, it is an intensive quantity. But an intensive quantity is not at all like an extensive quantity. An intensive quantity is inseparable from a threshold, that is an intensive quantity is fundamentally, in itself, already a difference. The intensive quantity is made of differences. Does Spinoza go so far as to say a thing like this?

Letter to Meyer on infinity Here, I make a parenthesis of pseudo scholarship. It is important. I can say that Spinoza, firstly, said explicitly pars potentiae, part of power (puissance), and he said that our essence is a part of our divine power (puissance). I am saying, it is not a question of forcing the texts, part of power‚ is not an extensive part, it is obviously an intensive part. I am always pointing out in the domain of scholarship, but here I need it in order to justify everything that I‚m saying, that in the Scholastics of the Middle Age, the equality of two terms is absolutely current: gradus or pars, part or degree. Now the degrees are very special parts, they are intensive parts; this is the first point. Second point: I point out that in letter XII to Meyer, a gentleman named Meyer, there is a text that we will surely see the next time because it will allow us to draw conclusions on individuality. I point it out from this point on and I would like, for the next time, those who have the correspondence of Spinoza to have read the letter to Meyer, which is a famous letter, which is concerned with the infinite. In this letter, Spinoza develops a very bizarre, very curious geometrical example. And he made this geometrical example the object of all sorts of commentaries and it looked quite bizarre. And Leibniz, who was himself a very great mathematician, who had knowledge of the letter to Meyer, declared that he particularly admired Spinoza for this geometrical example which showed that Spinoza understood things that even his contemporaries didn't understand, said Leibniz. Therefore the text is that much more interesting with Leibniz’s benediction.

Here is the figure that Spinoza proposes for our reflection: two circles of which one is inside the other, but above all they are not concentric. Two [non-]concentric circles of which one is inside the other. Note the greatest and the smallest distance from one circle to the other. Do you understand the figure? Here is what Spinoza tells us. Spinoza tells us something very interesting, it seems to me, he tells us: in the case of this double figure, you can not say that you don't have a limit or threshold. You have a threshold, you have a limit. You even have two limits: the outer circle, the inner circle, or what comes down to the same thing, the greatest distance from one circle to the other, or the least distance. You have a maximum and a minimum. And he says: consider the sum, here the Latin text is very important, the sum of the inequalities of distance. You see: you trace all the lines, all the segments which go from one circle to the other. You evidently have an infinity. Spinoza tells us: consider the sum of the inequalities of distance. You understand: he doesn't literally tell us to consider the sum of the unequal distances, that is of the segments which go from one circle to the other. He tells us: the sum of the inequalities of distance, that is the sum of the differences. And he says: „it is very curious, this infinity here. We will see what he means, but I mention this text for the moment because I have a specific idea, he tells us: „it is very curious, it is an infinite sum. The sum of the inequalities of distance is infinite. He could also have said that the unequal distances is an infinite sum. And yet there is a limit. There is a limit since you have the limit of the big circle and the limit of the small circle. So there is something infinite and yet it is not unlimited. And he says that it is an odd infinity, it is a very particular geometrical infinity: it is an infinity that you can say is infinite even though it is not unlimited. And indeed, the space encompassed between the two circles is not unlimited, the encompassed space between the two circles is perfectly limited. I take up exactly the expression of the letter to Meyer: the sum of the inequalities of distance‚, even though he could have made the same reasoning by taking holding of the simpler case: the sum of unequal distances. Why does he want to sum up the differences?

For me it is truly a text which is important, because, what does he have in his head that he doesn’t say? He needs it by virtue of his problem of essences. Essences are degrees of power, but what is a degree of power? A degree of power is a difference between a maximum and a minimum. It is in this way that it is an intensive quantity. A degree of power is a difference in itself.

(End of tape.)

How to become reasonable? Like many thinkers of his time, he is one of the philosophers who have said most profoundly: you know, you are born neither reasonable, nor free, nor intelligent. If you become reasonable, if you become free, etc., it is a matter of a becoming. But there is no author who is more indifferent, for example, to the problem of freedom as belonging to the nature of man. He thinks that nothing at all belongs to the nature of man. He is an author who thinks everything, really, in terms of Becoming. So then, good, okay, without doubt. What does this mean, becoming reasonable? What does it means, becoming free, once it is said that we are not? We are not born free, we are not born reasonable. We are completely at the mercy of encounters, that is: we are completely at the mercy of decompositions. And you must understand that this is normal in Spinoza; the authors who think that we are free by nature are the ones who make of nature a certain idea. I believe we can only say: we are free by nature if we don't conceive it as a substance, that is as a relatively independent thing. If you conceive yourself as a collection of relations, and not at all as a substance, the proposition I am free‚ is plainly deprived of sense. It is not at all that I am for the opposite: it makes no sense, freedom or no freedom. On the other hand, perhaps the question has a sense: How to become free?‚ Similarly to be reasonable‚ can be understood if I am defined as a reasonable animal‚, from the point of view of substance, this is the Aristotelian definition which implies that I am a substance. If I am a collection of relations, perhaps they are rational relations, but to say that this is reasonable, is plainly deprived of all sense. So if reasonable, free, etc., make any sense it could only be the result of a becoming. Already this is very new. To be thrown into the world is precisely to risk at every instant encountering something which decomposes me.

Hence I said: there is a first aspect of reason. The first effort of reason, I believe, is very curious in Spinoza, it is a kind of extraordinarily groping effort. And there you can’t say that it is insufficient because it encounters concrete gropings. It is all a kind of apprenticeship in order to evaluate or have signs, I did say signs, to organize or to find signs that tell me a little of which relations agree with me and which relations don't agree with me. It is necessary to try, it is necessary to experiment. And my own experience, I can not even transmit it because perhaps it doesn't agree with another’s. That is, it is like a kind of groping so that each discovers at the same time what he likes and what he supports. Good, it is a little like this that we live when we take medication: it is necessary to find their doses, their things, it is necessary to make selections, and the prescription of the doctor will not be sufficient. It will come in handy. There is something which goes beyond a simple science, or a simple application of science. It is necessary to find your thing, it is like an apprenticeship in music, finding at the same time what agrees with you, what you are capable of doing. This is already what Spinoza will call, and it will be the first aspect of reason, a kind of double aspect, selecting-composing. To select, selection-composition, is to manage to find by experience those relations with which mine compose, and drawing from them the consequences. That is: at any cost flee as best as I can ˜ I can’t totally, I can’t completely ˜ but flee as much, to the maximum, the encounter with relations which don’t agree with me, and compose to the maximum, be composed to the maximum with the relations which agree with me. Here again is the first determination of freedom or of reason. So Rousseau‚s theme, what he himself called the materialism of the wise‚, you remember when I spoke a little of this idea of Rousseau‚s, very very curious, a kind of art of composing situations, this art of composing situations that consists above all of withdrawing from situations which don't agree with you, of entering into situations which agree with you, etc.. This is the first effort of reason. But I insist overall: at this level, we have no previous knowledge, we have no preexisting knowledge, we don't have scientific knowledge. It is not about science. It is really about living experimentation. It is about apprenticeship: I never stop deceiving myself, I never stop running into situations which don't agree with me, I never stop etc., etc.

And little by little is sketched out a kind of beginning of wisdom, which brings us back to what? Which brings us back to what Spinoza says from the beginning: but the fact that each knew a little, had a vague idea of what he is capable of, once it‚s said that the incapable people are not incapable people, it is people who rush to what they are not capable of, and who drop what they are capable of. But, Spinoza asks: What can a body do?‚ It doesn't mean: what a body in general can do, it means: yours, mine. Of what are you capable? It is this kind of experimentation with capacity. To try to experiment with capacity, and at the same time to construct it, at the same time that one experiments with it, is very concrete. Yet we don't have prior knowledge (savoir). Good, I don't know what, there are domains [] of what am I capable? Who can say, in the two senses, there are people who are too modest who say: „I am not capable of it because I would not succeed, and then there are the people too sure of themselves, who say: „Ha that, such a nasty thing, I am not capable of it, but they would perhaps do it, we don't know. No one knows what he is capable of.

What am I capable of? I think that one of the things, in the beautiful era of existentialism, there was as it was all the same very much connected to the end of the war, to the concentration camps etc. There was a theme that Jaspers had launched, and which was a theme, it seems to me, which was very profound: he distinguished two types of situation, limit situations and simple everyday situations. He said: limit situations could befall us at any time, they are precisely situations which we can’t anticipate. What do you want: someone who was not tortured what does that mean? He has no idea if he will hold out or if he won't hold out. If need be, the most courageous types collapse, and the types that one would have thought, in that way, pathetic, they hold out marvelously. One doesn't know. The limit situation is really a situation such as this, I learn at the last moment, sometimes too late, what I was capable of. What I was capable of for better or worse. But we can’t say in advance. It is too easy to say: Oh that, me, I would never do it! And inversely, we ourselves pass our time doing things like that, but what we are really capable of, we pass right by. So many people die without knowing and will never know what they were capable of. Once again: in atrocity as in the very good. It is the surprises, it is necessary to surprise oneself. We tell ourselves: Oh look! I would never have believed that I would have done it. People, you know, they are quite artful. Generally we always speak of the manner ˜ it is very complicated for Spinozism because we always speak of the manner in which people destroy themselves, but I believe that, finally, it is often so for discourse too. It is sad, it is always a very sad spectacle, and then it is annoying! They also have a kind of prudence: the cunning of people! the cunning of people is odd, because there are a lot of people who destroyed themselves over points which, precisely, they themselves have no need of. Then evidently they are losers, you understand, yeah, I suppose someone who, at the limit, renders himself impotent, but it is someone who doesn't really have the desire to do it, it is not their thing. In other words it is a very secondary relation for them. To budge is a very secondary relation. Good. He manages to put himself in states where he can no longer budge, in a certain way he has what he wanted since he set on a secondary relation. It is very different when someone destroys himself in what he himself experiences as being his principal constituent relations. If running doesn't interest you a lot, you can always smoke a lot, hey. We will say to you: You destroy yourself, then very well. I myself would be satisfied to be on a small chair, on the contrary it would be better like this, I would have peace! Very well. So, I destroy myself? No, not so. Obviously I destroy myself because if I can no longer budge at all, in the end I risk dying of it, in the end I would have the boredom of another nature that I would not have foreseen. Oh yes, it is annoying. But you see, even in things where there is self-destruction, there are tricks which imply a whole calculus of relations. One can very well destroy oneself over a point which is not essential for the person himself, and try to keep the essential, all this is complex. It is complex. You are sly, you don't know to what extent you are all sly, everyone. There you go.

I would call reason, or effort of reason, conatus of reason, effort of reason, this tendency to select, to learn the relations, this apprenticeship of the relations which are composed or which are not composed. Now I wouldn‚t mind saying: as you have no previous science, you understand what Spinoza means: science, you are perhaps going to arrive at a science of relations. But what will it be? Funny science. It won't be a theoretical science. The theory will perhaps be a part, but it will be a science in the sense of vital science.

The sign is the equivocal expression: I manage as best I can. And the signs are what? It is the signs of language which are fundamentally ambiguous, according to Spinoza, they are on one hand the signs of language, and on the other hand the signs of God, prophetic signs, and on the other hand the signs of society: rewards, punishments, etc. Prophetic signs, social signs, linguistic signs, are the three great types of signs. Now each time it is the language of equivocity. We are forced to set out from there, to pass by there, in order to construct our apprenticeship, that is in order to select our joys, eliminate our sadness, that is to make headway in a kind of apprehension of the relations which are composed, to arrive at an approximate knowledge (connaissance) by signs of the relations which agree with me and of the relations which don't agree with me. So the first effort of reason, you see, exactly, it is to do everything in my power (pouvoir) in order to increase my power (puissance) of acting, that is in order to experience passive joys, in order to experience of the joys of passion. The joys of passion are what increase my power of acting according to still equivocal signs in which I don't possess this power (puissance). Do you see? Very well. The question which I have come to is: supposing that it is like this, that there is this moment of long apprenticeship, how can I pass, how can this long apprenticeship lead me to a more sure stage, where I am more sure of myself, that is where I become reasonable, where I become free. How can this be done?

We will see next time.

Cours Vincennes - 17/02/1981

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?

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.

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.

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.

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.

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. There is an outline-limit and there is a tension-limit. There is a space-limit and there is a spatialization-limit.

Cours Vincennes : the actual infinite-eternal, the logic of relations - 10/03/1981

Confrontation with Gueroult's commentary.

This week and next week I will be speaking again of Spinoza, and then that‚s it. Unless you have questions to pose, which I would like very much.

Ok then: my dream is that it is very clear for you, this conception of individuality, such that we‚ve tried to bring it out in the philosophy of Spinoza, because, finally, it seems to me that this is one of the newest elements of Spinozism. It is this manner in which the individual, as such, is going to be conveyed, related, reported in Being. And in order to try to make you understand this conception of individuality which seems to me so new in Spinoza, I will always return to the theme: it is as if an individual, whatever individual, had three layers, as if it was composed, then, of three layers. We have advanced, at least into the first dimension, into the first layer of the individual, and I say: oh yes, all individuals have an infinity of extensive parts. This is the first point: an infinity of extensive parts. In other words, there are only individuals that are composite. A simple individual, I believe that, for Spinoza, it is a notion lacking in sense.

Every individual, as such, is composed of an infinity of parts.

I‚ll try to summarize very quickly: What does this mean this idea that the individual is composed of an infinity of parts? What are these parts? Once again, they are what Spinoza calls Œthe simplest bodies‚: all bodies are composed of an infinity of very simple bodies. But what are these: Œvery simple bodies‚? We have arrived at a precise enough status: they are not atoms, meaning finite bodies, and neither are they indefinites. What are they? And there Spinoza belongs to the 17th century. Once again, what really strikes me, in regard to the thought of the 17th century, is the impossibility of grasping this thought if we don‚t take into account one of the richest notions of this era, a notion which is simultaneously metaphysical, physical, mathematical, etc: the notion of the Œactual infinite‚. Now the actual infinite is neither finite nor indefinite. The finite signifies, above all, it refers to, if I seek the formula of the finite, it is: there is a moment where you have to stop yourself. That is to say: when you analyse something there will always be a moment where it will be necessary to stop yourself. Let‚s say, and for a long time, this moment of the finite, this fundamental moment of the finite which marks the necessity of finite terms, it is all of this which inspired atomism since Epicurus, since Lucretius: the analysis encounters a limit, this limit is the atom. The atom is subject to a finite analysis. The indefinite is as far as you can go, you can‚t stop yourself. That is to say: as far as you can take the analysis, the term at which you arrive will always be, in turn, divided and analysed. There will never be a last term.

The point of view of the actual infinite, it seems to me, of which we have completely lost the sense, and we have lost this sense for a thousand reasons, I suppose, among others for scientific reasons, all this ? But what matters to me, is not why we have lost this sense, it is as if I have happened to be able to reconstruct for you the way in which these thinkers thought. Really, it is fundamental in their thinking. Once again, if I consider that Pascal wrote texts that are representative of the 17th Century, these are essentially texts on man in relation to the infinite. These are people who truly thought naturally, philosophically, in terms of the actual infinite. Now this idea of an actual infinite, that is to say neither finite nor indefinite, what does that tell us? What it tells us is that: there are last terms, there are ultimate terms ˜ you see, this is contrary to the indefinite, it is not the indefinite since there are ultimate terms, only these ultimate terms are ad infinitum. Therefore, they are not the atom. They are neither finite nor indefinite. The infinite is actual, the infinite is in action. In effect, the indefinite is, if you like, infinite, but virtual, that is to say: you can always go further. This is not it; it (the actual infinite) tells us: there are last terms: Œthe simplest bodies‚ for Spinoza. These are the ultimate terms, these are the terms which are last, which you can no longer divide. But, these terms are infinitely small. They are the infinitely small, and this is the actual infinite. Note that it is a struggle on two fronts: simultaneously against finitism and against the indefinite. What does this mean? There are ultimate terms, but these are not atoms since they are the infinitely small, or as Newton will say, they are vanishings, vanishing terms. In other words, smaller than any given quantity. What does this imply? Infinitely small terms; you can‚t treat them one by one. This too is a non-sense: to speak of an infinitely small term that I would consider singularly, that makes no sense. The infinitely small, they can only go by way of infinite collections. Therefore there are infinite collections of the infinitely small. The simple bodies of Spinoza don‚t exist one by one. They exist collectively and not distributively. They exist by way of infinite sets. And I cannot speak of a simple body, I can only speak of an infinite set of simple bodies. Such that an individual is not a simple body, an individual, whatever it is, and however small it is, an individual has an infinity of simple bodies, an individual has an infinite collection of the infinitely small.

That is why, despite all the force of Gueroult‚s commentary on Spinoza, I cannot understand how Gueroult poses the question of knowing if simple bodies for Spinoza shouldn‚t have shape and magnitude ? It is obvious that if simple bodies are infinitely small, that is to say, "vanishing‰ quantities, they have neither shape nor magnitude. An atom, yes, has a shape and a magnitude: it is smaller than any given magnitude. What then has shape and magnitude? What has shape and magnitude, here, the response is very simple, what has shape and magnitude is a collection, it is a collection itself infinite of the infinitely small. This yes, the infinite collection of the infintely small has shape and magnitude. However, we come up against this problem: yes, but where does it come from, this shape and this magnitude? I mean: if the simple bodies are all infinitely small, what permits us to distinguish such an infinite collection of the infinitely small from another such infinite collection of the infinitely small? From the point of view of the actual infinite, how can we make distinctions in the actual infinite? Or even: Is there only one collection? One collection of all the possible infinitely smalls? Now Spinoza is very firm here! He says: to each individual corresponds an infinite collection of very simple bodies, each individual is composed of an infinity of very simple bodies. It is necessary therefore that I have the means of recognising the collection of the infinitely small that corresponds to such an individual, and that which corresponds to another such individual. How is that to be done? Before arriving at this question, let‚s try to see how these infinitely small are. They enter therefore into infinite collections, and I believe that here the 17th century grasped something that mathematics, with completely different means, with a completely different procedure˜ I don‚t want to make arbitrary connections ˜ but that modern mathematics rediscovered with a completely different procedure, that is to say: a theory of infinite sets. The infinitely small enter into infinite sets and these infinite sets are not the same. That is to say: there is a distinction between infinite sets. Regardless of whether it was Leibniz, or Spinoza, the second half of the 17th century is riddled with this idea of the actual infinite, the actual infinite which consists of these infinite sets of the infinitely small.

But then these vanishing terms, these infinitely small terms, what are their ? How are they? I would like this to take on a slightly more concrete shape. It is obvious that they don‚t have interiority. I‚ll try first to say what they are not, before saying what they are. They have no interiority, they enter into infinite sets, the infinite set could have an interiority. But these extreme terms, infinitely small, vanishing, they have no interiority, they are going to constitute what? They are going to constitute a veritable matter of exteriority. The simple bodies have only strictly extrinsic relations, relations of exteriority with each other. They form a species of matter, using Spinoza‚s terminology: a modal matter, a modal matter of pure exteriority, which is to say: they react on one another, they have no interiority, they have only external relations with one another. However, I‚ll return to my question: if they have only external relations, what allows us to distinguish one infinite set from another? Once again, all individuals, each individual, here I can say each individual since the individual isn‚t the very simple body, each individual, distributively, has an infinite set of infinitely small parts. These parts are actually given. But what distinguishes my infinite set, the infinite set that refers to me, and the set that refers to a neighbour? Hence, and already we are entering the second layer of individuality, which leads us to ask: under what aspect does an infinite set of very simple bodies belong to either this or that individual? Under what aspect?

It is understood, I have an infinite eset of infinitely small parts, but under what aspect does that infinite set belong to me? Under what aspect does an infinite set of very simple bodies belong to either this or that individual. It is understood that I have an infinite set of infinitely small parts, but under what aspect does that infinite set belong to me?

You see that I have only with difficulty transformed the question because when I ask under what aspect the infinite set belongs to me, it is another way of asking what allows me to distinguish such an infinite set from another such infinite set. Once again, at first sight, in the infinite everything must be confused, it must be the black night or the white light. What makes it so that I can distinguish infinities from one another? Under what aspect is an infinite set said to belong to me or to someone else?

Spinoza‚s response seems to be: an infinite set of infinitely small parts belongs to me, and not to someone else, insofar as this infinite set puts into effect [effectue] a certain relation. It is always under a relation that the parts belong to me. To the point that, if the parts which compose me take on another relation, at that very moment, they no longer belong to me. They belong to another individuality, they belong to another body. Hence the question: what is this relation? Under what relation can the infinitely small elements be said to belong to something? If I answer the question, I truly have the answer that I‚m looking for. I will show how, according to which condition, an infinite set can be said to belong to a finite individuality. Under what relation of the infinitely small can they belong to a finite individuality? Good. Spinoza‚s answer, if I stick to the letter of Spinoza, is: under a certain relation of movement and rest. But we‚re already there, relation of movement and rest, we know that it doesn‚t at all mean ˜ and here we would be wrong to read the text too quickly ˜ it doesn‚t at all mean, as in Descartes, a sum (which we have seen: the relation of movement and rest, this cannot be the Cartesian formula ? = mv, mass-velocity). No, he didn‚t say "relation‰. What defines the individual, is therefore a relation of movement and rest because it is under this relation that an infinity of infinitely small parts belong to the individual. However, what is this relation of movement and rest that Spinoza invokes in such a way?

Here, I recommence a confrontation with Gueroult‚s commentary. Gueroult makes an extremely interesting hypothesis, but here too I don‚t understand; I don‚t understand why he makes this hypothesis here, but it is very interesting. He says: finally the relations of movement and rest is vibration. At the same time it is a response that appears to me to be very curious. The answer must be very precise: it is a vibration! What does that mean? That would mean that what defines the individual, at the level of the second layer, that is to say the relation under which the parts belong to it, is a way of vibrating. Each individual ? Well, that would be good, that would be very concrete, what would define you, me, is that we would have a kind espèce of way of vibrating. Why not? Why not ? what does that mean? Either it is a metaphor, or else it means something. A vibration returns us to what, physics? It returns to something simpler, to a well known phenomenon which is that of the pendulum. Well, Gueroult‚s hypothesis seems to take on a sense that‚s very interesting because physics, in the 17th century, had considerably advanced the study of rotating bodies and pendulums, and notably had established a distinction between simple pendulums and compound pendulums. Well then good ? at this moment then you see that the Gueroult hypothesis becomes this: each simple body is a simple pendulum, and the individual, which has an infinity of simple bodies, is a compound pendulum. We would all be compound pendulums. That‚s very good! Or turning discs. It is an interesting conception of each of us. What does it mean? In effect, a simple pendulum is defined by what? It is defined, if you vaguely recall memories of physics, but very simple physics, it is defined in a certain way by a time, a time of vibration or a time of oscillation. For those who remember, there is the famous formula: t = py root of 1 over g [ ]? Yes, I think so. "t‰ is the duration of oscillation, "l‰ is the length of the thread on which the pendulum is suspended, "g‰ is what, in the 17th century, is called the intensity of gravity, it‚s of little significance ? Good. What is important is that in the formula, see that a simple pendulum has a time of oscillation which is independent of the amplitude of oscillation of the shaft of the pendulum, therefore completely independent of the amplitude of oscillation, independent of the mass of the pendulum ˜ this responds well to the situation of an infinitely small body, and independent of the weight of the thread. Weight of the thread, mass of the pendulum, only enter into play from the point of view of the compound pendulum. Therefore it seems that, in many respects, the Gueroult hypothesis works. Individuals for Spinoza would be kinds of compound pendulums, each composed of an infinity of simple pendulums. And what defines an individual is a vibration. Good.

Well then I say with a lot of freedom, like that, I am developing this for those who are very technically interested in Spinoza, as for the others you can retain what you want ? At the same time it is curious because, at the same time this hypothesis draws my attention, and I can‚t well see why. There is one thing which disturbs me: it is that it is true that all of the history of pendulums and of rotating discs, in the 17th century, is very encouraging; but precisely, if it had been this that Spinoza had wanted to say, why did he make no allusion to these problems of vibration, even in his letters? And then, above all, the model of the pendulum does not give a full account of what appears to me the essential, that is to say: this presence of the actual infinite and the term "infinitely small‰.

You see Gueroult‚s answer, insofar as he comments on Spinoza: the relation of movement and rest must be understood as the vibration of the simple pendulum. There you are! I am not at all saying that I am right, truly not ? I mean: if it is true that the very simple bodies ˜ this is why elsewhere Gueroult needs to affirm that the very simple bodies have nevertheless, for Spinoza, a shape and a magnitude. Suppose on the contrary ˜ but I am not at all saying that I am right˜ suppose that the very simple bodies were really infinitely small, that is to say that they have neither shape nor magnitude. At that moment then the model of the simple pendulum cannot work, and it cannot be a vibration that defines the relation of movement and rest.

On the other hand, we have another way, and then you can perhaps find others ˜ surely you can find others. The other way would be this: once again I return to my question, between supposedly infinitely small terms, what type of relations can they have? The response is very simple: between infinitely small terms, if we understand what is meant in the 17th century by the infinitely small, that is: which have no distributive existence, but which necessarily enter into an infinite collection, between infinitely small terms, there can only be one type of relation: differential relations.

Why? Infinitely small terms are vanishing terms, that is to say, the only relations which they can have between the infinitely small terms are relations which subsist while the terms vanish. A very simple question is: what are relations such that they subsist while their terms vanish? Let‚s do here some very very simple mathematics. I view , if I remain there in the 17th century and in a certain state of mathematics, and what I am saying is very rudimentary, I view as well known in the 17th century three types of relation. There are fractional relations which have been known for a very very long time; there are algebraic relations which are known ˜ which were anticipated well before, that goes without saying ˜ but which received a very firm status, in the 16th and 17th century ˜ in the 17th century with Descartes, that is in the first half of the 17th century, with algebraic relations; and finally differential relations, which at the moment of Spinoza and Leibniz, are the big question of mathematics of this era. I‚ll give some examples: I want it to be clear for you, even if it is not mathematics that I‚m doing, not at all. Example of a fractional relation: 2/3. Example of an algebraic relation: ax+by = etc. From which you can get x/y =. Example of a differential relation, we have seen: dy/dx = z. Good. What difference is there between these three types of relation? I would say that the fractional relation is already very interesting because otherwise we could make like a scale: the fractional relation is irreducibly a relation. Why?

If I say 2/3, 2/3, once again it is not a number. Why is it that 2/3 is not a number, it is because there isn‚t a number assignable which multiplied by 3 gives 2. Therefore it is not a number. A fraction is not a number, it is a complex of numbers, which I decide, by convention, to treat as a number; that‚s to say that I decide by convention to submit to the rules of addition, of subtraction, of multiplication. But a fraction is obviously not a number. Once I have found the fraction, I can treat numbers like fractions, that‚s to say: once I employ fractional symbolism, I can treat a number, for example the number 2, as a fraction. I can always write 4 over 2. 4 over 2 = 2. But the fractions, in their irreducibility to whole numbers, don‚t have numbers, but are complexes of whole numbers. Good. Therefore already the fraction brings forward a sort of independence of the relation in relation to its terms.

In this very important question of a logic of relations, the point of departure of a logic of relations is obvious: in what sense is there a consistency of the relation independent of its terms? The fractional number already gives me a kind of first approximation, but that doesn‚t allow us to avoid the fact that in the fractional relation, the terms must again be specified. The terms must be specified, that‚s to say that you could always write 2 over 3, but the relation is between two terms: 2 and 3. It is irreducible to these terms since it is itself not a number but a complex of numbers; but the terms must be specified, the terms must be given. In a fraction, the relation is as independent of its terms, Yes! But the terms must be given.

One step further. When I take an algebraic relation of the type x over y, this time I don‚t have given terms, I have two variables. I have variables. You See that everything happens as if the relation had acquired a superior degree of independence in relation to its terms. I no longer need to assign a determinate value. In a fractional relation I cannot escape this: I must assign a determinate value to the terms of the relation. In an algebraic relation I no longer need to assign a determinate value to the terms of the relation. The terms of the relation are variable. But that doesn‚t allow me to avoid the fact that it is again necessary that my variables have a determinable value. In other words, x and y can have all sorts of singular values, but they must have one. See, in the fractional relation, I can only have a singular value, or equivalent singular values. In an algebraic relation I no longer have to have a singular value, but that doesn‚t allow me to avoid the fact that my terms continue to have a specifiable value, and the relation is quite independent of every particular value of the variable, but it is not independent of a determinable value of the variable.

What is very new with the differential relation is that it takes something like a third step. When I say dy over dx, remember what we saw: dy in relation to y = 0; it is an infinitely small quantity. Dx in relation to x equals zero; therefore I can write, and they wrote constantly in the 17th century, in this form: dy over dx = 0 over 0: dy/dx=0/0. Now, the relation 0 over 0 is not equal to zero. In other words, when the terms vanish, when the terms vanish, the relation subsists. This time, the terms between which the relation is established are neither determined, nor determinable. Only the relation between its terms is determined. It is here that logic is going to make a leap, but a fundamental leap. Under this form of the differential calculus is discovered a domain where the relations no longer depend on their terms: the terms are reduced to vanishing terms, to vanishing quantities, and the relation between these vanishing quantities is not equal to zero. To the point where I would write, here I‚ll do it very summarily: dy over dx equals z: dy/dx = z. What does this mean "= z‰? It means, of course, that the differential relation dy over dx [dy/dx], which is made between vanishing quantities of Œy‚ and vanishing quantities of Œx‚, tells us strictly nothing about Œx‚ and Œy‚, but tells us something about Œz‚. For example, as applied to a circle, the differential relation dy over dx tells us something about a tangent called the "trigonometric tangent‰. In order to keep it simple, there is no need to understand anything, I can therefore write dy/dx = z. What does this mean then? See that the relation such as it subsists when its terms vanish is going to refer to a third term, Œz‚. It is interesting; this must have been very interesting: it is from here that a logic of relations is possible. What does this mean then? We will say of Œz‚ that it is the limit of the differential relation. In other words, the differential relation tends towards a limit. When the terms of the relation vanish, Œx‚ and Œy‚, and become dy and dx, when the terms of the relation vanish, the relation subsists because it tends towards a limit, Œz‚. When the relation is established between infinitely small terms, it does not cancel itself out at the same time as its terms, but tends towards a limit. This is the basis of differential calculus such as it is understood or interpreted in the 17th century.

Now you obviously understand why this interpretation of the differential calculus is at one with the understanding of an actual infinite, meaning with the idea of infinitely small quantities of vanishing terms.

Now, me, my answer to the question: but what is it exactly, this that Spinoza speaks to us of when he speaks of the relations of movement and rest, of proportions of movement and rest, and says: the infinitely small, a collection of the infinitely small belonging to such an individual under such a relation of movement and rest, what is this relation? I would not be able to say like Gueroult that it is a vibration which assimilates the individual to a pendulum: it is a differential relation. It is a differential relation such that it is manifested in the infinite sets, in the infinite sets of the infinitely small. And, in effect, if you take Spinoza‚s letter on blood, of which I have made great use, and the two components of blood, chyle and lymph, this now tells us what? It tells us that there are corpuscles of chyle, or better chyle is an infinite set of very simple bodies. Lymph is another infinite set of the very simple bodies. What distinguishes the two infinite sets? It is the differential relation! You have this time a dy/dx which is: the infinitely small parts of chyle over the infinitely small parts of lymph, and this differential relation tends towards a limit: the blood, that is to say: chyle and lymph compose blood.

If this is right, we could say why infinite ensembles are distinguished. It is because the infinite sets of very simple bodies don‚t exist independently of the differential relations which they put into effect. Therefore it is by abstraction that I began by speaking of them. But they necessarily exist, they exist necessarily under such and such a variable relation, they cannot exist independently of a relation, since the notion even of the term infinitely small, or of vanishing quantity, cannot be defined independently of a differential relation. Once again, Œdx‚ has no sense in relation to Œx‚, Œdy‚ has no sense in relation to Œy‚, only the relation dx/dy has a sense. That‚s to say that the infinitely small don‚t exist independently of the differential relation. Good. Now, what permits me to distinguish one infinite set from another infinite set? I would say that the infinite sets have different powers [puissances], and that which appears quite obviously in this thought of the actual infinite is the idea of the power [puissance] of an set. Let‚s understand here that I don‚t at all mean, it would be abominable to make me mean that they have anticipated things which closely concern set theory in the mathematics of the beginning of the 20th century, I don‚t mean that at all. I mean that in their conception, which is in absolute contrast with modern mathematics, which is completely different, which has nothing to do with modern mathematics, in their conception of the infinitely small and of the differential calculus interpreted from the perspective of the infinitely small, they necessarily brought out ˜ and this is not peculiar to Leibniz, it is also true of Spinoza, and of Malebranche, all these philosophers of the second half of the 17th century ˜ brought out the idea of infinite sets which are distinguished, not by their numbers, an infinite set by definition, it can not be distinguished from another infinite set by the number of its parts, since all infinite sets excede all assignable number of parts ˜ therefore, from the point of view of the number of parts, there cannot be one which has a greater number of parts than another. All these sets are infinite. Therefore under what aspect are they distinguished? Why is it that I can say: this infinite set and not that one?

I can say it, it is quite simple: because infinite sets are defined as infinite under such and such a differential relation. Between other terms the differential relations can be considered as the power [puissance] of an infinite set. Because of this an infinite set will be able to be of a higher power [puissance] than another infinite set. It‚s not that it will have more parts, obviously not, but it is that the differential relation under which the infinity, the infinite set of parts, belongs to it will be of higher power [puissance] than the relation under which an infinite set belongs to another individual ? [end of tape]

If we eliminate that, any idea of an actual infinite makes no sense. It is for this reason that, with the reservations that I‚ve just mentioned, for my part, the answer that I would give to: what is this relation of movement and rest that is for Spinoza characteristic of the individual, that is as the second layer of the individual, I would say that, no, it is not exactly a way of vibrating, perhaps we could bring together the two points of view, I don‚t know, but it is differential relation, and it is the differential relation that defines power [puissance]. Now, you understand the situation, yes? ˜ you recall that the infinitely small are constantly influenced from the outside, they pass their time by being in relation with other collections of the infinitely small. Suppose that an infinite collection of the infinitely small is determined from the outside to take another relation than the one under which it belongs to me. What does this mean? It means that: I die! I die! In effect, the infinite set which belongs to me under such a relation which characterises me, under my characteristic relation, this infinite set will take another relation under the influence of external causes. Take again the example of poison which decomposes the blood: under the action of arsenic, the infinitely small particles which compose the blood, which compose my blood under such a relation, are going to be determined to enter under another relation. Because of this, this infinite set is going to enter in the composition of another body, it will no longer be mine: I die! Do you understand? Good. If all of this is true, if it is true ? we are still missing something, because this relation, it comes from where, this relation? You can see that I‚ve progressed, but it is necessary for me to have my three layers. I cannot pull through in any other way. I need my three layers because I can‚t otherwise pull through. I start by saying: I am composed of an infinity of vanishing and infinitely small parts. Good. But be careful, these parts belong to me, they compose me under a certain relation which characterises me. But this relation which characterises me, this differential relation or better, this summation, not an addition but this kind of integration of differential relations, since in fact there are an infinity of differential relations which compose me: my blood, my bones, my flesh, all this refers to all sorts of systems of differential relations. These differential relations that compose me, that is to say which determine that the infinite collections which compose me belong effectively to me, and not to another, insofar as it endures, since it always risks no longer enduring, if my parts are determined to enter under other relations, they desert my relation. Ha! ? they desert my relation. Once again: I die! But that is going to involve lots of things.

What does it mean to die, at that very moment? It means that I no longer have parts. It‚s stupefying! Good. But this relation which characterises me, and which determines that the parts which put into effect the relation belong to me as soon as they put into effect the relation, insofar as they put into effect the differential relation, they belong to me, this differential relation, is this the last word on the individual? Obviously not, it is necessary to give an account of it in its turn. What is it going to express, it depends on what? What does it do that ? it doesn‚t have its own reason, this differential relation. What does it do that, me, I am characterised by such a relation or such an set of relations?

Last layer of the individual, Spinoza‚s answer: it is that the characteristic relations which constitute me, that is to say which determine that the infinite sets which verify these relations, which put into effect these relations which belong to me, the characteristic relations express something. They express something which is my singular essence. Here Spinoza says this very firmly: the relations of movement and rest serve only to express a singular essence. That means that none of us have the same relations, of course, but it isn‚t the relation that has the last word. It‚s what? Couldn‚t we here return to something of Gueroult‚s hypothesis? Last question: there is therefore a last layer of the individual, that is to say that the individual is a singular essence. You can now see what formula I can give to the individual: each individual is a singular essence, each singular essence expresses itself in the characteristic relations of the differential relation type, and under these differential relations, the infinite collections of the infinitely small belong to the individual.

Hence a last question: what is it, this singular essence? Couldn‚t we find here, at this level ˜ though it would be necessary to say that Gueroult, in all rigour, is mistaken about this level ˜ at this level something equivalent to the idea of vibration? What is a singular essence? Be careful that you have understood the question, it is almost necessary to consent to press the conditions of such a question. I am no longer in the domain of existence. What is it, existence? What does it mean, to me, to exist? We will see that it is just as complicated in Spinoza, because he gives a very rigorous determination to what he calls existing. But if we start with the most simple, I would say: to exist is to have an infinity of extensive parts, of extrinsic parts, to have an infinity of infinitely small extrinsic parts, which belong to me under a certain relation. Insofar as I have, in effect, extensive parts which belong to me under a certain relation, infinitely small parts which belong to me, I can say: I exist.

When I die, once again, then it is necessary to work out the Spinozist concepts, when I die what happens? To die means, exactly this, it means: the parts which belong to me cease to belong to me. Why? We have seen that they only belong to me insofar as they put into effect a relation, relation which characterises me. I die when these parts which belong to me or which belonged to me are determined to enter under another relation which characterises another body: I would feed worms! "I would feed worms‰, which means: the parts of which I am composed enter under another relation ˜ I am eaten by worms. My corpuscles, mine, which pass under the relation of the worms. Good! That could happen ? Or better, the corpuscles of which I am composed, precisely, they put into effect another relation, conforming to the relation of arsenic: I have been poisoned! Good. Do you see that in one sense it is very serious, but it is not that serious, for Spinoza. Because, in the end, I can say that death ? concerns what? We can say in advance, before knowing what it is that he calls an essence, death concerns essentially a fundamental dimension of the individual, but a single dimension, that is the relationship of the parts to an essence. But it concerns neither the relation under which the parts belong to me, nor the essence. Why?

You‚ve seen that the characteristic relation, the differential relation, or the differential relations which characterise me, they are independent in themselves, they are independent of the terms since the terms are infinitely small, and that the relation, itself, on the contrary, has a finite value: dy/dx = z. Then it is actually true that my relation or my relations cease to be put into effect when I die, there are no longer parts which effect. Why? Because the parts have been set up to put into effect other relations. Good. But firstly there is an eternal truth of the relation, in other words there is a consistency of the relation even when it is not put into effect by actual parts, there is an actuality of the relation, even when it ceases to be put into effect. That which disappears with death is the effectuation of the relation, it is not the relation itself. You say to me: what is a non-effectuated relation? I call upon this logic of the relation such as it seems to be born in the 17th century, that is to say it has effectively shown in what conditions a relation had a consistency while its terms were vanishing. There is a truth of the relation independent of the terms which put the relation into effect, and on the other hand there is a reality of the essence that is expressed in the relation, there is a reality of the essence independent of knowing if the actually given parts putting the relation into effect conform with the essence. In other words both the relation and the essence are said to be eternal, or at least to have a species of eternity ˜ a species [espèce] of eternity doesn‚t at all mean a metaphoric eternity ˜ it is a very precise type of eternity, that is to say that: the species of eternity in Spinoza has always signified what is eternal by virtue of its cause and not by virtue of itself ˜ therefore the singular essence and the characteristic relations in which this essence expresses itself are eternal, while what is transitory, and what defines my existence, is uniquely the time during which the infinitely small extensive parts belong to me, that is to say put the relation into effect. But then there you are, this is why it is necessary to say that my essence exists when I don‚t exist, or when I no longer exist. In other words there is an existence of the essence which is not confused with the existence of the individual whose essence is the essence in question. There is an existence of the singular essence which is not confused with the existence of the individual whose essence is the essence in question. It is very important because you see where Spinoza is heading, and his whole system is founded on it: it is a system in which everything that is is real. Never, never has such a negation of the category of possibility been carried so far. Essences are not possibilities. There is nothing possible, everything that is is real. In other words essences don‚t define possibililties of existence, essences are themselves existences.

Here he goes much further than the others of the 17th century ˜ here I‚m thinking of Leibniz. With Leibniz, you have an idea according to which essences are logical possibilities. For example, there is an essence of Adam, there is an essence of Peter, there is an essence of Paul, and they are possibles. As long as Peter, Paul, etc. don‚t exist, we can only define the essence as a possible, as something which is possible. Simply, Leibniz will be forced, henceforth, to give an account of this: how can the possible account for, integrate in itself the possibility of existing, as if it would be necessary to burden the category of the possible with a kind [espèce] of tendency to existence. And, in effect, Leibniz develops a very very curious theory, with a word that is common to both Leibniz and Spinoza, the word conatus, tendency, but which actually has two absolutely different senses in Spinoza and Leibniz. With Leibniz singular essences are simply possibles, they are special possibles since they tend with all their force to exist. It is necessary to introduce into the logical category of possibility a tendency to existence.

Spinoza, I‚m not saying that it is better ˜ it‚s your choice ˜ it is truly a characteristic of the thought of Spinoza, for him, it is the same notion of the possible: he doesn‚t want to enrich the notion of the possible by grafting it to a tendency to existence. What he wants is the radical destruction of the category of the possible. There is only the real. In other words, essence isn‚t a logical possibility, essence is a physical reality. It is a physical reality, what can that mean? In other words, the essence of Paul, once Paul is dead, remains a physical reality. It is a real being. Therefore it would be necessary to distinguish them as two real beings: the being of the existence and the being of the essence of Paul. What‚s more, it would be necessary to distinguish as two existences: the existence of Paul and the existence of the essence of Paul. The existence of the essence of Paul is eternal, while the existence of Paul is transitory, mortal, etc. You see, from the point where we‚re at, if this is it, a very important theme of Spinoza is: but what is it going to be, this physical reality of the essence? Essences can‚t be logical possibilities, if they were logical possibilities they would be nothing: they must be physical realities. But be careful, these physical realities are not confused with the physical reality of the existence. What is the physical reality of the existence? Spinoza finds himself in the grip of a problem which is very very complicated, but so much the better. I want this all to be clear, I don‚t know how to do it.

Spinoza tells us, I‚ll tell you shortly when and where he tells us this, in a very fine text, he tells us: imagine a white wall. A totally white wall. There is nothing on it. Then you arrive with a pencil, you draw a man, and then next to it you do another. There your two men exist. They exist insofar as what? They exist insofar as you‚ve traced them. Two figures exist on the white wall. You can call these two figures Peter and Paul. So long as nothing is traced on the white wall, does something exist which would be distinct from the white wall? Spinoza‚s response very curiously is: ŒNo, strictly speaking nothing exists!‚ On the white wall, nothing exists so long as the figures haven‚t been traced. You‚re telling me that this isn‚t complicated. It isn‚t complicated. It is a fine example because I will have need of it for the next time. As for now, all I will do is comment on Spinoza‚s text. Now, where can this text be found? This text can be found in the early work of Spinoza, a work which was not written by him, but is the notes of an auditor, and is known by the title the Short Treatise. The Short Treatise. You see why this example is important. The white wall is something equivalent to what Spinoza calls the attribute. The attribute, extension. The question was asked: but what is there in extension? In extension there is extension, the white wall equals a white wall, extension equals extension! But you could say: bodies exist in extension. Yes, bodies exist in extension. OK. What is the existence of bodies in extension? The existence of bodies in extension is effectively when these bodies are traced. What does that mean, effectively traced? We have seen this answer, Spinoza‚s very strict answer, it is when an infinity of infinitely small parts are determined to belong to a body. The body is traced. It has a shape. What Spinoza will call mode of the attribute is such a shape. Therefore the bodies are in extension exactly like figures traced on the white wall, and I can distinguish one figure from another figure, by saying precisely: which parts belong to which shape, pay attention, such another part, it can have there common fringes, but what can this do? This means that there will be a common relation between the two bodies, yes, this is possible, but I would distinguish existing bodies. Outside of that, can I distinguish something? One finds that the text of the Short Treatise, of Spinoza‚s youth, seems to say: ultimately it is impossible to distinguish something outside of existing modes, outside of shapes. If you haven‚t traced the shape, you cannot distinguish something on the white wall. The white wall is uniformly white. Excuse me for dwelling on this, it is really because it is an essential moment in Spinoza‚s thought. Nevertheless, already in the Short Treatise he says: the essences are singular, that is to say there is an essence of Peter and of Paul which is not confused with the existence of Peter and Paul. Now, if essences are singular, it is necessary to distinguish something on the white wall without the shapes necessarily having been traced. What‚s more, if I leap to his definitive work, the Ethics, I see that in Part II, Proposition 7, 8, etc., Spinoza comes across this problem again. He says, very bizarrely: modes exist in the attribute in two ways; on the one hand they exist insofar as they are comprised and contained in the attribute; and, on the other, insofar as it is said that they have duration. Two existences: durational existence, immanent existence. Here I take the letter of the text. Modes exist in two ways, that is to say that: existing modes exist insofar as they are said to have duration, and the essences of modes exist insofar as they are contained in the attribute. Good! This is complicated because modal essences are once again, and here it is confirmed by all the texts of the Ethics, they are singular essences, meaning that one isn‚t confused with the essence of another, the one isn‚t confused with the other, good, very well. But then, how are they distinguished in the attribute, one from the other. Spinoza affirms that they are distinguished, and then here he abandons us! Does he really abandon us, it is not possible! A thing like this is not imaginable! He doesn‚t tells us, OK. He gives an example, he gives us a geometric example, precisely, which comes down to saying: does a shape have a certain mode of existence when it isn‚t traced? Does a shape exist in extension when it isn‚t traced in extension? The whole text seems to say: yes, and the whole text seems to say: complete this yourselves. And this is normal, perhaps he has given us all the elements of an answer. To complete it ourselves. It is necessary, we have no choice! Either we renounce being Spinozist ˜ that wouldn‚t be bad either ˜ or it is necessary to complete it yourself. How could we complete this ourselves? This is why I pleaded as I said at the beginning of the year, we plead with ourselves, on the one hand, with the heart, and, on the other, with that which we know. The white wall! Why does he speak of the white wall? What is this story of the white wall?

After all, examples in philosophy are also a bit like a wink of the eye. You tell me: well what do we do if we don‚t understand the wink of an eye? It‚s not serious, not serious at all! We pass by a million things. Let‚s make do with what we have, let‚s make do with what we know. White wall. But after all I‚m trying to complete it with all my heart before completing it with knowledge. Let‚s call on our hearts. I take on one side my white wall, on the other side my drawings on the white wall. I have drawn on the wall. And my question is this: can I distinguish on the white wall things independently of the shapes drawn, can I make distinctions which are not distinctions between shapes?

Here it is like a practical exercise, there is no need to know anything. Simply, I say: you are reading Spinoza well if you arrive at this problem or at an equivalent problem. It is necessary to read him literally enough in order for you to say: ah yes, this is the problem that he poses us, and the job for him is to pose the problem so precisely that ˜ it is even a present that he gives us in his infinite generosity ˜ is to pose the problem so well, he poses the problem for us so precisely that obviously, we tell ourselves, the answer is this, and we will have the impression of having found the answer. It is only the great authors who give you this impression. They stop just when all is finished, but no, there is a tiny bit that they haven‚t mentioned. We are forced to find it and we say to ourselves: I am good aren‚t I, I am strong aren‚t I, I found it, because at the moment when I come to pose the question like this: can something be distinguished on the white wall independently of the drawn shapes? It is obvious that I have the answer already. And that we respond in chorus, we respond: Of course, there is another mode of distinction which is what? It is that the white has degrees! And I can vary the degrees of whiteness. One degree of whiteness is distinguished from another degree of whiteness in a totally different way than that by which a shape on the white wall is distinguished from another shape on the white wall. In other words, the white has, one says in Latin ˜ we use all the languages in order to try to better understand the languages that we don‚t know, what! (laughs) ˜ the white has distinctions of gradus. There are degrees, and the degrees are not confused with the shapes. You say: such a degree of white, in the sense of such a degree of light. A degree of light, a degree of whiteness, is not a shape. And even though two degrees are distinguished, two degrees aren‚t distinguished like shapes in space. I would say that shapes are distinguished externally, taking account of their common parts. I would say of degrees that it is a completely different type of distinction, that there is an intrinsic distinction. What is this?

Accordingly I no longer need ? It is an accident. Each operates with what they know. I tell myself: ha, it is not at all surprising that Spinoza ? What is the wink of the eye from the point of view of knowledge? We started with our heart by saying: yes, it can only be that: there is a distinction of degrees which is not confused with the distinction of figures. The light has degrees, and the distinction of degrees of light is not confused with the distinction of shapes in the light. You tell me that all of this is infantile; but it is not infantile when we try to make them philosophical concepts. Yes it‚s infantile, and it isn‚t. That‚s good. Well then, what is this story, there are intrinsic distinctions! Good, let‚s try to progress, from the point of view of terminology. It is necessary to make a terminological grouping.

My white wall, the white of the white wall, I will call: Œquality‚. The determination of shapes on the white wall I will call: Œmagnitude, or length‚. ˜ I will say why I use the apparently bizarre word magnitude [grandeur]. Magnitude, or length, or extensive quantity. Extensive quantity is in effect the quantity which is composed of parts. Recall the existing mode, existing me, is defined precisely by the infinity of parts which belong to me. What else is there besides quality, the white, and extensive quantity, magnitude or length, there are degrees. There are degrees which are what, which we call in general: intensive quantities, and which are in fact just as different from quality as from extensive quantity. These are degrees or intensities.

Now there is a philosopher of the Middle Ages, one of great genius, here I appeal to a very small bit of knowledge, he is called Duns Scotus. He appeals to the white wall. It is the same example. Did Spinoza read Duns Scotus? [This is] of no interest, because I am not sure at all that it is Duns Scotus who invented this example! It is an example which can be found throughout the Middle Ages, in a whole group of theories of the Middle Ages. The white wall. Yes! ... He said: quality, the white, has an infinity of intrinsic modes. He wrote in Latin: modus intrinsecus. And Duns Scotus here innovated, invented a theory of intrinsic modes. A quality has an infinity of intrinsic modes. Intrinsic modes, what are they, and he says: the white has an infinity of intrinsic modes, these are the intensities of white. Understand: white equals light in the example. An infinity of luminous intensities. He adds this ˜ and note that he takes responsibility because here this is new ˜ you tell me, say: there is an intensity, there is an infinity of intensities of light. Ok, not much. But what does he draw from this and why does he say this? What accounts does he settle, and with whom? This becomes important. Understand that the example is typical because when he says white, or quality, he means as well: Œform‚. In other words, we are in open discussion of the philosophy of Aristotle, and he is saying: a form has intrinsic modes. Ha! If he means: a form has intrinsic modes, it doesn‚t go without saying, not at all! Why? Because, it goes without saying that all sorts of authors, all sorts of theologians would consider that a form would be invariable in itself, and that only existing things vary in which form puts itself into effect. Duns Scotus tells us: here where the others distinguish two terms, it is necessary to distinguish three: that in which the form puts itself into effect are extrinsic modes. Therefore it is necessary to distinguish form from extrinsic modes, but there is something else. A form has also a kind [espèce] ˜ as they say in the Middle Ages ˜ a kind of latitude, a latitude of form, which has degrees, the intrinsic degrees of form. Good. These are intensities, therefore intensive quantities. What distinguishes them? How is one degree distinguished from another degree? Here, I insist on this because the theory of intensive quantities is like the conception of differential calculus of which I have spoken, it is determinant throughout the whole of the Middle Ages. What‚s more, it is related to problems of theology, there is a whole theory of intensities at the level of theology. If there is a unity of physics and metaphysics in the Middle Ages, it is very centred ˜ understand this makes the metaphysics of the Middle Ages much more interesting, there is a whole problem of the Trinity, that is to say three persons for one and the same substance, that which obstructs the mystery of the trinity. It is always said: they fight like that, they are theological questions. Not at all, they are not theological questions, it engages everything because, at the same time: they determine a physics of intensities, in the Middle Ages; they determine an elucidation of theological mysteries, the Holy Trinity; and they determine a metaphysics of forms, all of this is way beyond the specificity of theology. Under what form are the three persons of the Holy Trinity distinguished? It is obvious that there is a kind of problem of individuation that is very very important. It is necessary that the three persons are, in a way, not at all different substances, it is necessary that they are intrinsic modes. Therefore how will they be distinguished? Have we not forged ahead here into a kind of theology of intensity.

When Klossowski in his literature finds a kind of very very strange connection between theological themes of which it is said: but after all where does all of this come from, and a very Nietzschean conception of intensities, it would be necessary to see, as Klossowski is someone extremely wise, erudite, it is necessary to see what link he makes between these problems of the Middle Ages and current questions or the Nietzschean questions. It is obvious that in the Middle Ages the whole theory of intensities is simultaneously physical, theological and metaphysical. Under which form? [end of tape ˜ very little time before the end of the course.]

Cours Vincennes - 24/03/1981

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. 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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nath1as · 9 years ago

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Deleuze/Kant

Cours Vincennes : synthesis and time - 14/03/1978

We are returning to Kant. May this be an occasion for you to skim, read or re-read The Critique of Pure Reason. There is no doubt that a tremendous event in philosophy happens with this idea of critique. In going into it, ourselves, or in going back into it, I had stopped reading it a very long time ago and I read it again for you, it must be said that it is a completely stifling philosophy. It's an excessive atmosphere, but if one holds up, and the important thing above all is not to understand, the important thing is to take on the rhythm of a given man, a given writer, a given philosopher, if one holds up, all this northern fog which lands on top of us starts to dissipate, and underneath there is an amazing architecture. When I said to you that a great philosopher is nevertheless someone who invents concepts, in Kant's case, in this fog, there functions a sort of thinking machine, a sort of creation of concepts that is absolutely frightening. We can try to say that all of the creations and novelties that Kantianism will bring to philosophy turn on a certain problem of time and an entirely new conception of time, a conception of which we can say that its elaboration by Kant will be decisive for all that happened afterwards, which is to say we will try to determine a sort of modern consciousness of time in opposition to a classical or ancient consciousness of time. Why it is that it was Kant who created the philosophical concepts of this new consciousness of time, making his philosophical expression possible, does not concern us or in any case does not interest me, but what I would like to say is that it is indeed this sort of consciousness of time which takes on a philosophical status in Kant, and which is completely new. I will proceed by numbered points because I'm always working with the idea that to each point corresponds a type of concept, and once again, I will be happy if you grant me at the end of these lessons that philosophers are precisely this, that they are no less creative than painters or musicians, simply that they create in a determinable domain that is the creation of concepts. Firstly, what does Kant understand by the a priori which he opposes to the a posteriori? These are common terms. In some cases new words must be invented, and this happens with Kant when he creates the notion of the transcendental, which is a very strange notion, transcendental subject... no doubt you will tell me that the word existed before, but it was rarely used and it marked no difference from the ordinary word transcendent, whereas Kant gives it a very special sense: the transcendental subject, he almost created a word... in the case of the a priori and the a posteriori he borrows a word, but he completely renews its sense. A priori, in the first place, means: independent of experience, that which does not depend on experience. In opposition to a posteriori which means: given or givable in experience. What things are a priori? Note that I don't ask myself: does the a priori exist, which is to say, are there things independent of experience? The question of existence is secondary, we must first know what a thing is in order to be able to say and reply to the question of existence: does it exist or not? I'm saying that if it exists, what is something that would be independent of experience? Thus not givable in experience. Nothing complicated so far, Kant takes this up very quickly, the a priori in this sense is the universal and the necessary. Everything that is necessary and universal is said to be a priori. Why? It certainly fulfills the first condition of the a priori: not given in experience, because, by definition, experience only gives me the particular and the contingent. With expressions of universality and necessity it is always so necessarily, as also with certain uses of the future tense, or expressions of the type "each time": each time I bring water to 100 degrees it will boil. Philosophers have said this for a very long time: there is something in this which is not given in experience. What is it? It's the expressions: "always", "necessarily", or even the future tense. What experience has given me is, strictly speaking, that each time I have effectively brought water to 100 degrees, it has boiled, but in the formula "water necessarily boils at 100 degrees", the necessarily is not an object of experience. Similarly if I say "all objects of experience" - do I have the right to say this? We don't even know if "all objects of experience" is not nonsensical. Supposing that it is not nonsensical, "all objects of experience" are not given in experience, for the simple reason that experience is ???? Thus you can always make a summation, a sum of the objects you have experienced, but this sum is indefinite. Thus the universal and the necessary by definition are not givable in an experience since an experience is always particular and contingent. So that gives us a second determination of the a priori. The a priori was first of all what is independent of experience, in the second place it is what is universal and necessary. Third point: how can this universal and necessary be defined? There is already something extremely delicate here. To say that something is independent of experience doesn't prevent this something perhaps being applied to experience and only to it. The question of application is entirely different. When I say "water will always come to a boil at 100 degrees", I don't know where this idea of "always" comes from, since it is not given to me in experience, I don't know where this idea of necessity comes from, since it is not given to me in experience, this doesn't prevent the fact that "always" is applied to water, boiling, 100 degrees, all things which are given in experience. Let's suppose then that the a priori is itself independent of experience but applies to objects given in experience. In other words the universal and the necessary are said of objects of experience; perhaps they are said of other things as well, but they are said of objects of experience. What is universal and necessary? What would these universals and necessaries be which can be said of objects of experience? Here is introduced a notion which is famous in philosophy, that of the category. A certain number of philosophers have even made or proposed what are called tables of categories. There is a famous table of categories in Aristotle. With Kant, who did not escape a strong influence from Aristotle, there will be another table of categories. What is a category? A category is not just anything in philosophy, it's as rigorous as a scientific notion in another domain. What is called a category is a universal predicate, or universal attribute if you want. Which is to say a predicate which is attributed to, or predicated of, or said of any object. This notion of "any object" is bizarre. I say "the rose is red". What is that? "The rose is red" is not complicated, it's a relation between two concepts, the rose and red, and if I say "what is universal or necessary in that?" I can reply: nothing. Not all objects are roses, not all roses are red. Not all reds are the colour of roses. I would say that there is an experience of the red rose and that this experience is particular, contingent, a posteriori like all experience. Compare this judgement: "the rose is red" to this other judgement: "the object has a cause" or even "the rose has a cause". I see a difference straight away, which is that the concept of rose defines what will be called a class in so far as it is an a posteriori concept, the concept of rose defines a class or set. Red is a property of a subset of this set, the subset formed by red roses. I can define a set according to what it excludes and in relation to what it excludes: all that is not a rose. The set of roses is carved out of a broader set which is that formed by flowers, and the set of roses can be distinguished from the rest, which is to say all the flowers which are not roses. When I say "all objects have a cause", am I not in another domain completely? Evidently I am, I am completely in a different domain because to have a cause is a universal predicate which is applied to all objects of possible experience, to the point that I don't even need to - or I believe that - but that makes no difference because "I believe" will become an act that we will have to analyse - I believe that if an unknown object emerged in experience before my eyes, this object would not be an object if it didn't have a cause. To have a cause or to be caused is a predicate of a wholly other type than the predicate "red". Why? Because the predicate "to be caused" - to the point where we can wonder, after reflection, is that really a predicate or is it something else? - the predicate "to be caused" is predicable of any object of possible experience, to the point where it is not going to define a set or a subset within experience because it is strictly coextensive with the totality of possible experience. Moreover, we must go back. When I said that the totality of possible experience has perhaps no sense, now we have the response: the totality of possible experience makes no sense in itself, but it is precisely to the extent that there are predicates which are attributed to all possible objects, which are thus more than predicates, and this is what Kant will call conditions, they are the conditions of possible experience, it is thus via the notion of conditions of experience that the idea of a whole of possible experience will take on a sense. There is a whole of possible experience because there are predicates or pseudo-predicates which are attributed to all possible objects and these predicates are precisely what are called categories. I'll cite some examples of categories according to Kant: unity, plurality, totality (with Kant they come in threes). Reality, negation, limitation. Substance, cause, reciprocity. I'll stop there. In what sense are these categories and not predicates of the type red, green, etc...? They are categories or conditions of possible experience for the simple reason that any object is only an object to the extent that it is conceived as one, but also as multiple, having the unit parts of a multiplicity, and in this forming a totality, any object whatever has a reality. On the other hand, it excludes what it is not: negation, and by virtue of this it has limits: limitation. Any object whatever is substance, any object whatever has a cause and is itself cause of other things. That's enough to be able to say that my notion of object is made in such a manner that if I encountered a something which did not allow the categories be attributed to it, I would say that it is not an object. So there we have as a last determination of the a priori, they are the conditions of possible experience, which is to say universal predicates as opposed to empirical predicates or a posteriori predicates. I could define the categories in the simplest way as being the predicates of any object whatever. Thus you can yourselves make your list of categories according to your mood, according to your character... what would be good would be to see if everybody came up with the same list of categories. In any case you do not have the right to cheat with the word. To make your list of categories is for you to ask yourselves what is for me predicable of any object whatever. I have already given a certain list of them, with nine categories. In fact, for Kant, there are twelve of them, but I left three aside for later; you see: unity, plurality, totality, affirmation, negation and limitation, substance, cause, reciprocity or community. To finish with this first point, I am saying that the categories, qua predicates of any object whatever, are a priori, and they are conditions of possible experience; understand that it is through them that the notion of possible experience takes on a sense. To the question: does the whole of possible experience mean something? No meaning [sens] at all if we remain in an a posteriori approach, because in an a posteriori approach I am led to make an addition: the roses, the flowers other than roses, the plants which are not flowers, the animals, etc.... I could go to infinity like that and nothing tells me that I have a whole of possible experience. On the contrary, experience is fundamentally fragmented, it is opposed to a totalisation. If Kant launches this very very new notion of a totality of possible experience it is because he is in a position to define, to say: yes, there is a level where the whole of possible experience takes on a sense, it is precisely because there are universal predicates which are attributed to all things, which is to say are attributed to any object whatever. Thus it is a priori that the notion of the totality of possible experience will be founded. Is there anything else besides the categories that can be a priori, which is to say, universal and necessary? The reply is yes, and this other thing is space and time. Because every object is in space and in time, or at least in time. But you will say to me straight away, very well then, why not make a category of them, why not add space and time as two categories? Because space and time are also, it seems, predicates. Obviously, Kant has the most serious reasons to not want to and he will go to great pains to distinguish the categories on the one hand, and on the other hand space and time. There will thus be two sorts of a priori elements: the categories and space and time. Why doesn't he want space and time to be among the categories? I will give a reason very quickly which will become clear afterwards: it is that the categories qua predicates of possible experience are concepts, whereas Kant fundamentally holds that, these are a priori representations, a priori representations or concepts, while space and time are presentations. There you also have something very new in philosophy, it will be Kant's work to distinguish presentation and representation. So there will be two sorts of elements in the a priori. My second point is Kant's importance at another level, which is the notion of phenomenon, and that also is very important. There Kant operates a kind of essential transformation of a word which was frequently employed previously in philosophy. Previously philosophers spoke of phenomenon to distinguish what? Very broadly we can say that phenomenon was something like appearance. An appearance. The sensible, the a posteriori, what was given in experience had the status of phenomenon or appearance, and the sensible appearance was opposed to the intelligible essence. The intelligible essence was also the thing such as it is in itself, it was the thing in itself, the thing itself or the thing as thought; the thing as thought, as phenomenon, is a Greek word which precisely designates the appearance or something we don't know yet, the thing as thought in Greek was the noumenon, which means the "thought". I can thus say that the whole of classical philosophy from Plato onwards seemed to develop itself within the frame of a duality between sensible appearances and intelligible essences. You can see clearly that this already implies a certain status of the subject. If I say that there are appearances and that there are essences, which are basically like the sensible and the intelligible, this implies a certain position of the knowing subject, namely: the very notion of appearance refers to a fundamental defect in the subject. A fundamental defect, namely: appearance is in the end the thing such as it appears to me by virtue of my subjective constitution which deforms it. The famous example of appearance: the stick in water appears broken to me. It's what is called the rich domain of sensory illusions. So much so that in order to reach the thing in itself the subject must in fact overcome this sort of constitutive infirmity which makes it live amongst appearances. It's Plato's theme: leave appearances to find essences. With Kant it's like a bolt of lightning, afterwards we can always play clever, and even must play clever, with Kant a radically new understanding of the notion of phenomenon emerges. Namely that the phenomenon will no longer at all be appearance. The difference is fundamental, this idea alone was enough for philosophy to enter into a new element, which is to say I think that if there is a founder of phenomenology it is Kant. There is phenomenology from the moment that the phenomenon is no longer defined as appearance but as apparition. The difference is enormous because when I say the word apparition I am no longer saying appearance at all, I am no longer at all opposing it to essence. The apparition is what appears in so far as it appears. Full stop. I don't ask myself if there is something behind, I don't ask myself if it is false or not false. The apparition is not at all captured in the oppositional couple, in the binary distinction where we find appearance, distinct from essence. Phenomenology claims to be a rigorous science of the apparition as such, which is to say asks itself the question: what can we say about the fact of appearing? It's the opposite of a discipline of appearances. What does an apparition refer to? The appearance is something that refers to essence in a relation of disjunction, in a disjunctive relation, which is to say either it's appearance or it's essence. The apparition is very different, it's something that refers to the conditions of what appears. The conceptual landscape has literally changed completely, the problem is absolutely no longer the same, the problem has become phenomenological. For the disjunctive couple appearance/essence, Kant will substitute the conjunctive couple, what appears/conditions of apparition. Everything is new in this. To make things a little more modern, I would just as well say: to the disjunctive couple appearance/essence, Kant is the first who substitutes the conjunctive couple apparition/sense, sense of the apparition, signification of the apparition. There is no longer the essence behind the appearance, there is the sense or non-sense of what appears. Grant me at least that even if what I say remains just a matter of words, it's a radically new atmosphere of thought, to the point where I can say that in this respect we are all Kantians. It's obvious that thought, at that time, was changing elements. People had for a long time thought in terms which didn't come from Christianity but which fit in very well with Christianity, in the appearance/essence distinction, and towards the end of the eighteenth century, prepared no doubt by all sorts of movements, a radical change takes place: for the whole appearance/essence duality which in a sense implies a degraded sensible world, which even implies if need be original sin, is substituted a radically new type of thought: something appears, tell me what it signifies or, and this amounts to the same thing, tell me what its condition is. When Freud comes up and says that there are certain phenomena which appear in the field of consciousness, what do these phenomena refer to, Freud is Kantian. How so? In a way that is at the same time very general but also very rigorous, namely that, like all those of his era and since Kant we spontaneously think in terms of the relation apparition/conditions of the apparition, or apparition/sense of what appears, and no longer in the terms of essence/appearance. If you don't see the enormity of the reversal, admire the fact that the subject, in my second couple, the subject is not at all in the same situation. In the disjunctive couple appearance/essence, the subject is immediately condemned to grasp appearances by virtue of a fragility which is consubstantial with it, and the subject requires a whole method, it needs to make a whole effort to get out of appearances and reach the essence. In the other case, what makes the subject take on an entirely different value? It's when I say that every apparition refers to the conditions of the appearing of the apparition, in this very statement I am saying that these conditions belong to the being to whom the apparition appears, in other words the subject is constitutive - and understand this well, otherwise it's a radical misinterpretation - the subject is constitutive not of the apparition, it is not constitutive of what appears, but it is constitutive of the conditions under what appears to it appears to it. I mean that the substitution of the conjunctive couple phenomena-conditions, or apparitions-conditions ensures a promotion of the subject in so far as the subject constitutes the very conditions of the apparition, instead of constituting and being responsible for the limitations of appearance, or the illusions of appearance. There is indeed a subject, Kant will say, which is subordinated to appearances and which falls into sensory illusions; it will be called the empirical subject, but there is another subject which is evidently neither you nor me, which above all is not reducible to any empirical subject, which will be from that point on named the transcendental subject for it is the unity of all the conditions under which something appears, appears to whom? Appears to each empirical subject. It's already beautiful as a system of ideas. I hope you can feel its extent, it's a tremendous machine. To finish this second point, I'll make two corrections: Kant is at the turning-point of something, so it's more complicated than I'm making it out to be because he keeps something of the old essence-appearance difference, and effectively he will say all the time: do not confuse the phenomenon with the thing in itself, the thing in itself is the pure noumenon, which is to say it is what can only be thought, while the phenomenon is what is given in sensible experience. So he maintains the disjunctive duality phenomenon/thing in itself, noumenon. It's the duality of the couple appearance/essence. But he gets out of it and he is already in another type of thought for a very simple reason for he says that the thing in itself, it is so by nature or the noumenon - the thing in itself can be thought, it is thus noumenon, but it cannot be known. So if it can be determined, it is a completely different point of view than that of knowledge; so we don't bother with it or at least we will bother about it in very special conditions. What counts from the point of view of knowledge and of all possible knowledge is the other couple, apparition-conditions of appearing, conditions of the fact of appearing. Once again if I sum up this reversal it's the one which consists in substituting for appearance-essence, apparition-conditions or apparition-sense of the apparition. If you ask me what these conditions of appearing are, fortunately we have got somewhere because our first point gave the answer, the conditions of appearing, which is to say the conditions of the phenomenon, in so far as the phenomenon is what appears, we will not look for an essence behind the phenomenon, we will seek the conditions of its apparition, and in fact the conditions of its apparition are, the categories on one hand and on the other space and time. Everything which appears appears under the conditions of space and time, and under the conditions of the categories. By this fact space and time on the one hand and on the other the categories are the forms of all possible experience and they belong not to things as they are in themselves, but as forms of all phenomena, as forms of all apparition, space and time on the one hand, the categories on the other hand are the dimensions of the transcendental subject. Time is already completely involved here. Are there any questions?

Richard: How is the difference between the transcendental subject and the empirical subject distributed? How is it very different from the domain of being?

Gilles: Obviously he needs another notion. We start from the idea: phenomenon equals apparition. The phenomenon is not the appearance behind which there would be an essence, it's what appears in so far as it appears. I can add that it appears to someone, all experience is given to someone. All experience is related to a subject, a subject which can be determined in space and time. It's here and now that I put my little saucepan on to boil and light the fire. I would say that all apparition appears to an empirical subject or to an empirical self. But all apparition refers not to an essence behind it but to conditions which condition its very appearing. The conditions of the apparition - these are thus forms since apparitions appear in these forms, or under these forms - the conditions of the apparition are space and time and the categories. In other words space and time are the forms of representation of what appears. Given this if the apparition presupposes conditions which are not like objective essences behind it, but are like the conditions of its apparition to a given empirical self, we already have no more choice: the formal conditions of all apparition must be determined as the dimensions of a subject which conditions the appearing of the apparition to an empirical self, this subject cannot itself be an empirical self, it will be a universal and necessary self. It's for this subject that Kant feels the need to forge or to extend a word which only had a very restrained theological use till then, thus the need to invent the notion of the transcendental, the transcendental subject being the instance which the conditions of all apparition are related to, while the apparition itself appears to empirical subjects. That doesn't tell you yet very well what the transcendental subject is, you'll have to wait because it will be so involved with the problem of time. We just need for one little thing to suddenly become concrete, we mustn't demand continuous concreteness. There is the concrete and the opposite of the concrete, the true opposite of the concrete is not the abstract, it's the discrete. Discretion is the moment of thought. My aim is to arrive at a fabulous conception of time.

Comptesse: inaudible comment

Gilles: The synthetic a priori was my third point. We have to begin somewhere. If I had begun there I would have needed a completely different organisation. Quite simply it seems to me that in all I have said I have not needed to assume synthetic judgements. Third point: what is a synthesis for Kant? It is common to distinguish two types of judgements. Judgements which are called analytic and judgements which are called synthetic. By definition, a judgement is called analytic if it expresses a predicate which is already contained in the subject, i.e. there will be an analytic relationship between two concepts when one of these concepts is contained in the other. An example of an analytic judgement: A is A, it's the principle of identity. When I say "A is A" I don't go outside of concept A. I predicate A of itself, I attribute A to itself, I'm in no danger of making a mistake. "Blue is blue", you will say to me that that doesn't go very far, it's obvious... because when I say "Bodies are extended" what is that? We want to reply that it's an analytic judgement. Why? Because I couldn't have thought the concept "body" - we're not saying "thing" - without having already included the concept of extension, thus when I say "Bodies are extended" I am formulating an analytic judgement. I think Kant would say something very malicious like: OK all bodies are extended is an analytic judgement, but on the other hand "all phenomena appear in space or in extension" is a synthetic judgement because if it is true that the concept "extended" is in the concept "body", on the other hand the concept "extended" is not in the concept "phenomenon" nor the concept "body" in the concept "phenomenon". Well, let's suppose that "all bodies are extended" is an analytic judgement. At least we can be sure of one thing which is that an analytic judgement is perhaps useless but it's true. "A is A" is true, no one has ever denied "A is A". In Hegelian-style dialectical contradiction no one says "A is not A", they say "A is not non-A", but just that a thing includes in its being this non-being that it is not. So they take seriously the formula "A is not non-A" in saying that the being of the thing is inseparable from the negation of the negation (is not...not), but they don't deny at all the principle of identity. In experience we have synthetic judgements, it's even in this way that we know things. When I say "Oh look, the rose is red", it's an encounter. "Red", at first glance is not contained in the concept of rose, the proof is that there are roses which aren't red. You will say that this is stupid because isn't "red" contained in the concept of this rose here? It gets complicated because is there a concept of this rose here, is there a concept of the singular? We'll leave that aside. We will say very broadly that, apparently, "the rose is red" is a synthetic judgement. You can see how this sorts itself out. All analytic judgements are a priori, it's independently of any experience that I can say that a thing is what it is. "A is A" is an a priori judgement. Still at first glance, the synthetic judgement seems by nature to be the combination of two heterogeneous concepts, the rose and the red, it establishes a link or a synthesis between two heterogeneous concepts and is by virtue of this a posteriori. The form of this judgement is "A is B". In a certain way, I'll just say very quickly, classical philosophy before Kant, just as I was saying a moment ago, is caught in the dualist couple, in the disjunctive duality essence/appearance, classical philosophy was caught, at least in appearance, in a certain duality: either a judgement is a priori and it is analytic, or it is synthetic and it is empirical or a posteriori. It became very complicated to know in what conditions an empirical judgement could be true. There is a famous and very prodigious attempt, Leibniz' attempt, before Kant. In order to found the notion of truth, he is led to try and show that all judgements are analytic, we just don't know it, we believe in the existence of synthetic judgements because we never take the analysis far enough, which is to say to infinity, it's because of this that we believe that there are synthetic judgements. But if we could take the analysis far enough, when we truthfully affirm one concept of another, the affirmed concept is always interior and contained in the one we affirm it of, to the point that - this gives Leibniz' famous theses - Caesar crossed the Rubicon, this proposition which seems eminently to be a synthetic proposition, implies the link between two representations: Caesar crosses the Rubicon on such and such a date, at such a point in space, here-and-now, which seems to be the very signature of the a posteriori, Leibniz says that if in the concept of Caesar there was the concept "crossing the Rubicon"... is it any accident that it's the same man who is one of the creators of differential calculus, which is to say a mathematical form of infinite analysis? Evidently not, it's not an accident. What does he mean when he manages to treat "crossing the Rubicon" as a predicate which is contained in the concept Caesar exactly as "extended" is contained in the concept body? Obviously he too will have to engage in a quite astonishing sort of gymnastics of concept-creation, because afterwards he will have to save freedom, he holds to this for his own reasons, so how can Caesar be free when from the beginning of time "he crossed the Rubicon here and now" is included in his concept? And what does such a proposition of Leibniz's imply, namely: there are only analytic judgements? That necessarily implies that space and time, the here-and-now be reducible and reduced to the order of concepts. Spatio-temporal position will be treated as a predicate, which is to say as an attributable concept. Why does Kant hold so fiercely to the heterogeneity of space and time on the one hand, and on the other hand the categories, i.e. a priori concepts. Precisely because he needs there to be something which is irreducible to the order of the concept. Classical philosophy is a long discussion between the respective proportion of a posteriori synthetic judgements and a priori analytic judgements. The possibility of reducing one to the other, or else the impossibility of reducing...

Richard: How is it that we don't manage to derive the principle of identity from experience? In the example "A is A".

Gilles:

Because it's a pure empty form, A is A. A is not at all given as a generality, it's pure thought, it's generic thought. Moreover, as soon as there is an identity in experience, it's a temporal identity, which is to say that it's not a necessary identity. So "A is A" is said to be a priori precisely because it is strictly without content, it will be a rule for all possible content. So now Kant comes along and everything happens as if he discovered a new type, a third type of judgement, and he will have to invent the concept to designate this third type of judgement, namely synthetic a priori judgement. In doing so he effects an amazing forced takeover [coup de force]. For a classical thinker, still very broadly, analytic a priori judgement, that meant something, synthetic a priori judgement, that meant something, but synthetic a priori judgement - that's truly a monster. So a philosopher cannot but create monsters as new concepts. It's a prodigious monster. What on earth can it mean? Here I will use some examples which aren't even in Kant, in order to be more faithful, to try and be clearer than he is, because he has other things to do.

The triangle is white. If I blithely ask you what that is you will reply it's a synthetic a posteriori judgement. I'll reply: very good, you've passed the course. If I say "we call triangle a figure formed by three straight lines enclosing a space", three straight lines enclosing a space, what is that? I can say that it is an analytic judgement. Why? Because I'm not saying anything but "A is A". The concept of triangle is precisely three straight lines enclosing a space. This was broadly the distribution in the world of classical philosophy, the terminological coordinates of classical philosophy. Kant comes along and says: if I say that the three angles of a triangle are equal to two right-angles - elementary geometrical proposition - what is that? Is it an a priori analytic judgement or an a posteriori synthetic judgement? Stunned silence! And yet this was something everybody had known for a long time, but nobody had used this case to explode the insufficiency of certain philosophical categories, the a priori analytic judgement and the a posteriori synthetic judgement. Here he is in the process of finding something which really appeals to the taste of philosophy qua philosophy, namely the simplest thing in the world which bursts a conceptual frame. In effect this story is very curious: the three angles of the triangle are equal to two right angles. It is the very example of what is called a geometrical necessity. It's universal and necessary, and yet is it analytic?

As for Leibniz, he would have laughed at Kant's observation, this is why philosophy is so good. Leibniz's simple reply is: yes of course the concept of the triangle, if you take the analysis far enough, it's obvious that its angles being equal to two right angles is contained in the concept. But again, under what condition can Leibniz say that? Because he has also invented a mathematical discipline which he has determined as already being a topology, and which allows a sort of reduction of spatial determinations to conceptual ones. But under what condition?

Kant began by noting the impossibility according to him of reducing spatio-temporal determinations to conceptual ones. In other words, there is an order of space and time which is irreducible to the order of the concept. So Kant: I say that [the equation of] the three angles of the triangle is so little contained in the concept that to demonstrate it you have to extend a side of the triangle, raise a parallel on the opposite side... already Leibniz would say that he doesn't agree, and he would be right because if he accepts something here he would be screwed, but we'll let it go, we'll go along with this attempt of Kant's. So here is my concept: three straight lines enclosing a space. To demonstrate the equality of three angles to two right-angles, I take for example the base of the triangle and I extend it; at point C I raise the parallel to AB and I show that the three angles of the triangle are equal to two right-angles. Kant tells us we mustn't get carried away, the side didn't grow all by itself, the triangle is not a flower, it doesn't raise a parallel to one of its sides all alone, parallel to a side of the triangle isn't part of the concept of the triangle thus it's a synthetic judgement. But it's a very curious type of synthetic judgement, not at all of the "the rose is red" type, since it's a universal and necessary synthetic judgement. How are you going to explain such a judgement?

I'll take another example. "The straight line is black". Everyone understands, no problem: synthetic a posteriori judgement; I encounter it in experience, which is to say I come across a straight line which has been drawn in black. I take Euclid's definition: "The straight line is the line which is ex aequo in all its points", it doesn't matter if you use another definition. In any case, I would say that it's an analytic judgement, it's already contained in the concept of the straight line, it's even the statement of the concept of straight line. And then comes the monster, I say: "the straight line is the shortest path between two points." Is it analytic, can I say that the shortest path is contained in the concept "straight line"?

Once again, Leibniz would say: yes. Kant says no. Why? For several reasons. I'll give a vulgar reason and a scholarly reason. The vulgar reason: if one looks very closely at "the shortest", is it a predicate or an attribute? It's a question of diagnostics. Is it something else? When I say "the straight line is the shortest path", it's bizarre, is "the shortest" an attribute? If you managed to demonstrate that it's an attribute, it would be via a very complex route. It wouldn't be an attribute because "the shortest"... I'll try putting it another way: if you want to find the straight line, take the shortest, what does that mean? The shortest appears to be a predicate, but it's not a predicate. In fact, it's a rule of construction. It's the rule according to which I produce in experience a line as a straight line. You will say to me; we still have to know what "the shortest" is... the shortest is not a predicate that I attribute to the straight line, it's a rule of construction for constructing straight lines in experience in order to determine a line as straight. We find this example in one of his disciples, Salomon Maïmon, a great, great philosopher. So the shortest is the rule of construction of the line as straight, it's the means of producing in experience a line as a straight line. What does that mean?

It's obvious that a concept does not give the rule of construction for its object. In other words, the rule of construction is outside the concept. Once again Leibniz would say "not at all"; if he admitted that his whole system is screwed. At first glance the rules of construction are something very different from concepts because the rule of construction is the rule according to which one produces in experience an object which conforms to the concept. It's thus obligatory that it's not in the concept, by definition. You say: "the circle is where points are situated at an equal distance from a common point named centre", that is the concept of circle, that doesn't give you any means of producing a circle. We are already at the heart of the problem of time. When you say that a straight line is a line ex aequo in all its points, you have no means of producing a straight line in experience, you still need a rule to produce a line that is ex aequo in all its points, you still need a rule of construction to produce a figure such that it presents points situated at an equal distance from a common point named centre. And when you have said that the triangle is three straight lines enclosing a space, you have no means of producing a triangle in experience. The rule of construction of a triangle will be something else completely which will go via the circle, by the way. To produce a triangle you have to go via the circle. It's bizarre.

What does Kant mean when he says it's a judgement of a synthetic kind? In effect you will define the rule of construction of a triangle by saying that if you give me a segment of a straight line - it assumes the straight line, that goes without saying, and the means of producing the straight line -, if you give me a segment of straight line, if the two end-points are taken as the centre, whether of the same radius or varying radii, if the two circles cross, if you link the two ends of the straight line to the point where the circles cross, if the circles are of equal radius, this triangle will be called equilateral. (correction: if the radius is equal to the circle). There, I have a rule of construction.

You see that there is something amazing in the a priori synthetic judgement, it's that instead of operating a synthesis between two heterogeneous concepts, it operates a synthesis between the concept, between a conceptual determination, the triangle or the circle, and a group of spatio-temporal determinations. In effect, a rule of construction is a spatio-temporal determination. Why is it a synthesis? We have seen it, the rule of construction fundamentally relates heterogeneous concepts. Where does this power of necessarily relating heterogeneous concepts come from, since the only way we thought that heterogeneous concepts could be linked was through the contingency of experience: ah yes, this rose is red. But when I say that the straight line is the shortest path, I claim to be saying something necessary, in this sense a priori, it's geometrical necessity; it doesn't depend on experience. It is said of experience, I can check on any straight line that it is in fact the shortest path, but I don't need to. I know it from the first time, I know it at the same time that I understand the judgement. I know that it is necessarily and universally valid for all straight lines.

... namely what underlies the necessary relation between the concepts is a group of spatio-temporal determinations by which one of the concepts is put into a necessary relation with the other.

At this point my scholarly reason comes in. When I say "the straight line is the shortest path between two points", at first glance I don't see how that gives me the means to construct a straight line, but in fact, those who were here other years will remember that I had tried to show something quite obvious in geometry. Namely that "the straight line is the shortest path between two points" is not a Euclidean-style proposition, it's an Archimedean-style proposition because it implies a fundamental comparison between two heterogeneous concepts, that of the straight line and that of the curve. In effect, "the straight line is the shortest path between two points" only has a meaning in the very precise situation of the arc of a circle and the chord. In other words, it implies the method "the straight line is the shortest path between two points", it's what would be called an already pre-differential proposition referring to a pre-differential calculus which is the famous calculus of Archimedes, the calculus of exhaustion by which one stretches a broken line towards a curved line, to infinity, it implies the passage to the limit. That is why the straight line is the shortest path between two points even though the curve is not stated explicitly, the concept of the curve is not named. This judgement is devoid of sense if we don't see that it effects a synthesis between two concepts, the straight line and the curve, that it's uniquely in the comparison between the straight line and the curve in the very precise Archimedean situation that this judgement is expressed, with the passage to the limit and exhaustion, and that Kant's response on this level is: you can clearly see that it's not an analytic judgement because two heterogeneous concepts are... just as in the example of triangles, once again in order to demonstrate the equality of three angles to two right-angles, you have to erect a parallel, but the parallel is a concept exterior to the triangle. What welds these heterogeneous concepts together in the synthetic a priori judgement? Solely an operation which consists this: being a determination of space and time.

It's the determination of space and time, for example in the figure of the circle's arc and the chord, in the elevation of the parallel to one side of the triangle, it's this spatio-temporal determination which will make possible the necessary link between these concepts which are nevertheless not contained in each other, i.e. you will have at that moment a synthetic a priori judgement.

What are Kant's reasons for telling us that space and time are not reducible to categories, that is, that there are two sorts of a priori forms: space and time on the one hand, the categories on the other hand, or if you like space and time are irreducible to the order of concepts. He gives lots of reasons, but he invites us to engage in at least one thought-experiment, as it's the simplest it's the one I'll give you. He says, you see two hands, it's the paradox of non-superimposable symmetrical objects. You see two hands, not only do you see two hands but you think two hands. Let's suppose that, in reality, there are never two hands, there are always little differences, prints, traits, from the point of view of thought that is of no interest, you can always say that there are no two things alike. But you can still think, you can still represent to yourself two absolutely identical hands. Note that if I make Leibniz speak from off-stage, he would say: not at all, you believe you think it, but you can't think it, you've just stopped the concept. But we will accept this sort of dare of Kant's.

So you can think two hands which are strictly identical in their concept. And however far you go in the concept, in the characteristics of the concept and you can even think that such a line is on each. And yet... Leibniz would say: OK maybe, but if you do that you will see that there remains only one hand. Kant says that there is something irreducible in them. Kant says that he can think two strictly identical hands and that there are nevertheless two of them. They are strictly identical in their concept, each characteristic of the one has its identical correlate in the other. And yet there are two of them. And why are there two? One is the right hand, the other is the left. Or else one is before and the other is after or behind. How can that be thought, in the two strictly identical hands, that one is on the right and the other on the left? You know that however well they can be thought as identical in each of their characteristics, they are not superimposable. They are absolutely symmetrical in their smallest details and yet they are not superimposable. Kant will say that that's what finitude is.

That's what the irreducibility of space and time is. The right, the left. Here-now. Before, after. You can conceive of two objects whose concept is strictly the same, there are still two objects, for this very reason that the one is here and the other there. One is on the right, the other on the left, one is before, the other is after. There is a spatio-temporal order irreducible to the conceptual order.

But Kant doesn't invoke that reason. He also gives this famous example: two like trihedrons, opposed at their vertex, you cannot make them coincide. Why is it that you can't make them coincide? Because superimposing two figures or making them coincide implies a rotation, a rotation in a dimension that is supplementary to the figure's number of dimensions. When you have two triangles opposed at the vertex, you can make them coincide, which is to say put one on the other by making one of the triangles undergo a rotation in the third dimension. You have in that case a supplementary dimension to the dimensions of the figure. When you come to volumes, i.e. three-dimensional figures, like the two hands or the two trihedrons opposed at the vertex, you can easily make the two hands superimpose on each other if you have a fourth dimension of space. You would effect the rotation in the fourth dimension. Finitude is the fact that space irreducibly has three dimensions and not n dimensions, or that time has one dimension. We could always be told that there are theories or spaces with n dimensions, or else that time has several dimensions. I think that there's little interest in such a thing because the idea of a space with n dimensions already implies a system of problems and concepts which have nothing to do with Kant's system of concepts and problems.

Why are space and time irreducible to the order of the concept?

It's because spatio-temporal determinations don't allow themselves to be reduced to conceptual determinations, to the extent that however far you take the identity of two concepts, the corresponding thing or things will always be able to be distinguished not only by contingent a posteriori characters, but by their situation in space and time. By their position in space and time. Spatio-temporal position is not a conceptual property.

In which case we are assured of the following principle that the a priori synthesis happens less between two concepts, it doesn't happen between two concepts because in the first place, because it happens between the general concept on the one hand, and the spatio-temporal determination on the other hand. The true a priori synthesis is not between concepts like the empirical synthesis, the true a priori synthesis goes from the concept to the spatio-temporal determination, and vice-versa. That is why there can be a priori syntheses between two concepts, because space and time have woven a network of determinations which can make two concepts, however different they are, from the moment that there are rules of production, form necessary relations with each other. Thus space and time will acquire a constitutive power [pouvoir] which will be the constitutive power of all possible experience.

To better mark the difference between the order of the concept and the spatio-temporal order, I'll return to terms that I used just before. Space and time are the forms of appearing, or the forms of presentation of what appears. In effect, we can understand this because space and time are indeed a form of appearing, but they contain no specific unity. What appears is always diverse, an apparition is always an apparition of diversity: the red rose, a smell, a colour etc. So what appears is, by nature, diverse. Space and time are forms of perception, but you can see that space and time themselves have a diversity, namely the diversity of "heres" in space, any point in space being a possible "here", and the diversity of moments for time, any point in time being a possible moment.

We have thus to distinguish the diversity of what appears in space and in time and the diversity of space and time themselves. The first diversity will be said to be empirical diversity, the second diversity, the diversity of space itself or of time itself will be a priori diversity. Diversity of space. Diversity of time. The a priori diversity of space and of time constitute the forms of presentation. By contrast, empirical diversity belongs to what appears. The categories or concepts, which we have just seen are of another order than space-time determination, have a unity, it's even the function of the concept to unify a diversity. To the extent that you can in fact sense that the concept will have to bear, in a certain way, on space and time. Space and time as the forms of appearing of what appears are what Kant calls Forms of Intuition. Intuition is precisely the presentation, intuition is the immediate. Phenomena are immediately in space and in time, which is to say immediately appearing in space and in time. Space and time are the forms of immediacy. The concept is always what we call a mediation. The concept refers to the concept and it effects a unification. It is in this sense that it is not simply a form of presentation of what appears, it will be a form of the representation of what appears. The prefix re- indicates here the activity of the concept in opposition to the immediate or passive character of space and time which are given or which are the form of what is given.

Space and time are, Kant says, the form of our receptivity, while the concept is the form of our spontaneity or our activity.

What incredibly new thing does Kant bring to the history of time? Once it is said that determinations of space and time are irreducible to conceptual determinations, there would be no possible knowledge unless nevertheless and despite everything we were able to establish a correspondence between spatio-temporal determinations and conceptual determinations, and that's the sort of miracle of knowledge. And Kant constructed his whole system of new concepts to get to that point.

He's an austere philosopher, a severe philosopher, he uses all sorts of complicated words but they're never just for effect, he's not a lyrical type. I refer you to his secretaries who wrote things about his life, he has a very calm life, very ordered? Thomas de Quincey has translated and somewhat arranged, embellished the accounts of Kant's secretaries, in "The Last Days of Immanuel Kant". It's a splendid text.

There is an formula, a first formula about time which seems to me to be one of the most beautiful things said about time, it's Hamlet who says it. The formula suits is so well: "the time is out of joint". It's beautiful! It's a very beautiful formula if we understand it. What is the joint? The joint is, literally, the hinge [pivot]. The hinge is what the door pivots around. But the door? we have to imagine a revolving door, and the revolving door is the universal door. The door of the world is a revolving door. The door of the world swings and passes through privileged moments which are well known: they're what we call cardinal points. North, South, East, West. The joint is what makes the door swing in such a way that it passes and re-passes through the privileged co-ordinates named cardinal points. Cardinal comes from cardo; cardo is precisely the hinge, the hinge around which the sphere of celestial bodies turns, and which makes them pass time and again through the so-called cardinal points, and we note their return: ah, there's the star again, it's time to move my sheep!

"The time is out of joint", time is no longer coiled up in such a way that it is subordinated to the measure of something other than itself, such as, for example, astronomical movement. Time has ceased to be the number of nature, time has ceased to be the number of periodical movement. Everything happens as if, having been coiled up so as to measure the passage of celestial bodies, time unrolls itself like a sort of serpent, it shakes off all subordination to a movement or a nature, it becomes time in itself for itself, it becomes pure and empty time. It measures nothing anymore. Time has taken on its own excessiveness. It is out of its joints, which is to say its subordination to nature; it's now nature which will be subordinated to it. I can say, going quickly, that the whole of ancient philosophy maintained a subordination of time to nature, even in its most complex forms; that classical philosophy, however complicated its conceptions of time were, never put into question this very very general principle. The famous definition: "time is the number of movement".

With Kant there is an indescribable novelty. It's the first time that time is liberated, stretches itself, ceases to be a cosmological or psychological time, whether it's the world or the soul makes no difference, to become a formal time, a pure deployed form, and this will be a phenomenon of extreme importance for modern thought. This is the first great Kantian reversal in the theory of time.

So I take Hamlet's formula literally to apply it to Kant: "the time is out of joint". It's with Kant, from the point of view of the concept of time, that we can effectively say that time is out of joint, which is to say has ceased to be subordinated to the measure of movement, and on the contrary movement will be completely subordinated to it. And time will be this sort of form which is also pure, and this kind of act by which the world empties itself, becomes a desert. This is why one of Kant's best disciples - it won't be a philosopher, we never find those who understand philosophers among philosophers - is Hölderlin, and Hölderlin who, drawing on Kant against the Kantians, understood by developing a theory of time which is precisely the pure and empty form in which Oedipus wanders.

Next time I would like to see what the formula "the time is out of joint" means, applied to Kant. It really means something quite literal.

The second formula that I want to develop truly belongs only to Kant and it is part of his last, most obscure texts. Kant, at the end of his life, compiles a book which will appear after his death. He begins a sketch of something which will be called the Opus Postumum. And the Opus Postumum is very strange because it's a mix of everything. There are laundry lists, there are little impressions of everyday life, and then there is a wonderful page. In these texts near the end the idea that time is like the form of auto-affection appears more and more. It's the form under which the subject affects itself. If anything is mysterious, that is. It would be clear for space, but he also says it of time. See how he divides things up: space is the form under which something exterior affects me and time is the form under which I affect myself. It's even more mysterious than "the time is out of joint".

They're Kant's three oracles: firstly disguised as Hamlet, time is out of joint, secondly disguised as himself he says time is the form of auto-affection, the form under which I affect myself. But why does he say that? He couldn't do otherwise. If you followed the first point, time is out of joint, it no longer measures a movement, it is no longer subordinated to nature. Already, on the most basic level it's very new. What is new with someone must already be grasped on the most basic level. Before him, what did they say, very broadly. With Leibniz no problem, time is the order of possible successions, space is the order of possible coexistences. Kant wants nothing of this and can no longer accept it. The whole way in which he has posed the problem means that he cannot: it's obvious that to define time by the order of possible successions implies, at first glance, a subordination of time to a content which measures it, a content to which it is subordinated. It must be the case that time is subordinated to succession. So once he has conceived of formal time, the pure form of time detached from a movement to measure, once he has straightened time, once he has let it go like a spring, he can no longer define it by an order of succession. It's all the more significant given that to define time as succession means nothing but - of course succession is temporal, but it's only a mode of time, as coexistence or simultaneity by which we claim to define space, is another mode of time, it's not space. It's a very bad distribution. Space cannot be defined by the order of coexistence since coexistence is an idea which can only be understood in relation to time, it means at the same time. Time cannot be defined by succession because succession is only a mode of time, coexistence is itself another mode of time. You can see that he arranged things to make the simple distribution: space-coexistence, and time-succession. Time, he tells us, has three modes: duration or permanence, coexistence and succession. But time cannot be defined by any of the three because you cannot define a thing through its modes. Moreover space cannot be defined as the order of coexistence since coexistence is a mode of time. He is very very good on this point.

He will say - and I want you to admire the simplicity - you will define space as simply the form - and above all not the order since order still refers to a measure of something to measure in time - as the pure form, of what? Space is the form of exteriority. That doesn't mean that it comes from outside, but it means that everything which appears in space appears as exterior to whoever grasps it, and exterior from one thing to another. It is not exteriority which ???? space, it's space which constitutes the form of exteriority or which constitutes exteriority as form, as pure form. As he has just defined space as the form of exteriority, it must be the case that time is the form of interiority. It's the form under which we affect ourselves, it's the form of auto-affection. Time is the affection of self by self.

I ask you to consider that this second point follows from the first. So, the first paradox is what does it mean that time is out of joint; the second is what does it mean that time is the form of interiority.

Cours Vincennes - 21/03/1978

Why wouldn't there also be a synthesised or electronic way of handling philosophy?

Last time I tried to determine a certain number of very precise Kantian notions: a priori, synthesis, etc... but very much as a function of what seemed the essential thing to me, namely a radical reversal in the position of the problem of time in relation to philosophy. It's a critical reversal, like a critical point. I proposed last time that we take as three arbitrary formulae, but it's very dangerous, but never mind there are three key formulae that aren't Kant's but under which, it seems to me, the three great novelties or the three great reversals that Kant operates on the notion of time group themselves. So if we can manage to eliminate everything that is facile in this evocation of literary formulae in relation to a conceptual study of philosophy, the first formula to which Kant would give a powerful content is that of Hamlet: the time is out of joint. The second formula is anonymous, and would be something like this: till now the task we have given ourselves was to represent space, the moment has come to think time. Third famous formula, given by an author who had nothing to do with Kant: "I is an other". I believe that if we separate these expressions from their contexts, they suit Kant admirably, if you take them as abstract declarations. Maybe that will allow me to understand in itself the formula "I is an other", as well as to understand in itself the formula "the time is out of joint". I have asked Gilles Châtelet to bring a contribution to the commentary of this first formula. So I'm taking us back to the level of the first formula "the time is out of joint", how is it that Kant's philosophy posits a time which is in the process of getting out of joint. The joint was this sort of pivot around which time turned, in other words, in a certain tradition of antiquity, time is fundamentally subordinated to something which happens in it, and this something can be determined as being change, the subordination of time to change, time will thus measure the changing of what changes, or else, which amounts to the same thing on another level, it will be subordinated to movement, the subordination of time to movement, I say that that amounts to the same thing on another level because movement qua local movement is the purest form of change, which is to say the perfect form of change; that goes back to things in Aristotle and which cover the whole of Greek philosophy. Or else, which again amounts to the same thing on another level, subordination of time to the course of the world, and it's in this sense that the classical definition of the Greeks appears: time is the number of movement. What does that imply? That implies a subordination of time to change, to movement, to the course of the world. That implies that time is as if bent, it becomes circular. It is a time, independent or not of questions of the eternal return which are posed in a completely different manner, time is cyclical. And indeed, to the extent that it is the number of movement, it will measure the movement of the planets - see all of Plato's prose writings on the eight movements of the eight planets - and the great circle that will measure the time it takes for the eight planets to come back to the same respective position, the eight circles of the world, you would have thus a great circle of circles whose point would be assigned by the planet's return to the same respective position, you would have the world's year. But this time become circular is but one with time subordinated to change, to movement, and to the course of the world, and it's the great idea which runs through all of ancient philosophy: time as the image of eternity. The circle of time, in so far as it measures planetary movement, and the return of the same, it's precisely this time become circular. In the Timaeus there were some very beautiful pages on the arc of the Demiurge which makes circles, this bending activity. However, this time as an image of eternity, the cyclical figure of time subordinated to movement and whose secret will be the periodic return of planets to the same position relative to each other, is indeed a time which is the image of eternity. I would say that all of the time of antiquity is marked by a modal character, and in effect the word appears all the time: time is a mode and not a being. No more than number is a being, it's a mode in relation to what it quantifies, in the same way time is a mode in relation to what it measures. Obviously, it's not a matter of just taking Kant like that, it doesn't happen only in his head, there's a very long scientific evolution which find its philosophical expression there, but it had already found, no doubt with Newton, a scientific expression. Everything happens as if time "deployed itself" [se déployait], but we must take "deployed itself" in its strict sense, which is to say unrolled itself, which is to say lost its cyclical form. What does that mean that time becomes a pure straight line. It's exactly as if you were holding a coiled spring and you let it go. Time becomes a pure straight line. It reminds me of Borges, the true labyrinth is the straight line. When time becomes a straight line, what does that mean and what change does that imply? Still speaking musically, I would say that with Kant time acquires a tonal character, it ceases to be modal. We can find no other images to indicate the violence of such an operation in relation to the thought that, truly, the circle snaps, like a spring that uncoils itself, which becomes a pure straight line. You can see that the cyclical line, when time is cyclical, is a line which limits [borne] the world and just saying that time becomes a straight line means that it no longer limits the world, it will traverse it. In the first case, cyclical time is a time which limits and which thus carries out - which has always been the supreme act for the Greeks - carries out the act of limitation. When time becomes a straight line, it no longer limits the world, it traverses it, it is no longer a limit in the sense of limitation, it is limit in the sense: it's at the extremity [bout], it never ceases to be at the extremity, it's the sense of a passage to the limit. The same word "limit" radically changes in sense, it's no longer the operation which limits something, it's on the contrary the term towards which something tends, and at the same time the tendency and that towards which it tends, that's time. How can we explain that. It's precisely a matter of assigning the importance of this time become straight line. It's not a simplification, it changes everything in the very atmosphere of time and in the operation of time. The simplest way is to refer ourselves to a poet who claims to be inspired by Kant. That's Hölderlin. For the moment our problem is solely to say what is the importance of the change when time ceases to be circular, ceases to be a circle in order to become a straight line. We must keep in mind both that Hölderlin claims to be inspired by Kant and that he has many things to say on what happens when time becomes a straight line. Hölderlin poses the problem at the level of Greek tragedy, and in particular he opposes Greek tragedy such as it appeared in Aeschylus and Greek tragedy such as it appeared in Sophocles, and above all in Oedipus and in Antigone. You will see straight away that the schema that Hölderlin develops, and that other commentators of Sophocles took up afterwards, concerns the very heart of our problem. It amounts to telling us that there is a certain sense of the tragic for the Greeks which is the tragic element of cyclical time. We find it very easily in Aeschylus. What is the tragic cycle of time? The tragic cycle of time is, broadly, like three unequal arcs of a circle; there is the moment of limitation; limitation is nothing other than justice, it's the lot assigned to each. And then there is the transgression of the limitation, the act which transgresses. The moment of the limit is the great Agamemnon, it's the beauty of royal limitation. Then there is the transgression of the limit, which is to say the excessive act [l'acte de la démesure]: it's Clytemnestra assassinating Agamemnon. Then there is the long atonement, and the tragic cycle of time is the cycle of limitation, of transgression and of atonement. The atonement is Orestes who will avenge Agamemnon. There will be the re-establishment of the equilibrium of the limit which for a moment was overstepped. Notice that this tragic time is modeled on astronomical time since in astronomical time you have the sphere of fixed points which is precisely the sphere of perfect limitation, you have the planets and the movements of the planets which, in a certain way, break through the limit, then you have the atonement, which is to say the re-establishment of justice since the planets find themselves in the same position again. And in this formula of the famous tragic destiny, as they say, it's settled from the beginning, and when the tragedy begins it's already done: as Aeschylus' text itself says, at the moment when Agamemnon goes into his palace and is about to be assassinated by Clytemnestra, it's already done. But at the moment when Clytemnestra assassinates him, an act of excess and injustice, of violation of the limit, the atonement is already there. It's this sort of cyclical destiny. Time is a curve. Whereas in some splendid pages, Hölderlin says: what is the novelty of Sophocles? In what respect does Sophocles found in the end the modern sense of the tragic? He is the first to un-curve [décourber] time. It's the time of Oedipus. He says that before Sophocles, in the Greek sense of the tragic, it's man who eludes the limit. You can see, in the limitation-limit, man transgresses the limit and in so doing eludes the limit; but with Oedipus one can no longer say that it has the atmosphere of someone who transgresses the limit, who eludes the limit. In the case of Oedipus, it's the limit which is elusive. Where is it? It's the limit which becomes passage to the limit. Splendid expression of Hölderlin's: in Oedipus, the beginning and the end no longer rhyme. And the rhyme is precisely the arc of the time bending in such a way that beginning and end rhyme with each other. There was atonement for the injustice. In Oedipus time has become a straight line which will be the line on which Oedipus wanders. The long wandering of Oedipus. There will no longer be any atonement, even if only in the form of a brutal death. Oedipus is in perpetual suspension, he will travel his straight line of time. In other words, he is traversed by a straight line which drags him along. Towards what? Nothing. Heidegger will be able to say later that it's towards death. Heidegger for his part will draw from the straight line the idea, which is not wholly un-Kantian, the idea of a sort of being-towards-death. We can see well indeed that in the case of Oedipus, in Sophocles' tragedy, the beginning and the end do not rhyme, and moreover there is a zero-instant. Hölderlin adds that this un-curved time, such that the beginning and the end no longer rhyme together, and it's precisely because there is a caesura in this time, thus a pure present, that there will be - and it's this caesura that will distribute it - a before and an after, and it's this before and this after which do not rhyme. For the schema of cyclical time is substituted a time as straight line, marked by a caesura, a caesura which distributes a non-symmetrical before and after. It's very important for us for time as a straight line contains the possibility of distributing a non-symmetrical before and after, of producing a non-symmetrical before and after using a caesura. We can call this caesura the pure present. Hölderlin's analysis is admirable however because he tries to show that this form of time, the caesura which distributes a before and an after, thus the linear form of this time marked by a pure present according to which a past and a future are produced in time, well this time is that of the modern consciousness in opposition to the consciousness of antiquity. Since I borrowed the formula from Hamlet, what strikes me, independently of dates, is the extent to which the whole schema that Hölderlin constructs for us to understand what he considers to be the novelty of Oedipus, the extent to which that applies to Hamlet. For those who remember Hamlet, it's curious the extent to which it's a linear time where something is always elusive, it is no longer Hamlet who eludes the limit, it's the limit which eludes Hamlet, as if it was spinning the straight line. And there is a caesura. For Oedipus, Hölderlin assigns the moment of the caesura to the intervention of Tiresias, the intervention of the seer. It will constitute the pure instant, the pure present from which a past and a future will be produced on the straight line, which is to say a before and an after which no longer rhyme together. And in Hamlet there is a moment which seems extraordinary to me: Hamlet hesitates a great deal in his task of avenging his father: the limit is literally elusive. When he hesitates a great deal to avenge his father it's the same story as Oedipus. For a long time it's as if it's the time before, but we can't yet say "before" since the before and after are only distributed by the caesura which is to say the moment of the pure present; and then his step-father, who wants to get rid of him, sends him on a sea trip. Well the sea trip is so fundamental that Hamlet returns from it saying: "there is something dangerous in me", which he would never have said before, as if the sea trip had made him capable of something which he was not capable of before. The sea trip has played the function of the caesura and has distributed on the straight line of time a before and an after which are non-coincident, non-symmetrical. We will see all that in this quite beautiful, obscure but beautiful text of Hölderlin's: "At the extreme limit of the rift nothing in fact remains any more except the conditions of time or of space [here Hölderlin is speaking like a Kantian]. At this limit man forgets himself because he is wholly inside the moment. God forgets because he is nothing but time. And there is infidelity on both sides, etc." The categorical turning-away [détournement], what is it? It's that in so far as time is cyclical, there is a sort of God-man relationship which is one with destiny in Greek tragedy. When time becomes a straight line, there is also something which separates. In Hölderlin's very beautiful commentary it's the double deviation in the same course of linear time which will separate man and God, God turns away from man who turns away from God. Which is why Oedipus is said by Sophocles to be "atheos", which does not mean atheist, but he who is separated from God. So much so that God is no longer the master of time, the one who curves time, and man is longer himself ???? encircled in a sort of harmony with God, in this sort of relationship with God, man is no longer anything but the caesura which prevents the before and after from rhyming together, which distributes a before and an after which do not rhyme together. I would simply like you to begin to feel the importance of this time which becomes a straight line. It doesn't mean simplification of the figure of time at all, on the contrary I would like you to feel an intense complication of the figure of time. Time is no longer subordinated to something which happens in it, on the contrary it's everything else which is subordinated to time. God himself is no longer anything but empty time. Man is no longer anything but a caesura in time. In The Critique of Pure Reason, there is a very famous passage, also very very beautiful, which is called "Anticipations of Perception". I would just like to show that, at a completely different level, Kant tells us a story which is the same one that Hölderlin told afterwards. But it's not in relation to Greek tragedy. Oddly enough it happens to be in relation to scientific physics. So there are twelve extraordinary pages entitled "Anticipations of Perception". Kant tells us that space and time are what are called extensive magnitudes. What does extensive magnitude mean? It's not complicated, in Latin an extensive magnitude is one which accepts the formula "partes extra partes", the exteriority of parts, which is to say an extensive magnitude is one whose parts are apprehended successively so that, all quantity being at the same time multiplicity and unity - when you say, for example, this is twenty metres long, it's the unity of a multiplicity - extensible magnitude or extensive magnitude will be defined in the following way: the multiplicity refers to a gathering of parts into a whole. That's an extensive quantity. But time is like that: a minute, another minute, and then you say that's it, that an hour has passed. You can see the succession of parts in their apprehension, the gathering into a whole: an hour. Space and time are extensive quantities, no difficulty there. Kant adds: but there you have it, the real in space and time - you recall that the real in space and time is what appears in space and time, it's the phenomenon since with Kant the phenomenon is no longer an appearance, it's the fact of appearing - the real in so far as it appears in space and time, no doubt it also has an extensive quantity, there is the space of the table. There's no more to go over on this point; it's precisely what Kant calls a synthesis. But the real in space and in time doesn't only have an extensive quantity, it also has an intensive quantity. What is an intensive quantity? It's what fills space and time to such or such a degree. We can see straight away the difference between extensive quantity and intensive quantity since the same extensive space can be filled to varying degrees. An example: the same space can be filled by a more or less intense red, the same room can be filled with a more or less intense heat, the same volume can be filled with a more or less dense matter. Kant will even distinguish the two questions fundamentally: can emptiness in space and time be conceived, and another question, namely that space and time can be filled without there being any void in them, can be filled varying degrees. So what is the intensive quantity of the real in so far as it fills space and time? Moreover, there is not just a real which fills space and time, there is a real of space and time, it's intensive quantity. In opposition to what we have just said about extensive quantity, the two fundamental characteristics of intensive quantity according to Kant - and this will be very important for all subsequent theories of intensity - first characteristic: the apprehension of an intensive quantity is instantaneous, which is to say that its unity no longer comes from the sum of its successive parts, the unity of a given intensive quantity is apprehended in an instant. Which amounts to saying that when I say "it's 30 degrees", the 30-degree heat is not the sum of three times ten degrees, it's at the level of extensive quantities that thirty is 10+10+10, but thirty degrees is not three 10-degree heats. In other words, the rules of addition and subtraction are not valid for intensive quantities. The apprehension of the unity of an intensive quantity happens in an instant. Second characteristic: the multiplicity contained in an intensive quantity is no longer referred to a succession of parts exterior to each other, but refers to a variable proximity to degree zero. I can say that each time there is something which fills space and time, I would say or rather Kant would say that he has before him an empirical intuition. Intuition, you will recall, is the faculty of receiving what is given, but the given is given in space and time, so intuition is not at all a magical faculty, it's the faculty of receptivity. I receive something which is given, and in this sense I have an empirical intuition. But to the extent that what is given has an intensive quantity, which is to say a degree, I grasp it in a relation to its production starting from zero, or its extinction... or the real which fills space and time from the point of view of its intensive quantity is grasped as produced starting from degree zero or as extinguishing itself, i.e., rejoining degree zero. At that point the question is not at all one of knowing if there is an empty space and time, the question is of knowing that in any case there is an empty consciousness of space and time. And there is an empty consciousness of space and of time as consciousness determined by and as a function of degree zero as the principle of production of all reality in space and time - production starting from zero or the principle of extinction. I don't want to make associations that are too forced, but at the physical level of intensity in Kant, you can do what Hölderlin ?????, namely the straight line of time marked by a caesura which is intuition = 0; what he will call the empty formal intuition, from which the real which fills space and time will be produced, and it's this intuition = 0, this empty intuition which constitutes the caesura. It's according to this caesura, this degree zero implied by all intensive quantity, which is naturally correlated with time as empty form, as pure line. So on time as a pure line the caesura of degree zero is marked, which will mean that before and after will no longer rhyme together. Again the question is not: is there an empty time and space, the question is whether there is an empty consciousness of time, by virtue of the nature of time itself. In other words God has become time, at the same time that man became caesura. It's hard, we understand nothing, but it's beautiful. That's all I wanted to say on time that's out of joint. Intensive quantity effects a synthesis between the degree zero that it implies, from which it is produced, and time as pure line or empty form. Intensive quantity as degree of the real which fills a space and a time effects the synthesis between a degree zero from which this real is produced or in which it extinguishes itself, and on the other hand time as empty form or pure line. So much so that there will be a complementarity between the function of the caesura which intensive consciousness plays in time and the empty linear form that time takes on. Hence, as Hölderlin will say: man (the consciousness of time) is no more than a caesura, God is no more than empty time. It's the double turning-away [détournement]. Kant didn't go as far as that, for a simple reason that I will explain: in effect Kant subtracted God and the soul from knowledge. He gave them a function in the field of knowledge, but God and the soul were not known as such since we only know phenomena, we only know what appears. But he didn't suppress either God or the soul since he was to give them a quite different function, a moral, practical function. But from the point of view of knowledge, Gods passes into empty time just as the soul passes into the caesura. Is that any better? True lived experience [le vécu] is an absolutely abstract thing. The abstract is lived experience. I would almost say that once you have reached lived experience, you reach the most fully living core of the abstract. In other words, lived experience represents nothing. And you can live nothing but the abstract and nobody has ever lived anything else but the abstract. I don't live representation in my heart, I live a temporal line which is completely abstract. What is more abstract than a rhythm? For the Stoics, they are at once so new in relation to antiquity, and at the same time they have nothing to do with it, they employ "limit" in a wholly different sense. The limit for them is no longer the limit assumed by philosophers of the Platonic type, neither is it the other limit... Kant's ?Anticipations of Perception? means something very simple, which is that you can't say anything about perception, a priori, if there is a colour that is called red and another that is called green, that's to do with the given, you cannot say it independently of experience, it's given in experience. There are two things that you can say a priori, which are: whatever there is that is given in space and time, what is given in space and time is an extensive quantity, but also has a degree, which is to say an intensive quantity. That is an a priori judgement. Which is to say nothing would come and fill space and time as extensive quantities if what comes to fill them did not also have a degree. So I anticipate perception since in this I have a determination, it's the only a priori thing I can say. So there is anticipation. With Epicurus it's not at all in this sense. The Epicurean definition of time will not even be the novelty of a Stoic form of time, it's typically modal time. Here I would very much like Gilles Châtelet to come in and say, from his rather mathematical point of view, precisely how this conception of time as straight line is fundamental.

Gilles Châtelet (summarised because the taped recording is inaudible): With Plato there is a time which is created, which is to say there is a transcendence somewhere which is above time and which has, in correlation with this, a higher dimension. This time of Plato's measures periods, it's a set of periods and it assures the repetition of identities in the stars, the calendar. The fundamental thing to retain is that time is a number. This time above the market measures order. Time in Plato describes order, chaos has no time for example. Time is a sort of calendar that expresses the order of the world: it's a system of coordinates of order, it is in the world, it's a worldly being. In Aristotle everything is set out through movement and time is in movement, it is interior to mass. Time is attached to the body. Time will be purely astrological, but we owe to Aristotle the notion of an eternal, infinite and uniform time. But with Plato and Aristotle we have a cyclical representation. In Plotinus there is an abstract operator which is called the One, which is without any qualification and something degrades once we leave the One. Certainly time measures degradation in relation to eternity. Plotinus says that time is the irreparable addition of being to itself. Time is a fall, i.e. a degradation, and Plotinus speaks of aspiring towards God. The mathematical figure which would go with what Plotinus says is called a projective straight line, time is a straight line, but a straight line which has been curved. It's not a circle either. It's a circle minus one point (the One). Time in Plotinus would be a sort of projective time, there is already the idea of irreversibility. In Plotinus time flows from the One and the One is transcendent to time. Time is not exactly a cosmic being, it's the soul which appreciates time in so far... Time is already an equivalent of eternity, it has neither beginning nor end and the point outside the circle is not in time, the One is above, we never begin. It's rather paradoxical. In Kant time becomes a condition of possibility of phenomena. The succession of phenomena implies time, so it is time which is transcendent. Time is what is called a multiplicity, it's clearly said, it is uni-dimensional and above all it is ordered. In the end he says that it tends towards a straight line. But what is a straight line?... Time as a parameter gives the trajectory... The real straight line is a function, time becomes the condition of a function; it's not the image of representation, it's the function itself. There is the possibility of having a function of time. In what sense is Kant completely modern? Because temporality is defining a topology... a straight one... But Kant's essential idea is that his abstract space is pure parameter. There are two things in Kant: firstly a technological revolution in the sense that it is clearly affirmed that time is a real straight line, but there is also a notion of function.

Gilles Deleuze: You're saying something very important, namely that with Kant time ceases to be a number or measure and becomes parameter. I would like you to explain the difference between a number or measure and a parameter?

G. Châtelet: The parameter is not a result. A number, for the Greeks, is simply a measure, here the measure of time is possible because... In mathematics parameter has no definition, it's simply a notion. Time become parameter is no longer a result, it becomes an initial given. A parameter is what is given, what varies.

Deleuze: I think that it amounts to exactly the same thing: to say that time ceases to be a number or that time ceases to measure something and thus is subordinated to what it measures, and that time becomes a parameter, time is related to a problem of constitution. When I said that time un-curves itself, becomes a straight line... There is something equivalent in this modern conception of time where it is at the same time that an empty form of parametric time appears and a complementarity with something which makes a function, whether it is the caesura in the tragedy, or else the cut in mathematical instrumentation. I am just a bit bothered by the key role that Gilles Châtelet gives to Plotinus. In antiquity it is much more complicated than has been said till now. There were in fact two directions and the two directions had at least something in common: in the two directions time only has a modal character and never a ???? character. However the two directions are time as number of movement, thus subordinated to the physical cosmos, subordinated to physis, and then Plotinus breaks away there, but he is not the first to break away, and he makes a conception of time which is subordinated not to physis but to the soul. I wouldn't completely agree with Gilles Châtelet on the importance of this point, of Plotinus, and on the one hand the two attempts: time subordinated to the soul, time subordinated to physis maintain or at least have in common the affirmation of a purely and uniquely modal character of time, thus time as the image of eternity, a secondary and derived character of time, and the two have a point of convergence in the Antique theory of the soul of the world. I would not make of Plotinus a...

Comptesse: [inaudible comment]

Gilles: Transcendent in relation to Kant. Once again there are two notions. The Kantian notion is transcendental, time is transcendental, but the whole Kantian notion of the transcendental is created in order to refute the classical notion of the transcendent. The transcendental is above all not transcendent. I would like to move very quickly to the second point. I'm going very quickly. I would say that the second formula that I would like to apply to Kant is... but thinking time is really the most difficult thing - it's the phase of philosophy as critical philosophy, as modern philosophy defined by Kant under the form of a critical philosophy. In classical philosophy, what is the other of thought. The other of thought is above all space. It's space. Space is conceived as limitation. It was conceived as an obstacle and a resistance, it is also limitation. Why? Because it happens that my thought is referred to a thinking substance that is itself unextended, thought is the attribute of a thinking substance that is itself unextended, but this thinking substance is finite in body. It is finite in body: it's the famous problem which will poison classical philosophy, namely the union of the soul as thinking substance and the body as extended substance. And the fact that the soul is finite in body, even though the soul is in itself unextended (you can see that it's an inextricable problem: how is it that something unextended can be finite in something extended, it will produce all sorts of paradoxes), this in fact introduces a fundamental limitation of thought since it will be the source of all the errors, of all the illusions which not only create an obstacle to thought, but limit thought. Third characteristic: if space is the other of thought, I'm saying that it's an other of, literally, alterity. Extended substance is other than thinking substance even though it is uni-substantially opposed, hence the well-known position of Descartes in which there were three substances: thinking substance, extended substance and the union of thinking substance and extended substance. With the Kantian transformation the aspect of everything changes. Why? We remember time become straight line, and I can no longer say that what is important is space as obstacle or resistance to thought, or as limitation of thought. Here it's time which ceases to be subordinated to space, it takes on an independence at the same time that it acquires this form that we have seen, this pure form, and it's not time which takes the place of space, it is not an obstacle to thought, it is the limit which works thought from the inside. For the notion of external limitation is substituted the notion of internal limit. Time is the limit which works thought over, which traverses thought through and through, it is the inherent limit, a limit interior to thought, whereas in classical philosophy it's space which is determined as the exterior limitation of thought. So everything happens as if the "enemy" of thought was within. It does not receive it from outside. There we have a sort of fundamental change. To think time means to substitute for the classical schema of an exterior limitation of thought by the extended, the very very strange idea of an interior limit to thought which works it from the inside, which doesn't at all come from outside, which doesn't at all come from the opacity of a substance. As if there was in thought something impossible to think. As if thought was worked over from the inside by something that it cannot think. From this point the problem, in Kant, will no longer be that of the union of the soul and the body, which is to say the union of two substances one of which is extended and the other unextended. The problem will no longer be the union of two distinct substances, it will be the coexistence and the synthesis of two forms (they're completely different, two forms and two substances) of one and the same subject. Instead of the union of two substances, the synthesis of two forms of the same subject, which implies that the subject is not substance. What are these two forms which will have to unite - I can no longer even say in the same subject since substance will not be inherent in the subject - they are two forms for the same subject. Now this subject will be traversed by this line of time; the subject is as if traversed by two forms and is himself nothing other than the synthesis, namely the most mysterious point, the synthesis of these two forms. What are these two forms? They're on the one hand the form of thought, and on the other hand the form of the internal limit of thought. What does that mean in concrete terms? The form of thought is in the first place the act of "I think", the "I think" as act or as determination. To say "I think" is to determine something. What? We will see later. The form of equal thought, in the most universal sense "I think" which is to say that it's thought in so far as it is related to a subject; but I don't have the right to say that it's a substance. Second determination of the form of thought: as Kant says, "I think" is the slightest [la plus pauvre] of representations, it's the slightest of thoughts which accompanies all thoughts. Self = self, it's the "I" of "I think". The "I think" is the universal form of determination, but in a sense I determine nothing and in "I think" the determination is at its emptiest. Concretely acts of thought are concepts. We have seen that a priori acts of thought are particular concepts called categories. So the form of thought is the "I think" and the categories taken together, the "I think" together with what it is that "I think", namely the categories or the predicates of any given object. These are what the forms of thought are. Kant will also use the term ?forms of spontaneity?, when "I think" is the act of determination and that implies an activity which is the activity of thought. Kant will reserve the word ?spontaneity? to qualify the form of thought in these two cases. But what else is there besides these two forms of thought? We have seen the form of receptivity or the form of intuition. In the form of intuition we also have two things, just as a moment ago we saw that the form of thought is the self, the "I" of "I think" and it's also the concept as act of thought, the a priori concepts, which is to say the categories, the forms of receptivity are space and time. There are two forms twice. Last time I said that space is the form of exteriority, time is the form of interiority, this doesn't prevent these two forms from having in common the fact of being two forms of intuition or two forms of receptivity. The form of receptivity is double: form of exteriority = space, form of interiority = time, but the two together are the form of receptivity. On the other hand there is the form of spontaneity which is the "I think" and the categories. You can see, and this is very important, how it unfolds: you have a first great duality: form of intuition and form of spontaneity, form of receptivity and form of spontaneity, and each one of these two great forms has two aspects. The form of receptivity has two aspects: exteriority-space, interiority-time, the form of spontaneity has two aspects: the self of the "I think", the I = I, and the concepts that I think, the a priori concepts. Kant's problem is howthe same subject, or self, can have two forms which are irreducible to each other (irreducibility of space and time on the one hand, and of the concept on the other hand), how = the same subject can have two forms, principally the form of time and the form of thought, and that according to the form of time, it is receptive, it is accepted, and according to the form of thought it is spontaneous, it is determining, it effects determinations. It is no longer at all a matter of knowing how the soul is united to the body, the answer to the union of the soul and the body will evidently follow from the problem reworked in this way, namely the synthesis of the two irreducible forms of the same subject, or for a subject. Which amounts to saying that for the same subject there is the form of spontaneity of thinking and the form of receptivity of time. It is by virtue of this that time is already the author of thought. And the Kantian synthesis is obvious: the synthesis is something which separates or rends and this sort of Kantian self is rent by these two forms which traverse it and which are completely irreducible to each other. So where does the harmony come from, how can this limping subject function, he who can think nothing without what he thinks having a correlate in space and time, who finds nothing in space and time without it having a correlate in thought, and yet space and time and thought are two absolutely heterogeneous forms. It's literally a subject who is fundamentally split, it is traversed by a sort of line which is precisely the line of time. So much so that I would say, as a third point, that in classical philosophy the other of thought was the other of alterity; with Kant something absolutely new begins: the other within thought. It's an other of alienation. Of course Kant does not use this word, but the post-Kantians will produce a fundamental theory of alienation which will be revealed in its most perfect state in Hegel. The difference between the other of alterity, which is really an exterior other which creates an obstacle for thought, it is the other of alienation which is this interior limit. What is this alienation? The alienation of the subject in Kant is precisely this fact that it is as if torn by the duality of the two forms, each of which belongs to it as much as the other, form of receptivity and form of spontaneity. Suddenly we are on the verge of understanding what Rimbaud's formula "I is an other" could mean. "I is an other" is in the first place a formula of Rimbaud's, it's in the letters. It's the most classical context possible, it is purely Aristotelian for the two times Rimbaud comments on the expression "I is an other", he issues this formula with an extremely classical philosophy as its philosophical support. It is obvious that Rimbaud had a teacher who gave him a course on Aristotle. It's letter II in the Pléiade edition, 1971: "I is an other. Too bad for the wood which finds itself a violin." Letter to Paul Dominique: "For I is an other. If the tiger awakens... I witness the hatching of my thought, I watch it, I study it." Aristotle tells us that there is matter and then there is form which informs [informe] matter. Matter is the copper, the bugle is the copper which has been poured into this form. Nothing could be more classical, and Rimbaud assimilates himself to a matter and says: thought forms me. In the other example, the wood becomes violin, it is given the form of the violin and it receives its capacities. Rimbaud draws from this the formula "I is an other" which obviously exceeds the context. His business is to find the poem, the appropriate poetic act. It's Kant who will do the philosophical work which corresponds to the formula "I is an other". We must at all costs, for Kant makes reference to this, without even saying it, we must start from the cogito in Descartes. Obviously I would like to spare you a lesson on Descartes, but everything comes from this formula: "I think therefore I am", I am a thing that thinks. That is the Cartesian development exactly, but it is summarised as "I think therefore I am". But the complete formula is "I think therefore I am", it being understood that in order to think it is necessary to be, what am I? I am a thing that thinks. You can see the progression: I think, I am, I am a thing which thinks. I think = determination. ?I am? is the position of something indeterminate; I am a thing which thinks, the thing qua determined. Follow me, there are three terms: a determination, I think; a thing to determine, namely an existence or a being; thirdly the determined, namely the thinkable thing. The determination determines something to be determined. You will tell me that if that's all there is, that doesn't go very far. I have indeed three things then: I think, I am, I am a thing that thinks. The "I think" determines the "I am" as a thing that thinks. At first glance that seems to be impeccable. And now Kant comes along and says: not at all, he has forgotten a term, it's not at all complicated enough. And Kant will correct, he says, OK, I think = determination - and here we are fully in the future of German philosophy - in order to think it is necessary to be, OK, so the determination implies something indeterminate which is to be determined by the determination. I need this complicated formula for a very simple thing. You can see, I think therefore I am, it's quite simple, I think is a determination, the determination implies something indeterminate which is precisely to be determined by the determination. So, I think, I am, that works. At that point he makes a cut, a caesura: he says: I think therefore I am, very well, but you cannot conclude from this "I am a thing that thinks". Kant saw a flaw there in what the other believed to be a sort of continuity that nobody could refuse him. Why does it go from "I think" to "I am"? Once again, OK, the determination implies something indeterminate to be determined by the determination. But, Kant says, that doesn't yet tell us the form, under what form the indeterminate (which is to say the I think) is determinable by the determination. ... The determination, the indeterminate existence, the existence determined by the determination, and Descartes thought he had a continuum of thought. The determination was the "I think", the indeterminate existence was the "I am", the determination determined the indeterminate: I am a thing which thinks. Kant says: I think = determination, I am = indeterminate existence implied by the I think; in order for there to be a determination there must indeed be something to be determined. But now, we still must be told under what form the indeterminate, the to-be-determined, what must be determined, we still must be told under what form the indeterminate existence is determinable by the determination. Descartes has only forgotten one thing, namely to define the form of the determinable. So there were not three terms, the determination, the indeterminate and the determined, there were four terms: the determination, the indeterminate, the determinable form and the determined. If you understand that you have understood everything because you have Kant's reply. Under what form is the indeterminate existence such as it is implied by the I think, under what form is it determined? The "I think" is a determination, which is to say a spontaneous act. It implies an "I think", but a completely indeterminate "I think". Descartes told us: well yes it's completely indeterminate, but what difference does that make? Since the determination "I think" is enough to determine its determinate, "I am a thing that thinks"... What he has forgotten is that "I think" is a determination which implies something indeterminate, but also that does not tell us under what form the "I am" is determinable by the determination "I think". Kant's reply: the form under which the "I am" is determinable is obviously the form of time. It will be the form of time; and you will come across this paradox that Kant will himself define in an admirable formula: the paradox of inner sense, the paradox of interior sense, namely the active determination "I think" determines my existence, the active determination "I think" actively determines my existence, but it can only determine my existence under the form of the determinable, which is to say under the form of a passive being in space and in time. So "I" is indeed an act, but an act that I can only represent to myself in so far as I am a passive being. I is an other. Thus I is transcendental. In other words, the active determination of the "I think" can only determine my existence under the form of existence of a passive being in space and in time. Which amounts to saying that it's the same subject which has taken on two forms, the form of time and the form of thought, and the form of thought can only determine the existence of the subject as the existence of a passive being.

Cours Vincennes - 28/03/1978

Kant was very interested in a bizarre author called Swedenborg, and Swedenborg had a certain conception not only of spirits, in the spiritualist sense, but he had a conception of space and time as a function of spiritualism. To answer your question: it seems to me that you aren't posing the problem in Kantian terms. When you say, for example: "I'm thinking of someone", and then this someone comes into the room. You are using "thinking" in an extremely general sense, that is, any activity of any given faculty referable to a so-called thinking subject, whatever the mode of thought. When you say that I am thinking of someone that means that I am imagining someone, or I remember someone, and then by chance, by coincidence, this someone comes into the room. "Thinking" can very well be used in vague and general terms. At the point we are at in our analysis, Kant has substituted a restricted use, in which to think does not mean to imagine or to remember, or to conceive, but in which thinking means solely to produce concepts. To feel means solely: to receive a sensible diversity, to apprehend a sensible diversity. To imagine means: either to produce images, or else to produce the concept's corresponding spatio-temporal determinations. So grant me that, at the level that we are on, whatever these restricted definitions and their value are, to think, to imagine, to feel, are not treated by Kant as modes of a same type of thought which could be substituted for one another, but as specific faculties. So that when you say "I remember someone", and this someone comes in, there is no activity of thought, there is an act of imagination, there is suddenly the sensible diversity which gives me this someone. That's what Kant would say. Kant says, in a text of the Critique of Pure Reason: "if cinnabar was sometimes red, sometimes red and sometimes black, sometimes heavy and sometimes light... I would never have the opportunity to associate - i.e. my imagination would never have the occasion to associate - the heavy cinnabar with the colour red..." If nature was not subject to concrete rules, there would be no associations of ideas. In other words, when I have an association of ideas, this implies that things, and no longer ideas, that things are themselves subject to rules analogous to the rules which are associated in us. Which is to say if Pierre did not come to Vincennes, or had not come to Vincennes, I would never have had the opportunity to associate the idea of Vincennes and the idea of Pierre. I will try to clarify this story of faculties, but you can well see that you can't invoke the example that you just gave as transforming the problem of the thought-imaginary relationship, because in fact it would be a matter of one of the forms of thought. When I think "of Pierre" and then Pierre is there, in fact I haven't thought anything since I haven't formed any concept at all. I imagined or remembered. There's something very, very curious in Kant. When Kant writes his three great critiques, the Critique of Pure Reason is in 1781, Kant is 57 years old, the Critique of Practical Reason is in 1788, and finally the last very great work by Kant is the Critique of Judgement in 1799, he is 76 years old. I was saying to myself that there aren't that many precocious philosophers. If he had died at the age of 50 he would be a sort of secondary philosopher, a good disciple of Leibniz, a good run-of-the-mill philosopher. There is only one case, the extraordinary case of Hume. With him, he has his whole system, all his concepts, at the age of 22-25, after which he only repeats, improves. Today, I would like to speak about this extraordinary book that is the Critique of Judgement; if I say that it is an extraordinary book it's because it is a book which founds a discipline, even if the word existed before. There is a particular discipline which will be radically founded by the Critique of Judgement, namely the foundation of all possible aesthetics. Aesthetics came into existence as something different from the history of art with the Critique of Judgement. It's really a very difficult book, don't try to understand each line of it, follow the rhythm. I would like to develop a bit the difference between the Cartesian "I think", such as it appears in Descartes, and the "I think" such as it appears in Kant. We must schematise at the level of a certain labor of thought. Already with Descartes, something appears which, it is said, will be of very great importance in the evolution of philosophy, namely: substance, that certain substances are therein determined as subjects. We can say very schematically that these formulae have been helpful. Not all substances, but a type of substance called thinking substance (?). Thinking substance is determined as subject. It's the discovery which will mark all philosophy said to be modern, from the 17th century onwards, it is the discovery of subjectivity. Why the discovery of subjectivity, why would subjectivity have to be discovered? It's the discovery of a subjectivity which is not the subjectivity of the empirical self, namely you and me. From the point of view of the labor of the concept, if I say: the Cartesian cogito is the assignation of substance as subject: "I think", the Kantian I think is very different. Everything happens as if a further step was taken, namely that the form of subjectivity breaks away from substance. The subject is no longer determinable as a substance. Subjectivity liberates itself from substantiality. Philosophers do not contradict each other, it's like with scholars, there is a whole labor of the concept. I will try to express Descartes' "I think" very concretely. Descartes' point of departure is a famous operation called doubt. He says, in some very beautiful texts, "perhaps this table on which I rap does not exist", and "perhaps my hand which raps on this table does not exist"; everyone knows very well that this is a manner of speaking. There is necessarily a discrepancy between the style and the content. It's not a matter of saying the table doesn't exist. Descartes' problem is something else entirely, it's the ground [fondement] of certainty, which is to say a certainty which would be exempted from all possible doubt. If I say "the table exists", its existence is of no matter to me, I am wondering whether it is a certainty which contains in itself its own ground. No. Certainly the table exists, it's understood, but this certainty does not contain in itself its own ground. Are there certainties which contain their own ground in themselves? At this point I move up a level: we say that we are sure that two and two make four; Dostoyevsky's heroes say: "I don't want two and two to make four". Can one not want two and two to make four? And when he says: I am certain that two and two make four, is that also a certainty which has its own ground in itself? Why would two and two make four? In this case one can demonstrate that two and two make four, which is complicated. On the other hand Descartes thinks that it is the operation of doubt which will give us a certainty which contains in itself its own ground. Namely that there is one thing which I cannot doubt, I can doubt the existence of the table, I can doubt the proposition "two and two make four", I cannot doubt one thing, which is that in so far as I doubt, I think. In other words, the operation of doubt, in so far as doubting is thinking, will provide me with a certainty which contains in itself its own ground: I think! "I think" - it's a funny sort of formula. In certain texts Descartes goes so far as to say that it is a new mode of definition. It's a definition of man. Why is it a definition of man? Before Descartes philosophy proceeded by definitions, scholasticism, definitions were given above all through generic and specific differences. Man is a rational animal. Animal is the genus, rational is the specific difference. Descartes says that when a definition of this type is given we are always referred to something else that we are supposed to know. In order to understand that man is a rational animal, we are supposed to know what an animal is, we must know what rational is. He will substitute a definition of another form entirely: I think. It's very curious, this "I think", because there is no need to know what thinking is. It is given in the act of thinking. There is a kind of implication, which is not at all an explicit relation between concepts, it's an act which is one with the act of thinking. With doubt, when I doubt, there is one thing which I cannot doubt, which is that as a self who doubts, I think. Self, what is the self? Is it my body, is it not my body? I have no idea since I can doubt my body. The only thing I cannot doubt is that since I doubt, I think. You can see that it is absolutely not a matter of an operation in which doubt would come to bear on ?????, but of an operation which consists in requiring a certainty which contains in itself its own ground as certainty. "I think" is thus an act through which I determine my certainty. The "I think" is a determination. It's an active determination. Not only can I not doubt my thought, but I cannot think without it, which is to say that the same implicit relation which goes from doubting to thinking, goes from thinking to being. In the same way that doubting is thinking, in order to think one must be. You can see the progression of the Cartesian formulae: I doubt, I think, I am. I doubt, I think, I am, I think is the determination, I am is the indeterminate existence, I am what? Well, the determination will determine the indeterminate existence. That the determination determines the indeterminate means: I am a thing that thinks. I am a thinking thing. Thus it is that what I am is determined by the determination "I think", is determined as the existence of a thinking thing. Descartes is told that that's all very well, but what proves to us that it is not the body which thinks in us? A materialist of the time says this to him. And Descartes replies - as soon as anyone makes an objection to him, he is very rude - he says: you haven't understood anything, I never claimed that it is not the body which thinks in us, he says exactly this: what I am claiming is that the knowledge which I have of my thought cannot depend on things which are not yet known. In other words, it is not a matter of knowing if it is the body or not the body which thinks in us, it is a matter of observing that, within the perspective of the Cartesian method, the consciousness which I have of my thought cannot depend on things which are not yet known, namely the body since doubt [also bears on this?]. Thus this procedure, from a logical point of view, but a new type of logic since it is no longer a logic that operates through genera or differences, it's a logic of implications since Descartes is in the process of... in opposition to classical logic which was a logic of explicit relations between concepts. He launches a new type of logic which is a logic of implicit relations, a logic of implication. So, he has determined with the "I think", which is a determination, he has determined the existence of what thinks, and the existence of what thinks is determined as the existence of the thinking thing. He thus goes from the determination to the indeterminate, from the determination "I think" to the indeterminate "I am" and to the determined: I am a thing that thinks. He threads along his logic of implications: I doubt, I think, I am, I am a thing that thinks. He has thus discovered the zone where substance was subject. And Kant appears. What Descartes affirms is that the soul and the body are really distinct. It's more than an ontological separation. But what is it that he calls a real distinction, in conformity with the whole tradition? Again, words here are as defined as in science. A real distinction is not the distinction between two things, it's the distinction, a mode of distinction, between two things, it's the distinction, a mode of distinction, between two ideas and representations : two things are said to be really distinct when I can form the idea of one of them, which is to say when I can represent to myself the idea of one of them without introducing anything about the other. Representations thus form the criteria for real distinction. Two things being completely distinct is a proposition which, ultimately, has no meaning. We will get to the level of substance, Comptesse, you who know Descartes as well as I, after the fifth meditation. In the second meditation, there is absolutely no way of knowing if it is the body which thinks in me. Descartes says it categorically. The soul and the body, thought and extension are really distinguished - which is not the same thing as really distinct - as two ontologically separate, or separable, substances. He is not able to say this before the end of the meditations. In the second meditation, when he discovers the "cogito", the "I think", he absolutely cannot say it yet, and it's for this reason that among the novelties of Descartes' text, there is something which he very much insists on, and this is the true novelty of the meditations, even if you don't like Descartes very much, namely that it is the first book which introduces time into philosophical discourse. There is something tremendous in this. What he says in the second meditation, then what he says in the fifth, there is a temporality which has unfolded which meant that he could not say in the second what he will say in the fifth. This is not true of all philosophies; if I take Aristotle or Plato, there is a succession in the reading, but this succession corresponds to a chronological order and that's all. In Descartes there is the establishment of a temporal order which is constitutive of the metaphysical dimension. Broadly speaking, during the whole of the middle ages, there was a theory of forms of distinction, each author will create his own forms of distinction, but broadly there were three major types of distinction: real distinction, modal distinction and the distinction of reason. And if you relate these three types of distinction to things themselves, you produce an absurdity, if you give them an ontological bearing, they don't have an ontological bearing yet, they only have a representative bearing, namely: there is a real distinction between A and B when I can think A without thinking B, and B without thinking A. You can see that it is a matter of a criterion of thought, a criterion of representation. For example: two things are really distinct, and not truly distinguished, two things are really distinct when you can form the representation of one without introducing anything of the other, and reciprocally. This lighter is on this book, are they really distinct? Yes, I can represent the lighter to myself without introducing anything of the representation of the book, they are really distinct. It's possible that they are also truly distinguished, it would be enough for me to put the lighter in my pocket. Between the front and back of a piece of paper, there is a real distinction, I can represent to myself one side of the paper without having the least representation of the other. In things, front and back are not separate, but in my representation front and back correspond to two representations. I would say that there is a real distinction between the front and back of the paper. So there can be a real distinction between two things which are not truly distinguished. Second type of distinction: modal distinction. There is a modal distinction when I can think A, I can represent A to myself without B, but I can't represent to myself B alone. For example: extension and the figure. Let's suppose, broadly, that I can represent to myself extension without figure, I cannot represent to myself a figure without extension. I would say that between extension and figure there is a modal distinction. In relation to this, we must not transport it to the level of ontology too quickly, it does not mean at all that there is an extension without figure in things, perhaps there isn't. You can see it's the same gesture, it's the criteria of representation. Third distinction: the distinction of reason. When I represent to myself as two, two things which are one in the representation. In other words, the distinction of reason is abstraction. When I distinguish the front and back of the piece of paper, I do not make an abstraction since they are given as two in my representation, since there are two representations, but when you speak of a length without breadth, however small this length, there you make an abstraction. When you can have no possible representation of a length which would have no breadth, however small. Thus between length and breadth there is a distinction of reason. The way people talk about abstraction is amazing, they have absolutely no idea what it is. Philosophy has a kind of technique and a terminology like mathematics. Generally the word abstract is used for things in which there is no abstraction. The problem of abstraction is how can I make two things out of what only exists as one in my representation. It's not difficult to make a thing into two when I have two representations, but when I say the back of the piece of paper, I am not abstracting at all since the back is given to me in a representation which itself exists. When I say a length without thickness, there I am abstracting because I am separating two things which are necessarily given in each other in my representation. There is indeed a philosopher who started the theory of distinctions. And then the theologians of the middle ages were not guys concerned with God, that's like saying that the painters of the Renaissance were guys who thought about God, no, they thought about colours, they thought about lines, and they draw out the most bizarre things from Christ's body. What we call theologians are people who are in the process of inventing a logic, a physics, a dynamics, and one of the great things in the theology of the middle ages is the theory of distinctions... ok... up to this point it's completely independent of the question of knowing if things are truly distinguished or confused in themselves, so that in the whole story of the cogito, I doubt, I think, I am, I am a thing that thinks, Descartes can only conclude: the representation that I have of my thought, and the representation that I have of an extended body, are such that I can represent my thought to myself without representing anything to myself of extension; I can represent to myself an extension without representing anything to myself of my thought. This is enough for Descartes to say that thought and extension are really distinct. He cannot add yet that it is not the body which thinks in me...

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So he will have to, in order to draw from the real distinction between representation-substance the ontological separation between substances, he will have to go through a whole analysis of the concept of God in which he says: if the real distinction between representation and substance was such that there was no corresponding true separation in things, an ontological separation in things, then God would be deceitful, God would be lying to us since the world would be double, God would be duplicitous, God would be full of duplicity since he would have made two non-conforming worlds: the world of representations and the world of things. You can see what that implies, philosophically, if God is deceitful... it would imply an entirely new way of posing of the problem of evil. But if I had the power to establish real distinctions between representations without there being a corresponding true separation between things, the world would be double: there would be the world of my representations and the world of things, so God would be always misleading me since he would inspire true ideas in me and these true ideas would correspond to nothing in things. To reply to Comptesse, I'm just saying that it's true that it's a story of ontological separation, but not so quickly, it will become a matter of ontological separation when Descartes is able to conclude: since I can represent thinking substance as really distinct from extended substance, then thinking substance and extended substance are two substances ontologically, and from that point on it is not the body which thinks in me. But before having gone through [the fifth meditation?], he absolutely cannot say this, he can only say: I conceive thinking substance as really distinct from extended substance, they are really distinct, since, once again, to be really distinct is the same thing as to be conceived as really distinct, two things whose representations are caused without one implying anything of the other are really distinct, he cannot yet affirm that it is not extension which thinks in me, that it is not the body which thinks in me. The one thing that seems interesting to me is this idea of implicit relations, but Descartes does not call it that, and from this the promotion of an order of time in the writing of philosophy... You are going to tell me that you understand everything. What does Kant do here? Kant wants to go further. It's inevitable, he wants to go further in relation to a previous philosopher, only this further has no pre-existence, he must create it. One of Kant's most beautiful texts is: "What does it mean: to orient oneself in thinking?" In this very beautiful text he develops a whole geographical conception of thought; he even has a new orientation, we must go further, Descartes did not go far enough: since he determined certain substances as subject, we must go further and break the link between the subject and substance. The subject is not substance. OK. What does that mean? He takes it up again and I will try to mark the stages: he says: "I think", fine. Which is to say that it is an active determination, and it's in this sense that Kant will name the "I think" as the form of spontaneity. It seems strange when he says that "I think" is the form of spontaneity, but everything is clear if you stick closely to the terminology; it means precisely: "I think" is a determination - he takes that from Descartes - and the "I think" accompanies each production of concepts. I cannot think a concept without thereby including the "I think". In other words, the "I" of the "I think" is the subject of all concepts, or, as he will say, it's the unity of the synthesis. Thus on this point, he changes the vocabulary, but he remains in agreement with Descartes. Why does he change vocabulary? It was to be expected, if he changes vocabulary while remaining in agreement with Descartes, it's because he will need this vocabulary for the moment when he will not agree, that's the first point. Second point: in order to think one must be, in other words, there is a relation of implication between the determination "I think" and the position of an indeterminate existence "I am". Kant says it all the time: the "I think" implies - often the words vary - a feeling of existence (here we can clearly see the lineage, between Descartes and Kant there was Rousseau). Sometimes he says a consciousness of an indeterminate existence; the "I think" implies a pure consciousness of an indeterminate existence. Agreement with Descartes up to this point. From this point on Descartes has no more problems, and it's when a philosopher has no more problems that the next philosopher is about to arrive. Descartes has no more problems because he has a determination, and he has posited an indeterminate existence hence something to be determined, and he will say that the determination determines the indeterminate. The determination: I think, the indeterminate: I am, the determination determines the indeterminate: I am a thing that thinks. Here Kant says no; it's the birth of German philosophy. I'm thinking of Leibniz. There are objections which are like reproaches. Beneath objections there are always theoretical reproaches. Leibniz already said of Descartes: he is too quick. It's like a judgement of taste. Kant takes on something of this, it's too quickly said. Kant: "I think" is a determination, agreed, determination implies the positing of an indeterminate existence "I am", agreed, but this doesn't tell me under what form this indeterminate existence is determinable, and this Descartes doesn't care about because he hasn't seen the problem. I think, I am, agreed. But what am I? Descartes replied: "I am a thing that thinks" since he applied the determination to the indeterminate. Now what I'm saying is becoming very clear: Descartes carried out an operation whereby he directly applied the determination to the existence to be determined. He directly applied the "I think" to the "I am" in order to get "I am a thing that thinks." Kant says OK, I think, I am. But what am I, what is it that I am? A thing that thinks? But by what right can he say that? Descartes would have become angry... Kant says to him: but you're stuck, you have posited an indeterminate existence and you claim to determine it with the determination "I think". You have no right to do that. You have a determination, you have posited an indeterminate existence, you can turn it around as much as you like, you will not make any headway. You are stuck there. Why? Because to draw from this the conclusion "I am a thing that thinks", it assumes - and you have no right to assume it - it assumes that the indeterminate existence is determinable as a substance or a thing. Res cogitans, in Latin, the thinking thing. Kant says, in accordance with all that has come before, which is to say what I tried to say the last time - the extraordinary change in the notion of phenomenon, the phenomenon no longer designating the appearance but the apparition, what appears in space and time - Kant can now say to us that the form under which an existence is determined within the conditions of our knowledge (what happens with angels, we have no idea), well, the form under which an existence is determinable under the conditions of our knowledge is the form of time. Thus the "I think" is the form of spontaneity or the most universal form of determination, but time is the most universal form of the determinable. Descartes' fatal conclusion was to confuse the indeterminate and the determinable, but the determination can only bear on the indeterminate as the mediation of the form of the determinable. In other words, I think, I am, the determination must determine the indeterminate existence "I am", but the indeterminate existence "I am" is only itself determinable under the form of time. It is only under the form of time, as the form of the determinable, that the form of thought will determine the indeterminate existence "I am". This is how my existence can be determined only as time. But if time is the form of the determinable, under which my indeterminate existence can be determined by the "I think", what form do I receive from the determinable? The form that I receive from the determinable is that of a phenomenon in time, since time is the form of apparition of phenomena. I appear and I appear to myself in time. But what is it to appear and to appear to oneself, to appear in time? They are the coordinates of a receptive, which is to say passive, being. Namely a being which has a cause, which does not act without also undergoing effects. Ok, we're at the end, and it's here that Kant will name the paradox of inner sense, the paradox of intimate sense: the "I think" is an active determination, it's the same form of the active determination, but the existence which it implies, the "I am", the indeterminate existence that the active determination of the "I think" implies, is only determinable in time, which is to say as the existence of a passive subject which undergoes all its modifications following the order and the course of time. In other words, I cannot - there is one sentence which is splendid, it's the Kantian version of what I was saying last time, namely that I is an other. This is what Kant says in the Critique of Pure Reason: "I cannot determine my existence as that of a spontaneous being, I only represent the spontaneity of my act of thinking". It's exactly "I is an other". I cannot determine my existence as that of an I, but I only represent the I to myself. The spontaneity of my act of thinking. The fact that I represent to myself the spontaneity of my act of thinking means that I represent the active determination of the "I think" to myself as the determination which determines my existence, but which can only determine it as the existence of a being which is not active, but a being on time [tre sur le temps]. This is the line of time which separates the "I think" from the "I am". It's the pure and empty line of time which traverses, which effects this sort of crack in the I, between an "I think" as determination and an "I am" as determinable in time. Time has become the limit of thought and thought never ceases to have to deal with its own limit. Thought is limited from the inside. There is no longer an extended substance which limits thinking substance from the outside, and which resists thinking substance, but the form of thought is traversed through and through, as if cracked like a plate, it is cracked by the line of time. It makes time the interior limit of thought itself, which is to say the unthinkable in thought. From Kant onward, philosophy will give itself the task of thinking what is not thinkable, instead of giving itself the task of thinking what is exterior to thought. The true limit traverses and works thought from within. We rediscover what I tried to say the last time, namely: we find a sort of tension between two forms: the active form of spontaneity, or if you prefer, the "I think" as form of active determination, or form of the concept since "I think" is the formal unity of all concepts, so on the one hand the active form of determination, on the other the intuitive or receptive form of the determinable, time. The two are absolutely heterogeneous to each other, and yet there is a fundamental correlation: the one works in the other. Thought shelters in itself what resists thought. In what sense is Heidegger Kantian? There are famous phrases such as: "we are not yet thinking"; when he talks about time in relation to thought, it's in this way that he is Kantian. The direct line from Kant to Heidegger is truly the problem of time and its relation to thought. The big problem that Kant discovers is the nature of the relation between the form of determination, or activity, or spontaneity, and on the other hand the form of receptivity, or form of the determinable, time. If I shift slightly, I would no longer say the form of determination and the form of determinable, but: two types of determination which are heterogeneous. You will ask me by what right I can make this shift; passing from the form of determination: I think, form of the determinable: time, the idea that there are two types of determination remains to be seen, but you can sense that it is the outcome of a series of shifts which must be justified, namely the two types of determination, in this case the conceptual determination, as all concepts refer to the "I think", concepts are the acts of the "I think", thus on the one hand a conceptual determination, and on the other hand a spatio-temporal determination. The two are absolutely heterogeneous, irreducible, the conceptual determination and the spatio-temporal determination are absolutely irreducible to each other, and yet they never cease to correspond to each other in such a way that for each concept I can assign the spatio-temporal determinations which correspond to it, just as, the spatio-temporal determinations being given, I can make a concept correspond to them. In what way, this is what remains to be seen. If you grant me these shifts which we will define in a moment, it amounts to the same thing to say that Kant poses the problem of the relation between the form of determination "I think" and the form of the determinable = time, and in so doing completely upends [bouleverse] the element of philosophy, or to say, on a more precise level: no longer the "I think" but concepts, no longer time but the determinations of space and time, in this case it is a matter of the relation between the conceptual determination and the spatio-temporal determination.

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Our point of departure is this: how can we explain that conceptual determinations and spatio-temporal determinations correspond with each other when they are not at all of the same nature? What is a spatio-temporal determination? We will see that there are perhaps several kinds. Kant poses the question concerning the relation between the two types of determination on very different levels. One of these levels will be called that of the synthesis, another of these levels he calls that of the schema, and it would be disastrous for a reader of Kant to confuse the synthesis and the schema. I'm saying that the schema and the synthesis are operations which, in a certain way, put a conceptual determination and a spatio-temporal determination into relation, but then it's as if the synthesis will be shattered, pierced, will be overcome by a stupefying adventure which is the experience of the sublime. The experience of the sublime will knock over all the syntheses. But we do not live only on this. We live only on the syntheses and then the experience of the sublime, which is to say the infinity of the starry vault, or else the furious sea... The other case, the schema, is another case where spatio-temporal determinations and conceptual determinations come into correspondence, and there again there are conditions where our schemas shatter, and this will be the astonishing experience of the symbol and of symbolism. But the whole analysis of the sublime, and the whole analysis of the symbol and symbolism, the English had analyzed the sublime before him, but the whole novelty of Kant's analysis is obvious: it will be the Critique of Judgement, in his last book, as if to the extent that he aged, he became aware of the catastrophe. Of the double catastrophe of the crushing of the sublime, the sublime crushes me, and the irruption of the symbol, where our whole ground, the whole ground of our knowledge which we had constructed with syntheses and schemas, starts to shake. What is the synthesis? It's the synthesis of perception. But don't think that that goes without saying. I'm saying that it's from this level of the analysis of the synthesis of perception that Kant can be considered as the founder of phenomenology. That is, that discipline of philosophy which has as its object the study, not of appearances, but apparitions and the fact of appearing. What is the synthesis of perception? All phenomena are in space and time. There is strictly speaking an indefinite diversity in space and time. Moreover, space and time are themselves diverse: they are not only the forms in which diversity is given, but they also give us a properly spatial and temporal diversity: the diversity of heres and the diversity of nows; any moment in time is a possible now, any point in space is a possible here. Thus not only is there an indefinite diversity in space and time, but also an indefinite diversity of space and time itself. Thus for perception, certainly the diverse must be given to me, but if I had nothing but this given diverse, this receptivity of the diverse, it would never form a perception. When I say "I perceive", I perceive a hat, I perceive a book, for example, this means that I constitute a certain space and a certain time in space and time. Space and time are indefinitely divisible: any portion of space is a space, any portion of time is a time. So it is not space and time themselves which account for the operation by which I determine a space and a time. I perceive a piece of sugar: I perceive a complex of space and time. You will tell me: that works for space, I can see that, there is the form, the grain; but why time? Because it forms part of my perception to wait for the sugar to melt. When I perceive a thing, I perceive a certain temporality of the thing and a certain spatiality of the thing. So there we have, according to Kant, a properly logical order, not at all chronological, he doesn't say that we must start with one. There are three operations which constitute the synthesis, the synthesis operating on diversity in space and in time, and diversity in space and time at the same time. The synthesis consists in limiting a diversity in space and in time, and a diversity of space and time themselves, in order to say: it begins, it ends, etc.... The first aspect of the synthesis is what Kant calls the successive synthesis of the apprehension of parts, that is: every thing is a multiplicity and has a multiplicity of parts; I perceive parts, my eye runs over the thing. You will tell me that there are things small enough for me to perceive them at once. Yes and no, perhaps not, maybe so; moreover, however small something is, my perception can begin from the right or begin from the left, from the top or the bottom; it doesn't take very much time, it's a very contracted temporality. I carry out a synthesis of successive apprehension of parts. But by the same stroke things already become complicated, we must distinguish two cases, we have not finished. In any case the apprehension of parts is successive. There are cases where the succession is objective, this already complicates things. I perceive a house, for example: ... the foreground, the background, the perspective, the foreground becoming background etc. ... there is a kind of subjective apprehension. But I begin from the right, or I begin from the left, and I keep going; in both cases my apprehension is successive, but the succession has only a subjective value. I can begin with the top or the bottom, with the right or the left; this will be reversible or retrograde, whether from right to left or from left to right, I can say that it's the wall in front of me. The succession is in my apprehension, it is not in the thing, it is not in the phenomenon. By contrast, you are sitting on ?????, there again you have a succession, a successive apprehension of parts, but the succession is objective. When the succession is objective, you will say: I perceive an event. When the succession is grasped as solely [subjective?], you perceive a thing. We could say that an event is a phenomenon whose successive apprehension of parts is such that the succession therein is objective. By contrast a thing is such that the succession therein is only subjective. Thus the first aspect of the synthesis which consists in determining the parts of a space and a time is the synthesis of apprehension. Through this I determine the parts of a space. Let's suppose that you have carried out your successive apprehension of parts, suppose that you are in a curious situation, suppose that is that when you have arrived at the following part you have forgotten the previous one, you would not be able to perceive. There must in fact be an operation of contraction such that when you come to the following part, the preceding one is conserved, otherwise if you lose on one side what you gain on the other, you will never manage to determine a space and a time. This second aspect of the synthesis is the synthesis of reproduction. You must reproduce the preceding part when you come to the following part, so not only must you produce successive parts, but you have to reproduce the preceding parts with the following ones. The two aspects of the synthesis refer to the synthesis as the act of what? Not receptivity, receptivity is solely space and time and what appears in space and time is intuition. The concept is something else. The synthesis refers to the imagination, it is the act of the imagination. This act of the imagination is bizarre; see what he means: it's that through the two aspects, the apprehension of parts and the reproduction of parts, I effectively determine a space and a time. But according to Kant, to imagine is not to fabricate images, it is not to think of Pierre who is not there. To imagine is to determine a space and a time in space and time. There is certainly an empirical imagination. Empirical imagination is when Pierre is not there, I think of Pierre, or else I imagine Pierre, I dream. But the imagination which Kant will call transcendental is the act by which the imagination determines a space and a time, and it determines a space and a time through the synthesis of apprehension and the synthesis of reproduction. But something else again is needed. I am no longer in the situation of a diversity in space and in time, or a diversity of space and time itself, I am in the situation of a space and a time determined by the synthesis of the imagination. And yet I cannot yet say that I perceive. In order to perceive we still need for this space and this time, determined by the synthesis, or what comes to the same thing, that which contains this space and this time, must be related to a form, to a form of what? Not to a form of space or time since we have the form of space and time. What other form? You can see the progression. We started from the form of space and time in general, as the form of intuition, then the act of imagination determines a space, a given space and a given time, through the two aspects of the synthesis. In this case it's a form - not the form of space and time - but a spatio-temporal form, the form of a house or the form of a lion for example, but we need yet another form in order for there to be perception. It is necessary for this space and time, or what contains this determined space and time, to be related to the form of an object. At this point it becomes difficult to understand. What does it mean that I have to relate it to the form of an object? We can imagine a number of sensations where the sensible givens, the diverse, sensible diversity, are not related to the object-form. It's my perception which is constituted in such a way that sensible diversity is related to the form of an object. In other words, I do not perceive an object, it is my perception which presupposes the object-form as one of its conditions, it's not something, it's an empty form. The object-form is precisely the index by which sensible qualities, such as I experience them, are supposed to refer to something. What something? Precisely a something = nothing. Kant will invent the splendid formula: a something = x. You will tell me that it's not a something = x when I say it's a table or it's a lion, it's not nothing, but the any-object-whatever [l'objet quelconque], the object = x, only receives a determination as lion, table or lighter by the diversity that I relate to it. When I relate to the object = x a diversity comprising: long hair in the wind, a roar in the air, a heavy step, a run of antelopes, well, I say it's a lion. And then I say: look a mouse! What I would like you to understand is that in any case there is an any-object-whatever, the object = x is a pure form of perception. I do not perceive objects, and it's my perception which presupposes the object-form. So the object is specified and qualified by myself according to a given diversity, a given space and time that I relate it to; when I relate a given spatio-temporal diversity, when I relate a given spatio-temporal form to the object = x, the object = x is no longer x, I can say that it's a lion or a house. But inversely I could never say that it's a lion or a house if the empty form of the object = x, the any-object-whatever was not available to me, for it is not the sensible diversity and it is nothing in the sensible diversity which accounts for the operation by which the sensible diversity goes beyond itself towards something that I call an object. Thus, apart from the form of space and of time (the form of intuition), apart from the determined spatio-temporal form (the synthesis of the imagination), I also need a third form: the form of the any-object-whatever such as this form is related to the spatio-temporal form in saying "it's this". Such that the third aspect of the synthesis, after apprehension and reproduction, is what Kant calls recognition. To recognize. I effect a recognition when I say: "it's this". But "it's this" implies an operation whereby I go beyond what is given to me, I go beyond the forms of space and time, I go beyond purely spatio-temporal forms towards the form of an any-object-whatever that the spatio-temporal form will determine as such or such an object. But just as the two first acts of the synthesis, apprehension and reproduction, refer to the imagination, because it consists in determining a space and a time, so recognition is an act of the understanding. Why? You remember the concepts which are the representations of the understanding, they are the predicates of the any-object-whatever, of the object = x. Not every object is a lion, not every object is red, but every object has a cause, every object is one, every object is a multiplicity of parts, etc.... The predicates that you can attribute to any-object-whatever are the categories of the understanding, they are the concepts of the understanding. So recognition, the form of recognition, the form of the any-object-whatever is no longer in this case the synthesis of the imagination but the unity of the synthesis of ????? [understanding?]. It's the three aspects, apprehension, reproduction and recognition which constitute perception under the conditions [of an other of perception?]. A small note in parenthesis: above all never confuse, in the Kantian vocabulary, the object = x and the thing in itself. The thing in itself is opposed to the phenomenon since the phenomenon is the thing as it appears, whereas the object = x is not at all opposed to the phenomenon, it is the referring of all phenomena to the object-form. The thing in itself is situated outside of our possible knowledge, since we only know what appears, the form of the any-object-whatever is on the contrary a condition. The form of the object = x is a condition of our knowledge. We begin again from zero. I have all the elements [ensemble] of the synthesis: apprehension of successive parts, reproduction of preceding parts in the following ones, reference to the form of an any-object-whatever. So I have referred a spatio-temporal form to a conceptual form: the object-form. So Kant says to himself... let's begin again at the beginning. We have tried to analyze an edifice which emerges from the ground: the edifice which emerges from the ground is the synthesis. What is underneath it? I have said: in order to perceive an object I apprehend its successive parts, but how do I choose these parts? It's a funny sort of thing because it varies greatly according to the object. Apprehending successive parts implies, even at the level of perception, it already implies something like a lived evaluation of a unit of measure. But in following the nature of objects there is no constant unit of measure. In reflection, yes; from the point of view of the understanding, yes, I indeed have a constant unit of measure. I can fix a standard and even so, we will see that this is not even true, but we could fix a standard, put it into place for example and say that there are so many meters. But this is obviously not what Kant means by the successive apprehension of parts. It's like a sort of qualitative measure according to the object. What does that mean? When I see a tree, for example, I carry out my apprehension of successive parts, I begin with the top, then I go towards the bottom, or the other way round, and I say that this tree must be as big as ten men... I choose a kind of sensible unit to carry out my successive apprehension of parts. And then, behind the tree, there is a mountain, and I say how big this mountain is, it must be ten trees tall. And then I look at the sun and I wonder how many mountains it is; I never stop changing the unit of measure according to my perceptions. My unit of measure must be in harmony with the thing to be measured; there are some amazing variations. Kant tells us in the Critique of Judgement, he is very careful not to before, he tells us that the most elementary act of the synthesis of perception presupposes a logical act. This synthesis of perception is in spite of everything a logical synthesis. I say in spite of everything because at the same time he gives "logic" an entirely new meaning. So once again I must choose a unit of measure, and this unit of measure is variable in each case in relation to the thing to be perceived, just as the thing to be perceived depends on the chosen unit. Beneath the successive apprehension of parts, which is a logical synthesis, even though it refers to the imagination, we need an aesthetic comprehension... this is no longer of the same order as measure; the aesthetic comprehension of a unit of measure such as it is supposed by measuring... Kant is in the process of discovering a sort of basis for the synthesis of apprehension, how an aesthetic comprehension of the unit of measure can be carried out because an aesthetic comprehension of the unit of measure is presupposed by the synthesis of the imagination in perception, namely the apprehension of an [evaluation of a rhythm?]. The evaluation of a rhythm will allow me to say: yes, I'll take that as a unit of measure in a given case; and the rhythms are always heterogeneous, we plunge into them in a sort of exploration. Beneath measures and their units, there are rhythms which give me, in each case, the aesthetic comprehension of the unit of measure. Beneath the measure there is the rhythm. But this is the catastrophe. Again we can no longer stop. We had the synthesis, we remained on the ground and the synthesis was established on the ground; we wanted to dig a bit and we discovered the phenomenon of aesthetic comprehension, and we can no longer stop. The rhythm is something which comes out of chaos, and the rhythm is something which can indeed perhaps return to chaos? What could happen? Let's approach this like a story. I look at something and I tell myself that I'm dizzy, or else my imagination wavers. What happens? In the first place I cannot choose a unit of measure. I don't have a unit of measure; it goes beyond my possible unit of measure. I look for an appropriate unit of measure and I don't have one. Each time I find one it is destroyed. So I am pushed as if by a wind at my back to choose bigger and bigger units of measure, and none is adequate. By the same stroke I cannot carry out my synthesis of apprehension. What I see is incommensurable to any unit of measure. Second catastrophe. In my panic I can perhaps distinguish parts, completely heterogeneous parts, but when I come to the next one everything happens as if I was struck by a dizzy spell: I forget the preceding one; I am pushed into going ever further and losing more and more. I can no longer carry out either my synthesis of apprehension or my synthesis of reproduction. Why? Because what I grasped, what struck my senses, was something which goes beyond any possibility of aesthetic apprehension! We have seen that aesthetic comprehension was - even though Kant does not say it, but it is what he is thinking of - was the grasping of a rhythm as basis of measure and the unit of measure. You can see the whole of the synthesis of perception: I can no longer apprehend the successive parts, I cannot reproduce the preceding parts as the following ones arrive, and finally I can no longer say what it is, I can no longer qualify the any-object-whatever. My whole structure of perception is in the process of exploding. Why? My whole structure of perception is in the process of exploding because we have seen that it was founded - not in the sense of a ground [fondement], but in the sense of a foundation [fondation] - we have seen that this whole perceptive synthesis found its foundation in aesthetic comprehension, which is to say the evaluation of a rhythm. Here it's as if this aesthetic comprehension, as evaluation of a rhythm which would serve as a foundation of measure, thus the synthesis of perception, is compromised, drowned in a chaos. The sublime. Two things are said to be sublime. Kant's response: two things are said to be sublime: the "mathematical" sublime (said to be mathematical because it is extensive), and what is called the dynamical sublime (an intensive sublime). Examples: the infinite spectacle of the calm sea is the mathematical sublime; the starry celestial vault when the sky is clear is the mathematical sublime; it inspires a sentiment close to respect within me, it's a dynamical [?] sublime. In this case the infinity of an expanse gives way to the infinity of material forces, the intensive infinity of forces which fill space and time. The dynamical sublime is the tumultuous sea, it's the avalanche. In this case it's terror. Think to what extent Kant is at the centre of a certain conception of German Romanticism. I'll pass over the reasons why the dynamical sublime is more profound than the mathematical sublime. My second question on the sublime is : what effect does it have on me? We can move forward. I can no longer apprehend parts, I can no longer reproduce parts, I can no longer recognize something, and in effect the sublime, as Kant says, is the formless and the deformed. It is the infinite as encompassing all of space, or the infinite as overturning all of space; if my synthesis of perception is suppressed, this is because my aesthetic comprehension is itself compromised, which is to say: instead of a rhythm, I find myself in chaos. Everything happens as if the imagination (the synthesis of perception) was pushed to its own limit. Great, we are in the process of rediscovering on the level of the faculty of the imagination something which we found on the level of the faculty of thought: it is not only thought which has a consubstantial relation, a fundamental relation, with an interior limit, the imagination is itself traversed by a limit specific to it, and the sublime confronts the imagination with its own limit. The beautiful, according to Kant, is not this at all, the beautiful is a reflection of the form of the object in the imagination. The sublime is when the imagination is in the presence of its own limit, it is alarmed. There was an enormous ambiguity between rhythm and chaos; I refer you to Paul Klee's famous text, how rhythm emerges from chaos, the way in which the grey point jumps over itself and organizes a rhythm in chaos. The grey point having the double function of being both chaos and at the same time a rhythm in so far as it dynamically jumps over itself; it will organize chaos and allow rhythm. Cézanne tells us that we never look at a landscape, it looks at something, and it is absolute chaos, "iridescent chaos". Cézanne says that it's like a landslide, a cave-in. At this point I am one with the painting - this is Cézanne speaking - we are an iridescent chaos, etc. ... geological strata... translated into Kantian terms, it's really: I go from the synthesis of perception to [aesthetic?] comprehension... Fortunately we are not caught up in the sublime all the time, this would be terrible, fortunately we hang on to our perception. At the moment that Kant says that in the sublime the imagination is taken to its own limit, and by the same stroke panicked, like a panicked compass, it is in the process of imagining what cannot be imagined; well at that moment, Kant says, in the respect of the mathematical sublime, or in the terror of the dynamic sublime, we suffer [éprouvons]. At the same time that my imagination is crushed by its own limit, it is a limit which is like its founding kernel, it is the bottomless [sans fond]. What is this bottomlessness of the imagination? It's something which makes me discover in myself something like a faculty which is stronger than the imagination, and this is the faculty of ideas.

Question:Can we say that music is the art of the sublime?

Gilles:

That wouldn't be difficult. If I think, out of convenience for you, in terms of the history of philosophy, we can distinguish the arts of the beautiful and the arts of the sublime. However, about the arts of the beautiful and the arts of the sublime, you will find a long history with Schopenhauer and Nietzsche. But how do they make the distinction? Broadly, if you like, all art rests on an Idea; but in the arts of the beautiful it's as if the Idea is mediated, which is to say it is represented. There is a representation of the Idea. In the sublime the will appears for itself. Nietzsche, in so far as he is concerned with the origin of tragedy, will remain with this idea of a preeminence of music over all the arts because music makes the Idea appear as such, in opposition to the other arts which are condemned to representation.

You should sense that an Idea is not from the imagination, but neither is it a concept of the understanding, it's something else still. We thus need a very particular status for the Idea since the whole game of the sublime is this: the imagination is vanquished and derailed before its own limit, but the joy which we experience is because an awareness arises in us of a superior faculty, which Kant will call the super-sensible faculty and which is the faculty of the Idea. With Kant we cease to think the problem of evil in terms of exteriority. Very broadly, in the classical tradition, there is a tendency rather to say that evil is matter, evil is the body, it's what opposes, it's what resists. It's with Kant that this very curious idea appears, which obviously comes from Protestantism, of reform, the idea that evil is something spiritual. It is truly within spirit and not matter as exterior. This is precisely what I was trying to say with the notion of limit in Kant: the limit is not something outside, it is something which works from within. Here evil is fundamentally bound to spirituality; it is not at all as it is in Plato, where if there is evil it is because souls fall, and obviously they incarnate themselves in a body. With the reform the devil is taken seriously, only taking the devil seriously can be a philosophical operation. Evil is not the body, evil is truly in thought qua thought.

Question:

Can you give the definitions of causality in Kant?

Gilles:

There are several. The first definition of causality is: causality is the faculty of making something begin in the order of phenomena. It's a simple definition which implies two causalities: a causality which Kant calls phenomenal, namely that phenomena follow on from each other, and a phenomenon begins something which will be called its effect, and, second causality, the so-called free causality - because phenomenal causality is a determined causality and free causality is the faculty of beginning something in the order of phenomena on the basis of something which is not itself caused. Second definition of causality, those before were nominal definitions, second definition: it's the relation between phenomena when the succession in their apprehension corresponds to an objective rule. Example: the boat which goes down the flow of the river, there the succession corresponds to an objective rule in opposition to succession in the perception of reason, where there is no causality. I would not say that the right side determines the left side, whereas in the perception of the boat I would say that the preceding state determines the following state.

Cours Vincennes - 04/04/1978

Today I would like to be as clear as possible within a problem which is nevertheless complicated. I have only one idea at best which I would like to develop today, and which is not only linked to the desire to help some of you in speaking about Kant in a precise way, but also to try and show a kind of development of an amazing problem throughout Kant's philosophy. The centre of everything I would like to say today is precisely this: if we stay with the Critique of Pure Reason, Kant's famous book, we can well see, in relation to the themes which concern us involving time, we can well see that there are two great operations. What these two great operations of knowledge have in common - since pure reason is concerned with knowledge - what these two great operations of knowledge have in common is that in both cases a correspondence is created, despite their heterogeneous elements, despite their difference in nature, between conceptual determinations and spatio-temporal operations. These two great operations by which a correspondence is created - whatever the difficulties this correspondence involves given their heterogeneity - between spatio-temporal determinations and conceptual determinations are both synthetic operations. They are synthetic for very simple reasons, they are necessarily synthetic since, as we have seen, spatio-temporal determinations on the one hand and conceptual determinations on the other hand, space-time and concepts, are heterogeneous, so the act which puts them into correspondence can only be a synthesis of heterogeneities. These two synthetic operations have names. These two operations also have in common the fact of being acts of the imagination. Obviously imagination no longer means making up ideas or imagining something, since Kant gives a fundamentally new meaning to the act of imagination, since it is the act by which spatio-temporal determinations will be put into correspondence with conceptual determinations. You will ask me why he calls that "imagination"? Understand that he is already at a level where he grasps imagination at a much deeper level than in the preceding philosophies; imagination is no longer the faculty by which we produce images, it is the faculty by which we determine a space and a time in a way that conforms to a concept, but that does not flow from the concept which is of another nature than the determination of space and time. It is really the productive imagination in opposition to the reproductive imagination. When I say: I imagine my friend Pierre, this is the reproductive imagination. I could do something else besides imagine Pierre, I could say hello to him, go to his place, I could remember him, which is not the same thing as imagining him. Imagining my friend Pierre is the reproductive imagination. On the other hand, determining a space and a time in conformity to a concept, but in such a way that this determination cannot flow from the concept itself, to make a space and a time correspond to a concept, that is the act of the productive imagination. What does a mathematician or a geometer do? Or in another way, what does an artist do? They're going to make productions of space-time.

The two synthetic operations which establish the correspondences of space-time to concepts. I said that Kant gives them very strict names, and it would be very unfortunate to confuse these two operations. One is designated under the name of synthesis strictly speaking, synthesis as the act of the productive imagination and the other - which is no less synthetic - Kant saves another name for it, that of the Schema. A schema. It is also an operation of the productive imagination. One of our problems is what the difference is between a synthesis strictly speaking and a schema. We have seen what they have in common: in both cases it is a matter of determining a space and a time in correspondence with a concept. But my second problem is that if we don't stay with the Critique of Pure Reason, if we go on to one of Kant's last works, where Kant goes deeper and deeper, which is to say if we effect a confrontation with the ultimate work, the Critique of Judgement, and if we see its effect on the Critique of Pure Reason, we realise that Kant reveals to us in the Critique of Judgement an amazing double adventure: how synthesis, as act of the imagination, can be overwhelmed by a fundamental experience which is the experience of the sublime; thus that there is an operation of extreme fragility in the synthesis: something which comes from the depths [le fond] puts ???? this operation at risk at each instant, drowning it. Drowning it in a simple destruction? No, in favour no doubt of the revelation of another level which is the revelation of the sublime and thus that the synthesis of the imagination risks being overwhelmed by another act, or rather by another passion, by a sort of passion of the imagination which is the spectacle and the experience of the sublime, where the imagination vacillates on its own ground.

On the other hand, it is quite curious how it's both inspired and works in symmetry; it is really the hinge of Classicism and Romanticism. The Critique of Judgement is really the great book which all the Romantics will refer to. They had all read it, it will be determining for the whole of German Romanticism. But on the other hand as well we experience the same adventure, but under another form. The schema, which is the other act of the imagination, risks being overwhelmed by something which comes from the depths of the imagination in the same way as the synthesis, namely the experience of the sublime, the schema - [the] other act of the imagination from the point of view of knowledge - also risks being overwhelmed by something monstrous, which Kant is the first to analyse, to my knowledge. It is symbolism. In the same way that the sublime threatens at each instant to overwhelm the imagination's act of synthesis, the operation of symbolism and symbolisation threatens at each instant to overwhelm this other act of imagination which is the schema. So much so that between symbolism and the sublime, there will obviously be all sorts of echoes, as if they brought about the emergence of a sort of ground [fond] which is irreducible to knowledge, and which will testify to something else in us besides a simple faculty of knowing. Feel how beautiful it is.

So first we must go via something more reasonable, duller: what is the difference between the schema and the synthesis? The last time I tried to show what the synthesis was. The synthesis as act of the imagination consists precisely in this - but I want this to be very concrete, which is good if one is in the world and in the world there are Kantian phenomena; if you come across a typically Kantian moment in the world, then it's very good, at that moment you must speak in Kantian terms; they are phenomena which can only be grasped through Kantian spectacles, if not you pass on by. The synthesis and the schema are always the forming of a correspondence between, on the one hand conceptual determinations, and on the other spatio-temporal determinations. What defines the synthesis as distinct from the schema? The synthesis is an act of the imagination which operates here and now; there is no synthesis if it is not an operation of your imagination that you do here and now. For example, here and now, you see a diversity; or else here and now you see an organisation of space and time. You will recall that this space and this time are not yet determined: there is something in space and time. A synthesis must yet be effected which will give you a certain space and time, in such a way that you carry out a sort of isolation: if you say "that is a table", you have carried out a synthesis of space and time in conformity with a concept. There is the concept table, and then you have synthesised, you have carried out a synthesis of a certain diversity. So the principle of the synthesis is recognition, it is this. The synthesis has as its rule the process of recognition. Given this, it is obligatory that the synthesis operates here and now: look, it's a house. What does the synthesis consist in? We saw it last time: successive apprehension of parts, synthesis of apprehension, reproduction of the preceding parts in the following parts; thus the two aspects of the synthesis, apprehension and reproduction, are what I use to determine a finite space and time.

The concept is the form of the object which I qualify according to the diversity whose synthesis I have effected: it's a table, it's a house, it's a small dog.

So, in the synthesis, I have indeed effected a correspondence between a determination of space and time and a conceptual determination, the determination of space and time being carried out by the synthesis of apprehension and reproduction, and the conceptual determination referring to the form of the any-object-whatever in so far as this form of object will be determined by the diversity upon which I effect the synthesis. I would almost say that in the synthesis I go from the spatio-temporal determination to the conceptual determination and that my point of departure is here and now. You can see that, at the beginning, I only have a concept of any-object-whatever; I only have the form of an any-object-whatever which is the empty form of the concept, object = x. Why is this a concept? Because it is not at all contained in the sensible diversity. So as the form of the pure concept I have only the form of the any-object-whatever, and the synthesis of the imagination will make a spatio-temporal determination correspond to the any-object-whatever in such a way that the any-object-whatever will be specified as such or such an object: this is a house, this is a table.

There is something quite curious in Kant. When things don't work, he invents something which doesn't exist, but it doesn't matter. The schema. Put yourself in the reverse situation. You have the concept, you start from the concept. So the path of the schema will no longer be the here and now, not what your productive imagination does here and now, that is determine space and time, the schema will be on the contrary an operation that you carry out, when you carry it out, as valid at all times. "This is a house" is not valid at all times. You recall the rule of the synthesis, it's a rule of recognition. The schema: you have a concept, and the problem is to determine the spatio-temporal relation which corresponds to this concept. The synthesis is just the opposite, it's this: you carry out a spatio-temporal operation and you specify the concept according to this determination. So the operation of the synthesis, valid here and now, will correspond with, in the other direction, the determination of the schema, valid at all times. There you have a concept and you are looking for the spatio-temporal determination which is likely to correspond to it. What does that mean? When I say: the straight line is equal in all its points, Euclid's definition, I have a concept of a straight line. You will tell me, yes, but it's already spatial. Yes it's spatial, but with space, I can make a concept of space for myself. A straight line defined as a line equal in all its points doesn't yet give me any determination, and while the synthesis went from the space-time intuition to the concept carried out by a rule of recognition, the schema on the contrary will operate by a rule of production. Given a concept, how can I produce it in intuition? Which is to say in space and in time, an object conforming to the concept. Producing in space and time, that is the operation of the schema. In other words, the schema does not refer to a rule of recognition, but refers to a rule of production. The synthesis of a house is the rule of recognition according to which I say "it's a house". You say "it's a house" in front of very different things. You effect a synthesis of the given such that you relate them to the any-object-whatever "it's a house". The schema of the house is very different, it is not a rule of recognition over random diversities. The schema of the house is a rule of production, namely that you can give yourself a concept of house. For example I can take a functional definition: house = apparatus made for sheltering men, this doesn't yet give us a rule of production. The schema of the house is what allows you to produce it in experience, in space and in time, something, objects conforming to the concept. But that definition does not get out of the concept; you can turn the concept around all you like in all directions, apparatus made for sheltering men, you will not draw rules of production from it, the rules of construction of the house. If you have the rule of production you have a schema. It is very interesting from the point of view of a study of judgement. Consider the two following judgements: the straight line is a line equal in all its points; there you have a logical or conceptual definition, you have the concept of the straight line. If you say "the straight line is black", you have an encounter in experience, not all straight lines are black. The straight line is the shortest path from one point to another, it's a type of judgement, a quite extraordinary one according to Kant, and why? Because it cannot be reduced to either of the two extremes that we have just seen. What is the shortest path? Kant tells us that the shortest path is the rule of production of a line qua straight. If you want to obtain a straight line, you take the shortest path. It is not a predicate at all. When you say: the straight line is the shortest path, you seem to treat the shortest path like an attribute or a predicate, when in fact it is not a predicate at all, it's a rule of production. The shortest path is the rule of production of a line qua straight line in space and in time.

Why in time? Here you must understand why time is involved in this, and even more deeply still than space. You can't define the shortest independently of time. How is it a rule of production? If someone says to you: you want to draw a straight line, very well, take the shortest! We no longer understand the judgement; we say so many things without knowing that we say them. Once again it is true historically that the judgement "the straight line is the shortest path between one point and another" has very very precise implications from a geometrical point of view, namely that while the Euclidean or conceptual definition of the straight line is indeed a line equal in all its points, the straight line as the shortest path from one point to another is an Archimedean notion, and Archimedean geometry has quite different principles than Euclidean geometry. The notion "the straight line is the shortest path" is purely nonsensical if you separate it from a whole calculus which is a comparison of heterogeneous elements. Here you find the theme of the synthesis again. The heterogeneous elements are not the different sorts of lines, straight or not straight, it's the confrontation of the curve and the straight line. It's the Archimedean theme of the minimal angle, of the smallest angle which is formed by the tangent and the curve. The shortest path is a notion which is inseparable from the calculus which in antiquity was called the calculus of exhaustion in which the straight line and the curve are treated in a synthetic confrontation. Given this, tracing the tangent to the curve is indeed a rule of production. So it is in this sense that I can say, despite appearances, that the straight line is the shortest path, we must see that the shortest path is not an attribute of the line and this is not surprising since "the shortest" is a relation. A relation is not an attribute. If I say Pierre is smaller than Paul, "smaller" is not an attribute of Pierre. Even Plato said that if Pierre is smaller than Paul, he is bigger than Jean. A relation is not an attribute. "The shortest" is the rule according to which I produce a line qua straight line in space and in time. In other words, I make a correspondence between a conceptual determination, that is the straight line defined as equal in all its points, and a spatio-temporal determination by which I can produce as many straight lines as I like in experience.

In one of Kant's distant successors, namely Husserl, there is something like this which also interests me very much, but I think Husserl has let something slip away. Husserl said to us: take two ends, at the two extremities of the chain, you have pure essences. For example the circle, as pure geometrical essence. And then, at the other end, you have things in experience which correspond to the circle. I can make an open-ended list of them: a plate, a wheel of a car, the sun. I would say, in technical terms, that all of these things in experience, a wheel, the sun, a plate, are subsumed under the concept of a circle. Can you not see a series of intermediaries between these two extremes, which will be of great importance from Kant onwards. But notions, they must be lived, the abstract is lived, it's really the same. At the moment when something becomes very very abstract, then you can say that it concerns something lived. We already know that "between the two" is not a mixture, that it will be a zone discovered by Kant. Take a word: "the ring" [le rond]. I can always say that the circle is a ring. The conceptual determination of the circle is: where points are situated at equal distance from a common point named centre. That's the conceptual determination, the empirical determination or determinations are the plate, the wheel and the sun. When I say: "oh what a beautiful ring [rond] !" - I was saying just before that the two extremes are the line conceptually defined as equal in all its points, and then "the straight line is black" which is an encounter in experience, a case of a straight line. But between the two, as a perfectly specific region, there is "the straight line is the shortest path."

Now between the circle and the illustrations of the circle in experience, I would almost say the images of the circle : the plate is an image of a circle, the wheel is an image of a circle, but I have this bizarre thing: a ring [rond]! It is very curious to do the logical analysis of a ring. I would say the same thing: if we go far enough in our analysis of the round, we will see that it's a rule of production; for example a round is the circumference [le tour], no, the round is what allows us to make a circumference.

The circumference is what allows us to make certain materials round. The ring must obviously be lived dynamically, as a dynamic process; in the same way that "the straight line is the shortest path" implies an operation by which the length of a curve is compared to that of a straight line, which is to say by which there is a linearisation of the curve, the ring implies an operation by which something in experience is rounded. It's a process of production of the circumference-type which allows the production in experience of things corresponding to the concept circle.

Where Husserl is obviously wrong is when he discovers this sphere of the ring - we have just shown how the ring is completely in the same domain as the shortest, it's the same domain of being - Husserl is wrong because he makes them into inexact essences, like subordinate essences. The direction that Kant went in seems much stronger to me, making them precisely into acts of the productive imagination. Here you can see in what respect the productive imagination is more profound than the reproductive imagination. The reproductive imagination is when you can imagine circles, concrete circles; you can imagine a circle drawn on a blackboard with red chalk, you can imagine a plate... all that is the reproductive imagination. But the circumference that allows you to make rounds, which allows you to round things, which is to say to produce in experience something conforming to the concept of circle, that doesn't depend on the concept of circle, that doesn't flow from the concept of circle, it's a schema, and that is the act of productive imagination.

You can see why Kant feels the need to discover a domain of the productive imagination distinct from the simply empirical or reproductive imagination. You can see the difference between a schema and a synthesis, if you have understood that I have finished with my first point: what the difference was between the two fundamental acts, within the context of knowledge: the schematism and the synthesis.

The schematism is not a case of reflective judgement, it is a dimension of determining judgement. I will do the story of reflective judgement on request.

The a posteriori is what is in space and in time. It's the plate, the wheel, the sun. A rule of production is solely a determination of space or of time conforming to the concept. Take another case. You make yourself a concept of a lion; you can define it by genus and specific difference. You can define it in this way: big animal, mammal, with a mane, growling. You make a concept. You can also make yourself lion images: a small lion, a big lion, a desert lion, a mountain lion; you have your lion images. What would the schema of a lion be? I would say in this case, not in all cases, that the concept is the determination of the species, or its the determination by genus and specific differences. The image in experience is all the individuals of this species, the schema of the lion is something which is neither the examples of a lion... [end of tape] ... there are spatio-temporal rhythms, spatio-temporal attitudes [allures]. We speak both of an animal's territory and an animal's domain, with its paths, with the traces that it leaves in its domain, with the times that it uses a particular path, all that is a spatio-temporal dynamism that you will not draw from the concept. I am not going to draw from the concept of a lion the way it inhabits space and time. From one tooth you can draw something of a mode of living: this is a carnivore. But really the spatio-temporal dynamism of an animal, that is really - I can't say its rule of production - but it's something productive, it's the way in which it produces a spatio-temporal domain in experience in conformity with its own concept. The lion is Kantian, all the animals are Kantian. What is the schema of the spider? The schema of the spider is its web, and its web is the way it occupies space and time. The proof is that the concept of the spider, I don't know how, but you can take the concept of a spider; the concept of a spider will include all of its anatomical parts and even the physiological functions of the spider. Thus one will encounter that funny sort of organ with which the spider makes his web. But can you deduce from it what we can now call the spatio-temporal being, and the correspondence of the web with the concept of a spider, which is to say with the spider as organism. It's very curious because it varies enormously according to the species of spider. There are cases of very extraordinary spiders which, when you mutilate one of their legs, which is nevertheless not used for fabrication, make abnormal webs in relation to their own species, they make a pathological web. What happened? As if a disturbance in space and time corresponded to the mutilation. I would say that the schema of an animal is its spatio-temporal dynamism.

Where Kant was determining, after Husserl, there were all sorts of experiments and I'm thinking of a funny sort of school which, at one time, had some success. It was the psychologists of the WŸrzburg school, they were closely linked to a Kantian lineage. They carried out psychological experiments. They said that there are three sorts of things: there's thought which operates with concepts, and then there's perception which grasps things, and if need be there is the imagination which reproduces things: but they said that there is also another dimension which they gave a very curious name to. They spoke of the direction of consciousness, or even of the intention of consciousness, or even of an empty intention. What is an empty intention? I think of a lion and an image of a lion comes to me; I think of a rhinoceros and I can see the rhinoceros very well in the image which comes to my mind, that is an intention. I have a conscious intention and an image comes to fill it, the image of the rhinoceros. So they carried out experiments on this, it was experimental psychology. They set the rules of the game, you're going to laugh: you stop yourself from having an image, you are given a word and you take a view which both excludes any image, and which nevertheless is not purely conceptual; what does that produce? It produces sorts of conscious orientations, i.e. spatio-temporal directions. The more abstract it was, the better. It was in order to persuade us that there were three possible attitudes of conscious: abstract thinking consciousness, for example proletariat, where one had to work for the proletariat. First reaction: proletariat = the class defined by... etc... I would say that that is the conceptual definition of the proletariat; it is a certain attitude of consciousness towards a word: I aim at the concept through the word. Second attitude of consciousness: through the word proletariat I evoke one, a proletarian: "ah yes, I've seen one!" That is really the empirical attitude, an image. Sartre, in his book The Psychology of Imagination, describes the third attitude, that of the WŸrzburg-type experiments, and he gives descriptions of people's responses; I see a sort of black wave advancing; it defined a sort of rhythm. Managing to grasp an attitude of consciousness, a sort of way of occupying space and time: the proletariat doesn't fill space and time in the same way as the bourgeoisie. At that moment you have the schema. Or else another method was to take a word that is empty for you, whose meaning you don't know: in a precious poem, and you carry out the direction of consciousness, you don't make an association, but a vague direction of consciousness, a sort of purely lived spatio-temporal opening. How does a consciousness orient itself following the sound of an understood word? There you have a whole dimension of spatio-temporal dynamisms which are somewhat similar to the schema. The schemas are subdivided, but while the concepts are subdivided according to genus and species, the schema will have another mode of division. In fact when I said that the true schema of the circle was the circumference, it is in fact a sub-schema because the circumference already implies certain modes, the circumference is the rule of production in order to obtain things in experience, but in these conditions of suitable materials. In other cases, something else would be required. I don't know how bicycle wheels are made? When phenomenology and then Heidegger, then all sorts of psychiatrists go on to define ways of being in space and in time, complexes or blocks of space-time, rhythmic blocks, I'd say that all that derives from Kant. Indeed the ethnologist constructs schemata of men to the extent that he describes manners: a civilisation defines itself, amongst other ways, by a block of space-time, by certain spatio-temporal rhythms which will vary the concept of man. It's obvious that an African, an American or an Indian won't inhabit space and time in the same way. What is interesting is when, in a limited space, we see the coexistence of different types of space-times. I could equally say that an artist operates through blocks of space-time. An artist is above all a rhythmicist. What is a rhythm? It's a block of space-time, it's a spatio-temporal block. But each time you have a concept, you don't yet have the rhythmicity of the things which are subordinated to it. A concept, at best, will give you the beat or the tempo. Which is to say a homogeneous beat, but rhythmicity is something entirely different from a homogeneous beat, something entirely different from a tempo.

I'll go on to my second point. You remember that we saw, in relation to the synthesis, this adventure of the sublime. Kant realises that the synthesis of the imagination, such as it arises in knowledge, rests on a basis of a different nature, namely that the synthesis of the imagination in all its aspects assumes an aesthetic comprehension, an aesthetic comprehension both of the thing to be measured and the unit of measure. You must be clear that aesthetic comprehension is not part of the synthesis, it's the basis [sol] that the synthesis rests on. I would say that it is not the ground [fondement] of the synthesis but that it is the foundation [fondation] of synthesis. At the same time that he discovers this basis, he discovers the extraordinary viability of this basis. He doesn't discover this basis without also seeing that this basis is ????? Why? Because what the synthesis rests on is fundamentally fragile, because the aesthetic comprehension of the unit of measure, assumed by all effective measurement, can at each instant be overwhelmed, which is to say that between the synthesis and its basis there is the constant risk of the emergence of a sort of thrust coming up from underground [sous-sol], and this underground will break the synthesis. For the synthesis rests on the aesthetic comprehension of the unit of measure, an aesthetic comprehension which is irreducible to the operations of knowledge. Why is this very fragile? Because at every instant there are types of phenomena in space and in time which risk overturning the aesthetic comprehension of the unit of measure, and it's the sublime, where the imagination finds itself before its limit. It is confronted with its own limit, it can no longer be at the service of the concepts of the understanding. To be at the service of the concepts of the understanding is to determine space and time in conformity with the concepts of the understanding, and here it can no longer do this: the imagination finds itself blocked before its own limit: the immense ocean, the infinite heavens, all that overturns it, it discovers its own impotence, it starts to stutter. And it is thus at the same time that the basis of the synthesis, namely aesthetic comprehension, and the underground of the synthesis, namely the sublime in so far as it overturns the base, is discovered. But there's a consolation; at the moment that the imagination finds that it is impotent, no longer able to serve the understanding, it makes us discover in ourselves a still more beautiful faculty which is like the faculty of the infinite. So much so that at the moment we feel for our imagination and suffer with it, since it has become impotent, a new faculty is awakened in us, the faculty of the supersensible.

When the storm is over, when the avalanche is finished, I rediscover my syntheses, but for a moment the horizon of knowledge will have been traversed by something which came from elsewhere, it was the eruption of the sublime which is not an object of knowledge. We must put ourselves in Kant's place, assuming that he has discovered all of this. He says to himself that there must be something analogous for the schema. The schema is also an operation of knowledge, we saw its relation to the synthesis; the schema must also follow its own limit and have something overwhelm it. It must be something different, a different adventure. There is no reason to treat philosophy in a different way from art or science. There are differences but they aren't at the level we think they are. Here is the schema of the schema: I make a big white ring [rond] up top and I put A on the side. To explain: this big white ring called A is the concept of a. Concept of a. Vertically, I make a dotted line, above all dotted, with an arrow at the end, and at the end of the arrow, beneath, I put a. I'll explain, but for those who want the complete schema: from the a which is beneath the end of my arrow, I make a filled line this time, a spray of little arrows, and under each of the little arrows I put a', a'', a '''. The big A is the concept a, at the end of my dotted arrow I have a, it's the schema of A, that is, the spatio-temporal determination A. If I take an example: A = concept of the circle, a = the ring or the schema of the circle, which is to say the rule of production. Then a', a'', a''' are the empirical things which conform to the schema, and led back to the concept by the schema. So a' = plate, a'' = wheel, a''' = sun, in our previous example. Why is it that the arrow which goes from the concept to the schema was dotted? Precisely in order to indicate subtly that the symbol which he opposes [to] or which he explicitly distinguishes from the schema in the Critique of Judgement, and it's among the most admirable pages in Kant. Well that's going to complicate things and here are the two schemas.

A = concept. a = schema of the concept, which is to say spatio-temporal determinations. B, dotted arrow and b. We need that to make a schema. I'll give examples. First example: A = the sun. a = to rise (spatio-temporal determination). Let's say that this is the auto-schema of the concept. B, the virtue of the concept, b: schema or intuition = x?

Second example: A = the sun, a = to set. You can see that these are two sub-schemas, I could have taken rising and setting in a single schema. B = death. b = intuition = x of death. Third example: A = a mill. a = a type of mill which implies a certain space-time, which is to say not the general schema of a mill, but a certain schema corresponding to category of mills = hand-mill. B = despotic constitution. b: intuition = ? = x.

I have two remarks to make if you understand these examples. There would be symbolisation when you use the schema or intuition a, not in relation to the corresponding concept A, but in relation to the quite different concept B for which you have no intuition of a schema. At that moment the schema ceases to be a rule of production in relation to its concept, and becomes a rule of reflection in relation to the other concept. So much so that you have the Kantian sequence: the synthesis refers to a rule of recognition, the schema refers to rules of production, the symbol refers to rules of reflection.

Why don't I have any intuition corresponding to the concept? Two possible cases: either because I don't in fact have one, because I lack the necessary knowledge, but I could have it, I could form a schema of the concept. Or else by virtue of the special nature of this concept.

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Bergson - Duration and Simultaneity

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Deleuze/Leibniz St. Denis

(excerpt)

St. Denis 10/03/1987

We’re working. The last time, I began a kind of overview or conclusion about the transformation that Leibniz brought about in the notion of substance. If you would allow me to leave that aside, I can come back to it later, especially since it was hardly begun. I feel the need to leave it aside because, as I announced to you, I need help not this time about mathematics, but about certain problems of physics. And since Isabelle Stengers is here today, and won’t be here in the coming weeks, I need to benefit from her presence, and this for two reasons: these problems concern Leibniz very closely and she knows him, and also because these problems equally concern the author who I’ve mentioned since the start of the year I wanted to discuss, specifically Whitehead. So you can consider that our meeting today is fully situated into our research on Leibniz, but also bears on Whitehead and his relations with Leibniz. You know, the Greeks had a great word, in the neo-Platonic school; there was a leader of the school, and he succeeded the preceding leader, and he had a word to designate the chief successor, it was “the diadoque”. The diadoque. If we imagine the Leibnizian school, Whitehead is the great diadoque, but at the same time, he renews everything. Hence my need – and why I so need to speak about this author whose dates are relatively old, 1861-1947, he died at in old-age. This [need] is because he belongs to these authors, to these very great philosophers who have been smothered, as if assassinated. What does that mean, assassinated? It means that on occasion, schools of thought arise that establish – in some ways, as regards the problem of thinkers, there are two dangers: there are all the Stalins, the Hitlers that you want, before whom thinkers have only two choices: resistance or exile. But sometimes, inside of thought, there is something else that happens, which are strange doctrines that arise, that get established, that take on a veritable power there where power resides in this domain, that is in universities, and that establish a kind of tribunal, an intellectual tribunal of a special kind, and behind them, or under them, nothing more can grow.  You really should turn off the recording devices because I am speaking quite freely. I will never write what I am saying, so I would like to be able to say: “I never said that”. In this sense, I am accusing British analytic philosophy of having destroyed everything in what was rich within thought, and I accuse Wittgenstein of having assassinated Whitehead, of having reduced Russell, his master, to a kind of essayist no longer daring to discuss logic. All of that was awful and is still going on. France was spared this, but we have our analytic philosophers; yet France was spared because it went through trials that were much worse. Well, this is just to say that everything is going badly. Nothing in the domain of thought dies a natural death, really. This British and American thought, before the war [WW II] was extraordinarily rich, full of richness, with authors that people now have gotten used to treating as if they were rather retarded [debile], like William James. William James was an astounding genius. He was in philosophy exactly what his brother was for the novel. For anyone looking for a doctoral thesis topic, I yet again tremble that there has never to my knowledge been a serious study of the two James brothers and their relations. And then there is Whitehead, and there was another, an Australian, the only very, very great Australian philosopher, Alexander. Whitehead is read by a handful of admirers and another handful of specialists. After all, Bergson as well… We cannot say that all of that was very serious. In 1903, Whitehead was in training as a mathematician, and with Russell he wrote the Principiae mathematicae, which are at the base of modern formalism and modern logic. These Principiae mathematicae that Wittgenstein will engender [perhaps Deleuze means Whitehead here] constitute a common, dramatic process. Ok, it matters little, I think Whitehead is British, but I get that wrong each time, and then afterward he settled in America around 1920-23 [actually at Harvard starting in 1924]. So the Principiae mathematicae with Russell was a great book of logic. The Concept of Nature, not translated into French, in 1920; Science and the Modern World, one of the rare books by Whitehead translated into French, very beautiful, very, very beautiful, very important, 1926 [actually, 1925], probably unfindable. His great book from 1929, Process and Reality; 1933, Adventures of Ideas. My goal is dual here: I want you to feel the grandeur of this thinking in itself, and at the same time that you grasp the link with Leibniz’s thinking, and henceforth, how literally Whitehead risks bringing to us a fundamental enlightenment about Leibniz. There is no problem with Whitehead’s knowledge of Leibniz. He is impregnated by Leibniz, and like Leibniz, he was a mathematician, a philosopher, and a physicist. Given that every philosophy tried to put something into question, what does Whitehead put into question? He puts into question the problem of what is called the categorial scheme. The categorial scheme is what? He tells us, generally, that the categorial scheme of classical thought is: subject-attribute, substance-attribute. And it is less a question of substance, which you can understand one way or another. What is important is not to ask if things are substances. The real question is that of the attribute, but in what sense? Precisely must substance be thought as function of an attribute, or must it be thought as function of something else? In other word, is substance is the subject of a predicate, or of predicates, of multiple predicates, is the predicate reducible to an attribute, an attribute like “the sky is blue”? You will tell me that it’s not a fundamentally new problem, but it’s new in a particular way, the cry of Whitehead. The cry that reverberates in all his work: no, the predicate is irreducible to any attribute. And why? Because the predicate is event. The fundamental notion is going to be that of event. And I think that it’s for the third time in the history of philosophy that this cry reverberates, and without doubt, each time it did so in a different way: Everything is event. You will tell me, no, everything is not event since the event is the predicate. For the moment, let’s say: everything is event since the subject is an adventure that only arises from the event. Is there a subject whose birth is not event? Everything is event. I am going to try to say it quickly. The first time, that reverberated with the Stoics, and they were opposed to Aristotle precisely in the Aristotelian enterprise of defining substance by the attribute. And they (the Stoics) maintained what must be called a “mannerism” since to the notion of attribute they opposed the manner of being. Being how, how to be. The attribute is what the thing is, but the how of the thing, the manner of being, that is something else entirely. And the Stoics created the first great theory of the event. And without doubt, there was a filiation [suite] in the logics of the Middle ages; one can locate the continuation of Stoic traditions, but one had to wait a very long time for this cry, this kind of cry to reverberate anew: everything is event! That is what I have tried to show from the start, namely it’s Leibniz, and there is no worse misunderstanding… I say that the result of our earlier research is that there is no worse error about Leibniz than to understand the inclusion of the predicate in the subject as if the predicate were an attribute. And far from the predicate being an attribute, Leibniz continually denies that the predicate is an attribute; for him, the predicate is a relation, or as he says it precisely in the Metaphysical Discourse: Event, predicate or event, “or”, it cannot be stated better, as he said it in the Metaphysical Discourse. So it seems to me particularly stupid to wonder how Leibniz can take into account once he has placed the predicate in the subject. Not only does he take relations into account, he has no difficulty taking relations into account for the simple reason that, for him, what he calls predicate is the relation, it’s the event. We already began to see a bit how he took account of the relation, but we are leaving that aside. We can well expect that this causes him no problems, a theory of relations. It is only a problem from the perspective of a false Leibniz for whom the reader would believe that the predicate, for Leibniz, is an attribute. In that case, one could ask, in fact, how can a relation be included in the subject. But if what is included in the subject are events, and by definition, as he says it very well, events are relations with existence. And there, we have to take seriously the word relation. Everything is event, at least all predicates are events. And there, for the third time, the cry reverberates with Whitehead: Everything is event. Everything is event, yes, including the great pyramid, says Whitehead. Even from the perspective of style, he’s quite Leibnizian. Generally, we consider an event as a category of very special things, for example, I go out into the street and get run over by a bus. It’s an event. But the great pyramid is not an event. At most, I would say, well ok, the construction of the great pyramid is an event, but not the great pyramid itself. A chair is not an event, it’s a thing. Whitehead said that the chair is an event, not only the chair’s production. The great pyramid is an event. It’s very important to understand that this is possible, the expression “everything is event.” In what way can the great pyramid be event? I jump to Leibniz, and I would like to jump perpetually from one to the other. We started off from certain determinations related to Adam. He was in the garden and he sinned, he committed a sin. To sin is obviously an event, it belongs to what everyone calls event. But the garden itself is equally an event. A flower is an event. Ok, so what? Does that mean insofar as it grows? Insofar as it emerges? But it never ceases to emerge, to grow. Or when it has finished growing, it never ceases to wither. It’s part of the flower itself, and at each instant of its duration, I must say it’s an event. And the chair? The chair is an event, not only its production. In what way is the great pyramid an event?  It is so insofar as it has duration, for example, five minutes. Insofar as the pyramid lasts five minutes, it is an event. Insofar as it lasts five more minutes, it’s another event. I can connect the two events by saying: it lasts ten minutes. Every thing, says Whitehead, is a passage of nature. In English, it’s “passage of nature”. Let’s correct a little in order to get back to Leibniz: every thing is a passage of God. This is strictly the same. Every thing is a passage of nature. The great pyramid is an event, and is even an infinite multiplicity of events. What does the event consist of? Literally every thing is a dance of electrons, or every thing is a variation of an electro-magnetic filed. And with that, we place a foot quite carefully into physics. For example, the event which is the life of nature in the great pyramid, yesterday and today. Perhaps we must foresee that there is not a single great pyramid, but that there are perhaps two great pyramids. That’s what he says in the text. But we are going too quickly… for the moment, that’s how it is. Ok, there are no things, there are only events, everything is event. An event is the support for an infinity of processes, processes of subjectivation, of individuation, of rationalization. Everything you’d like. Subjects are going to be born, rationalities, individualities are going to be traced, but all of that is in the events. Everything is event, but a classification of events is indeed required. For example, now must we pose the problem of freedom in terms of events? Is there a difference in nature between the events that a subject – assuming that I know what a subject is – that a subject undergoes, or that a subject brings forth? Which means: for create an event (faire événement). [turning over the tape] St Denis 10/03/1987

If I can identify the great pyramid through two passages of nature, by saying: it’s the same pyramid, it’s the great pyramid, it’s uniquely thanks to an eternal object. I wanted to make you grasp what this philosophy contains that’s at once very familiar and very strange for us. Philosophy should create such modes of thought. Besides, that the title of one of Whitehead’s books, Modes of Thought. If I summarize, I see three coordinates: the actual occasions defined by conjunctions, prehensions, and eternal objects. To the actual occasion correspond the concepts of conjunction, concrescence, and creativity; to prehensions correspond all the elements that we’ve not yet seen from prehension, all the components of prehension; to eternal objects correspond the different types of eternal object. For example, there are sensible eternal objects and there are conceptual eternal objects … no that’s bad, what I just said… there are eternal objects that refer to sensible qualities, and other that refer to scientific concepts. All of that is relatively easy. But we have three problems, and it’s there that I really need Isabelle. First problem: we started off from conjunctions, that is, from actual occasions, we already gave ourselves events and a world of events. Can we undertake the genesis of the event? How do we arrive at conjunctions? Are conjunctions just given like that? For it is not at all a given that there are conjunctions in the world. How are we to explain that there are conjunctions in the world. For me, I don’t know what Isabelle will say, it’s the fundamental problem of Whitehead’s philosophy. If that problem is managed, all the rest unfolds, not as a given, but all the rest unfolds rather well. That is really the most difficult problem, where Whitehead is both a physician and mathematician. He needs there an entire mode of physico-mathematics to take account of the formation of conjunctions, that is, of the formation of actual occasions. Why? Consider this: we start from an random distribution, a type like the random distribution of electrons, or a variation of an electro-magnetic field. How do conjunctions form in such a world? If we don’t have a precise answer to that, well then we will have failed. We need a precise answer to that question. The second question will be: what is a prehension made of? What are the elements of a prehension? And if it’s true that the actual occasion is a conjunction, we must say in Whitehead’s vocabulary, I forgot to indicate this, that an aggregate of prehensions is a nexus. Second problem: the components of prehensions. Third problem: the modes of eternal objects. The most difficult for me is this initial genesis. How do we arrive at conjunctions, why are there conjunctions? Is there a reason for conjunctions, a reason that can only be mathematical and physical? I would like Isabelle’s thoughts. How do you see all this? Isabelle Stengers: [Isabelle is quite far from the microphone, and her long intervention is barely audible]. Gilles Deleuze: That’s very interesting. We don’t have to discuss everything. What strikes me is that seems to interest Whitehead – the fundamental aspect of all great thinkers – what seems to interest Isabelle Stengers in Whitehead is not what interests me most. It’s not a question of saying who is right or wrong, it’s my turn to ask Isabelle questions because I am sure she is able to answer, without at all giving up her viewpoint. She told us this quite exactly: it is true that at the start of his work, for example in the Concept of Nature, Whitehead still thought it possible to create a genesis of the actual occasion, that is, a genesis of conjunctions. And OK, she tells me, at that moment, he thought only a mathematical physics can give us the key to this genesis. And then she says, he might have senses that, at the moment if he made a genesis of conjunctions, an idea to which he was greatly attached, since every conjunction is new, it is in fact novelty (nouveauté), in its essence it is novelty; there is not actual occasion that would not be new. It [the conjunction] is not the effect of preceding actual occasions, there is no determinism. An actual occasion is active, it is prehension, that is, prehending – well, since an actual occasion can not be deducted from anything other that itself, Isabelle thinks that he would have renounced, or at least less interested in its genesis in order to take the problem to a level of a finality and of a very particular conception of God which, ultimately, operates at the level of actual occasions. As for me, I think, as we will see, that the genesis of conjunctions, or the genesis of actual occasions, the physico-mathematical genesis, is something that Whitehead will not renounce, provided that this genesis fully respects the requirement that Isabelle signals, specifically that is must not be a genesis such that the actual occasion would derive, flow or result from its genetic components. It must be a genesis that takes account of this, that the only law of the actual occasion is always to be a novelty in relation to its components. And it is precisely this genesis of novelty that is essential, genesis of novelty as such, that is, that implies no reduction of the new to the former. It is this very genesis that Whitehead, because he knows so much math and physics, is going to create in conditions that, in fact, make of him and his philosophy one of the rare philosophies – in my view, with Bergson’s – to have operated a fundamental linkage with modern science. In this, we have to ask Isabelle each time, does that work, or does it not? He starts from something, he gives himself something. We are in the problem of the genesis of occasions, or the genesis of conjunctions. A conjunction in something new, of the type: there’s a concert this evening. It’s a novelty, and you won’t engender it; it is not a result. It is not the effect of a cause. A genesis is not causal. So then, what is it? Where does it come from? I am adding a question mark to all my sentences. It comes from “many,” you will excuse my accent, I’ll never be able to pronounce it. I say it in English… I would say it comes from the multiple, but a pure and random multiplicity. He gives it a name in Process and Reality, it’s the pure state of disjunctive diversity. He gives himself any disjunctive diversity whatsoever (une diversité disjunctive quelconque). The word disjunctive is very important since one starts from the opposite of conjunction. Disjunctive diversity, what is it? I don’t know. We’ll see. What matters is that at each of these steps, there is a kind of adjustment with Leibniz that is astounding, such that all of this is a prodigious reading of Leibniz, at the same time that it brings forth a new Leibniz for us. It’s a new actual occasion. Astounding. It comes in this way from “many”, a random multiplicity defined by the disjunctive diversity. Isabelle, do you grant me that? Second point, that is going to be the first step of the genesis. It will show us that, starting with this step of disjunctive diversity, something absolutely new is produced, the first step of novelty, sketched in this disjunctive diversity of infinite, limitless series, which tend toward no limit. Infinite, limitless series. It’s like the step, this first moment, it’s infinite divisibility. The disjunctive diversity, we will see how and why — there are many questions in what I am saying, I am setting out a map – undergoes a process of infinite divisibility that organizes infinite, limitless series [inaudible word]. So at this stage, a question: what are these limitless series, unlimited series, infinite series without limits? I will begin to answer by saying that this first step rests on an analysis of vibration. Ultimately, at the basis of the event, there are vibrations. At the basis of actual events, there are vibrations. The first step was the “many”, any old vibrations, random vibrations. For those who know Bergson, perhaps you recall the splendid ending of Matter and Memory: the basis of matter is vibration, and vibrations of vibration. The intersection with Bergson emerges at all sorts of levels, these philosophers are very close. Everything is vibration. Why does vibration already produce this initial order? It’s because every vibration has sub-multiples and extends on these sub-multiples. The property of vibration is to extend on these sub-multiples. In this I am not really speaking scientifically, it’s just so you can locate things in your head; that has a famous name in all domains, these are harmonics. In this I don’t need to underscore the wink at Leibniz. All this is important for your future. A color is a vibration, a sound is a vibration. As such, every sound has harmonics, every color has harmonics. My hypothesis is this: it is vibration that emerges in the “many,” but how does it emerge, there where we are pushed back… we have to answer, and I beg you please not to abandon me if I don’t answer everything, or else everything will collapse, and so fine. If everything collapses, we will say: we were wrong, Whitehead isn’t a great philosopher. Yet obviously Whitehead is a great philosopher, one of genius. So ok, a vibration is formed in the “many”, and with that moment, disjunctive diversity starts to be organized into an infinite, limitless series. We must assume that each vibration has sub-multiples, has harmonics into infinity, within pure cosmos. The cosmos was the “many”, that is, chaos. It was the chaos cosmos. Third step: infinite vibratory series… in other words, every infinitely divisible vibration has certain intrinsic characteristics. The intrinsic characteristics either concerning the nature of the envisaged vibration, or even – extrinsic characteristics – its relations with other vibrations. I would say that a sonorous vibration has characteristics of duration, height, intensity, timber. Color has characteristics, intrinsic and extrinsic, that are tint, saturation, value, the three great dimensions of color, of what color will be, but it’s open, we can always find a new one. For a long time, these three variables of color were noted: tint, saturation, and value. Since the end of the 19th century, we tend more and more to add to these the extent (l’étendue) of color to then define a very interesting new variable that also depends on extent and value, and that is called the weight of color.  You recall the vibration enters into infinite, limitless series; these are characteristics, or rather as Whitehead says, the quantities, the quantitative expressions capable of measuring them, of measuring these characteristics; the quantitative expressions able to measure these characteristics enter into series that converge toward limits. The vibratory series are not convergent and have no limits. It’s the first stage of genesis. Second stage of genesis: the series of intrinsic and extrinsic characteristics converge toward limits. This time we have an idea of converging series. The timbers are going to form a converging series; the intensities are going to form a convergent series; the heights are going to form a convergent series, etc. etc. The tints are going to form a convergent series. It’s beautiful. It’s a thing of very great beauty. It’s a genesis of the most… and it’ also so full of science, it’s a very modern way, but yet it’s very simple. So the first stage, the “many” or the disjunctive diversity; second stage, the organization of infinite, limitless series with the vibrations and the sub-multiples of vibrations; third stage, formation of convergent series toward limits. Fourth stage, everything is ready: the actual occasion is the conjunction. The conjunction comes after the convergence. The conjunction is a meeting of two convergent series, at least. You have engendered the actual occasion, and that does not prevent the actual occasion, which is a conjunction, from being radically new in relation to the genetic series that engender it, in relation to two convergent series, at least. It [the conjunction] is completely new. Hence, fifth [stage] then, from which the actual occasion is made – once we say that we must not confuse the elements of the actual occasion and the conditions of the actual occasion, I would say the requisites of the actual occasion. The requisites of the actual occasion are: the disjunctive diversity, the infinite, limitless vibratory series, the convergent series. These are the successive requisites of the actual occasion, that is, of the conjunction. So you have four terms: 1) the many, 2) the infinite, limitless series, 3) the convergence of series, that is, these are evidently not the same series that become convergent, these are new series; 4) the conjunction of series which yield the actual occasion; 5) what are the elements to be, and not the requisites, the elements of the actual occasion, that is, what is an actual occasion made of? Answer: it is made of prehensions. But what is a prehension made of, what are the elements of the prehension, what are the component elements and not the requisite conditions? So why does this matter to me? Is this very clear as a schema? Realize that this refers to all kinds of things in math and in physics, it correspond to each person’s taste, you don’t strictly need to know anything to understand, or at least to feel it. As for “feeling” as Whitehead says, you can even see this world being formed; the “many” is a kind of soup, it’s the great soup, it’s what the cosmologists call “the pre-biotic soup,” the disjointed members, what Empedocles already called the membrae disjunctae. That links so well with everything that is important in philosophy. It’s the river that carries along the membrae disjunctae, the scattered members, an arm then a nose, it’s chaos. But we must assume that it’s not a nose, it’s an electron of a nose. So that in this soup are traced limitless series without convergence. It’s so close to Leibniz. And then each one of these limitless series without convergence has a characteristic, and the characteristics of series enter themselves into convergent series. When they have entered into convergent series, then conjunctions are produced, like lumps in your soup. It’s an actual occasion precipitated by a lump; wow! An occasion, and you will notice that your lump is composed of prehensions. Well, is this clear, if not I will start it all over again! I am insisting on this; in my view, such a genesis escape the danger indicated by Isabelle, because the actual occasion is not at all presented as a passive result. Each time there is activity and retro-activity. The convergent series react on infinite series without convergence, the conjunctions react on the convergent series. At each level, there is emergence of a new type of activity. The series is an activity, the convergence of series is another activity, the conjunction another activity, etc… So there, she granted me the stage of “the many” or of the disjunctive diversity. We pass on to the second stage. Isabelle, when you wrote “States and Process”, did you already know Whitehead? Yes! My question is very simple. We don’t know very well what happened in the disjunctive diversity, but we grant ourselves vibrations. There is the formation of vibrations. Where do they come from, vibrations? On this point, I need Isabelle less. Can I say that these vibration form infinite series that convergent toward no limit, and it’s the case of a vibration in relation to its harmonics, assuming an infinity of harmonics within chaos? Can I say that, or else is it a physically stupid proposition? Isabelle Stengers: [Unfortunately still inaudible due to the distance from the microphone] Gilles: You said something quite marvelous. I insist on the following point because it’s a kind of philosophy in connection with modern science. I refer again to Bergson’s example, because to say that Bergson made a metaphysics from duration and liquidates science, one has to be profoundly retarded [débile] to say something like that. Bergson’s idea is that modern science gives us and brings us a new conception of time, scientific time. Modern scientific time which begins in physics around the 16th century can be defined scientifically, I say again scientifically, as follows: it’s the consideration of time at any instant at all [à un instant quelconque]. Why is this modern? Because ancient science defined time as a function of privileged moments. Bergson’s idea is very simple, and very beautiful: what did Galileo do, what did Galileo do? Based on that, what did Bergson try to do? He said that ancient metaphysics was the correlate to ancient science. Bergson tells us: what you call metaphysics, is ancient metaphysics, but to what extent? It was perfectly adapted to ancient science, and inversely ancient science was perfectly adapted to its metaphysics. Physics, metaphysics, we must retain these excellent terms. Aristotle created the physics of movement, and the metaphysics that corresponds to this physics of movement, and the physics of movement corresponds to Aristotle’s metaphysics. Today there is a series of cretins who thought, because science had evolved, it could do without metaphysics. Bergson said that this is completely idiotic; science has, in fact, sufficiently evolved – not at all that Aristotle is ancient, that has no sense – one must, including and thanks to Aristotle, take up metaphysics again from zero. One must make metaphysics into the correlate for modern science, exactly as modern science is the correlate of a potential metaphysics that we have not yet been abet to create. What is the metaphysics that corresponds to a scientific consideration of time taken as a any instant at all? Bergson said: it’s mine. He meant that it’s a metaphysics of duration, and no longer of eternity. You notice the common theme with Whitehead. What is metaphysics for Whitehead that corresponds to modern science? It would be a metaphysics of creativity. It will be a metaphysics of the new. Novelty. The something new. It’s marvelous what Isabelle just said. I say: is it possible to conceive of a vibration that extends into the infinity of harmonics, that is, into an infinity of sub-multiples? She answered, obviously yes; but that would not interest a physician. Notice the notion of “interest”: that would not interest a physician because the whole operation of science will be to find the average. A research would be solely interested in the average. Or in the case of acoustics, a research would be interested only in a number of finite, and close, harmonics. This is a researcher’s job. The metaphysics that correspond to this science is not a reflection on this science; it must say metaphysically what the science says scientifically, it must say with concepts what science says with functions. Metaphysics is prodigiously interested in not finding the average, and to constitute a series which, in fact, will have no physical interest, but will have considerable metaphysical interest, an infinite series without convergence constituted by vibration and the infinity of its sub-multiples, the infinity of its harmonics. Second point, which is more complicated. It is possible, in fact, that I understood poorly Whitehead’s these, and that hurts me. First, it’s in English, not translated obviously, and you have already guess that my relationship with English was painful. But for those who know English and this interest, it’s in Concept of Nature, it’s the marvelous chapter 4. I am translating little bits for you: “The character of the event (for the moment, the event is thus an infinite, not convergent sequence [suite] without limits) can be defined by the quantitative expressions expression relations between diverse intrinsic quantities in the event itself (i.e. in the series), or between such quantities and other intrinsic quantities in other events (that is, in other vibrations). In the case of events that have considerable spatio-temporal extension, the quantitative aggregate of expressions is highly complex. If ‘e’ an event, let us call Qe the aggregate of quantitative expression defining its character, and which includes its connections with the rest of nature.” You see that ‘e’ designate the infinite vibratory series extending to the sub-multiples, and that Qe designates one of the characteristics of the series. It yields as a schema of two series “e1, e2, e3, en, n + 1”, that the vibratory series, and Qen, Qen + 1, that’s the series of characteristics? “If Q1 is a quantitative measure found in Qe1, and Q2 the homologue of Q1 which is found in Qe2, and Q3 etc. etc… then we will have a series Q1-Q2-Q3-Qn+1, etc. … Although it has no final term,” thus it has in common with the preceding vibratory series, it has in common not to have a final term, it is indeed infinite… “Although it has no final term, it converges toward a definite limit.” So my agony is: Is my commentary correct? Whitehead gives no example. I therefore need Isabelle. The essential point is this birth of the convergent series, convergent toward a limit. What do you think? Isabelle Stengers: [inaudible] Gilles Deleuze: That interests me a lot because I believe in a kind of relay, a metaphysical relay in science, once we’ve said that the two disciplines are very different. But that does not prevent us from having relays if there is the complementarity that I indicated following Bergson, following Whitehead, if there is this complementarity between metaphysics and science, and that this complementarity has absolutely not gone stale; it’s just that people have absolutely understood nothing, it seems to me, and we have not [rejected] that there are relays [transcription seems to be missing a word] Question: [inaudible] Gilles Deleuze : … The Platonic theory of the receptacle does not presuppose space-time, it’s the reverse. Space and time will be born in certain conditions. The question is very correct, but it is yet to come. The actual occasion is something that is already in space and in time. My answer addressed what is the relation between space and time and the series, the initial series for the actual occasion. There series that I have ceaselessly discussed today, that are initial to the actual occasion, you remember? These are the conditions of the actual occasion, they [the series] are first in relation to the actual occasion. In order you have these series which condition the actual occasion, the series space-time, and the actual occasion. The actual occasion is certainly in space and in time. Isabelle Stengers: [still inaudible] Gilles : In my opinion, no, but I do grant you that. Those are your concerns. But that’s not bad, it’s not at all a criticism. My example of light, if I invoked it, it’s a pure example that consisted of using something that cannot intervene at that moment, by right, but which has the advantage of providing an understanding of how a screen [crible] functions. In fact, I said: the action of light consists in making a filter between shadow and dark ground [sombre fond] of colors, and on the contrary, the filter I mentioned made a filter between chaos and the dark ground, period. So I was not obligated to grant myself anything, in any case, like light. Does the screen – something more important in my view – does the screen already imply mirror equivalences, that would be a big problem. It must not. If we were obliged to include quasi-mirrors, that would complicate things a lot, but I hope there is no need for a quasi-mirror. Isabelle Stengers: When you read Whitehead to us, and you made your series of Q, Q1, Q2, Qn+1, this n+1, does that mean we continue like that to infinity, or does it just mean that we are in a space of three + dimensions? Gilles Deleuze: The symbols Q1, Q2, Q3, etc… it’s a series of characteristics, but each one animates a convergent series. Each characteristic has a convergent series, and on the other hand, you have an open, unlimited series of characteristics. Intervention : [inaudible] Gilles Deleuze : Well, good… then read Plato. Source: www.pierrejoris.com

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nath1as · 9 years ago

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Deleuze/Leibniz Vincennes

Cours Vincennes - 15/04/1980

We are going to be involved for a short while in a series on Leibniz. My goal is very simple: for those who don't know him at all, I want to present this author and to have you love him, to incite in you a sort of desire to read his works. To begin reading Leibniz, there is an incomparable working instrument. It is the life work, a very modest work, but a very profound one. It is by a lady, Madame Prenant, who had long ago published selected excerpts by Leibniz. Usually a collection of excerpts is of doubtful value, but this one is a work of art, for a very simple reason: Leibniz had writing techniques which no doubt were rather frequent during his era (beginning 18th century), but that he pushed to an extraordinary extent. Of course, like all philosophers, he wrote huge books. But one might almost be tempted to say that these huge books did not constitute the essential part of his works, since what was essential was in the correspondence and in quite tiny memoirs. Leibniz's great texts often ran 4 or 5, 10 pages, or were in letters. He wrote to some extent in all languages and in some ways was the first great German philosopher. He constitutes the arrival in Europe of German philosophy. His influence was immediate on the German Romantic philosophers in the 19th century, then continues particularly with Nietzsche. Leibniz is a philosopher who best helps us understand a possible answer to this question: what is philosophy? What does a philosopher do? What does philosophy grapple with? If you think that definitions like search for the true or search for wisdom are not adequate, is there a philosophical activity? I want to say very quickly how I recognize a philosopher in his activity. One can only confront these activities as a function of what they create and of their mode of creation. One must ask, what does a woodworker create? What does a musician create? For me, a philosopher is someone who creates concepts. This implies many things: that the concept is something to be created, that the concept is the product of a creation. I see no possibility of defining science if one does not indicate something that is created by and in science. And, it happens that what is created by and in science, I'm not completely sure what it is, but not concepts properly speaking. The concept of creation has been much more linked to art than to science or to philosophy. What does a painter create? He creates lines and colors. That suggests that lines and colors are not givens, but are the product of a creation. What is given, quite possibly, one could always call a flow. It's flows that are given, and creation consists in dividing , organizing, connecting flows in such a way that a creation is drawn or made around certain singularities extracted from flows. A concept is not at all something that is a given. Moreover, a concept is not the same thing as thought: one can very well think without concepts, and everyone who does not do philosophy still thinks, I believe, but does not think through concepts. If you accept the idea of a concept as the product of an activity or an original creation. I would say that the concept is a system of singularities appropriated from a thought flow. A philosopher is someone who invents concepts. Is he an intellectual? No, in my opinion. For a concept as system of singularities appropriated from a thought flow... Imagine the universal thought flow as a kind of interior monologue, the interior monologue of everyone who thinks. Philosophy arises with the action that consists of creating concepts. For me, there are as many creations in the invention of a concept as in the creation by a great painter or musician. One can also conceive of a continuous acoustic flow (perhaps that is only an idea, but it matters little if this idea is justified) that traverses the world and that even encompasses silence. A musician is someone who appropriates something from this flow: notes? Aggregates of notes? No? What will we call the new sound from a musician? You sense then that it is not simply a question of the system of notes. It's the same thing for a philosopher, it is simply a question of creating concepts rather than sounds. It is not a question of defining philosophy by some sort of search for the truth, for a very simple reason: this is that truth is always subordinate to the system of concepts at one's disposal. What is the importance of philosophers for non-philosophers? It is that although non-philosophers don't know it, or pretend not to be interested, whether they like it or not they think through concepts which have proper names. I recognize the name of Kant not in his life, but in a certain type of concept signed Kant. Henceforth, one can very well conceive of being the disciple of a philosopher. If you are situated so that you say that such and such a philosopher signed the concepts for which you feel a need, then you become Kantian, Leibnizian, etc. It is quite necessary that two great philosophers not agree with each other to the extent that each creates a system of concepts that serves as his point of reference. Thus that is not all to be judged. One can very well only be a disciple locally, only on one point or another, philosophy is detachable. You can be a disciple of a philosopher to the extent that you consider that you personally need this type of [concept]. Concepts are spiritual signatures, but that does not mean it's in one's head because concepts are also ways of living. And this is not through choice or reflections, the philosopher reflects no more than does the painter or musician. Activities are defined by a creative activity and not by a reflexive dimension. Henceforth, what does it mean to say: to need this or that concept? In some ways, I tell myself that concepts are such living things, that they really are things with four paws, that move, really. It's like a color, like a sound. Concepts really are so living that they are not unrelated to something that would, however, appear the furthest from the concept, notably the scream . In some ways, the philosopher is not someone who sings, but someone who screams. Each time that you need to scream, I think that you are not far from a kind of call of philosophy. What would it mean for the concept to be a kind of scream or a kind of form of scream? That's what it means to need a concept, to have something to scream! We must find the concept of that scream. One can scream thousands of things. Imagine something that screams: "Well really, all that must have some kind of reason to be." It's a very simple scream. In my definition, the concept is the form of the scream, we immediately see a series of philosophers who would say, "yes, yes"! These are philosophers of passion, of pathos, distinct from philosophers of logos. For example, Kierkegaard based his entire philosophy on fundamental screams. But Leibniz is from the great rationalist tradition. Imagine Leibniz, there is something frightening there. He is the philosopher of order, even more, of order and policing, in every sense of the word "policing." In the first sense of the word especially, that is, regulated organization of the city. He only thinks in terms of order. But very oddly in this taste for order and to establish this order, he yields to the most insane concept creation that we have ever witnessed in philosophy. Disheveled concepts, the most exuberant concepts, the most disordered, the most complex in order to justify what is. Each thing must have a reason. In fact, there are two kinds of philosopher, if you accept the definition by which philosophy is the activity consisting of creating concepts. But there are perhaps two poles: there are those who engage in a very sober creation of concepts; they create concepts on the level of a particular singularity well distinguished from another, and I dream finally of a kind of quantification of philosophers in which they would be quantified according to the number of concepts they have signed or invented. If I say: Descartes! That's the type of philosopher with a very sober concept creation. The history of the cogito, historically one can always find an entire tradition, precursors, but there is nonetheless something signed Descartes in the cogito concept, notably (a proposition can express a concept) the proposition: "I think therefore I am," a veritable new concept. It's the discovery of subjectivity, of thinking subjectivity. It's signed Descartes. Of course, we could always look in St. Augustine's works, to see if it wasn't already in preparation. There is certainly a history of concepts, but it's signed Descartes. Haven't we made rather quick work of Descartes though? We could assign to him five or six concepts, an enormous feat to have invented six concepts, but it's a very sober creation. And then there are exasperated philosophers. For them, each concept covers an aggregate of singularities, and then they always need to have other, always other concepts. One witnesses a mad creation of concepts. The typical example is Leibniz. He never finished creating something new. That's all I wanted to explain. He is the first philosopher to reflect on the power of the German language as a concept, as German being an eminently conceptual language, and it's not by chance that it can also be a great language of the scream. Multiple activities, he attends to all, a very great mathematician, great physics scholar, very good jurist, many political activities, always in the service of order. He does not stop, he is very shady . There is a Leibniz-Spinoza visit (he who was the anti-Leibniz): Leibniz has him read manuscripts, and one imagines Spinoza very exasperated, wondering what this guy wants. Following that when Spinoza was attacked, Leibniz said that he never went to see him, he said it was to monitor him... Abominable, Leibniz is abominable. His dates: 1646-1716. It's a long life, straddling plenty of things. Finally he had a kind of diabolical humor. I'd say that his system is rather like a pyramid. Leibniz's great system has several levels. None of these levels is false, these levels symbolize each other, and Leibniz is the first great philosopher to conceive of activity and thought as a vast symbolization. Thus, all these levels symbolize, but they are all more or less close to what we could provisionally call the absolute. And that belongs to his very body of work. Depending on Leibniz's correspondent or on the public to which he addressed himself, he presented his whole system at a particular level. Imagine that his system is made of levels more or less contracted or more or less relaxed; in order to explain something to someone, he goes to situate himself on a particular level of his system. Let us assume that the someone in question was suspected by Leibniz of having a mediocre intelligence: very well, he is delighted, he situates himself on one of the lowest levels of his system, and if he addresses someone of higher intelligence, he jumps to a higher level. As these levels belong implicitly to Leibniz's own texts, that creates a great problem of commentary. It's complicated because, in my opinion, one can never rely on a Leibniz text if one has not first discerned the system level to which this text corresponds. For example, there are texts in which Leibniz explains what, according to him, is the union of soul and body, right, and it's to one particular correspondent or another; to another correspondent, he will explain that there is no problem in the union of soul and body since the real problem is that of the relation of souls to one another. The two things are not at all contradictory, it's two levels of the system. The result is that if one does not evaluate the level of a Leibniz text, then one will get the impression that he constantly contradicts himself, when in fact, he does not contradict himself at all. Leibniz is a very difficult philosopher. I would like to give titles to each part of what I have to propose to you. The principal #1 I would call "a funny thought" . Why do I call it "a funny thought"?, Well, because among Leibniz's texts, there is a small one that Leibniz himself calls "funny thought." Thus I am authorized by the author himself. Leibniz dreamed a lot, he has a whole science-fiction side that is absolutely amazing, all the time he imagined institutions. In this little "funny thought" text, he imagined a very disturbing institution that would be as follows: an academy of games would be necessary. In that era, as well with Pascal, certain other mathematicians, and Leibniz himself, there developed a great theory of games and probabilities. Leibniz is one of the great founders of game theory. He was impassioned by mathematical game problems, he must have been quite a games player himself. He imagined this academy of games as necessarily being at once - why at once? Because depending on the point of view in which one is situated to see this institution, or to participate in it - this would be at once a section of the academy of sciences, a zoological and botanical garden, a universal exposition, a casino where one gambled, and an enterprise of police control. That's not bad. He called that "a funny thought." Assume that I'm telling you a story. This story consists in taking up one of the central points of Leibniz's philosophy, and I tell it to you as if it were the description of another world, and there I also number the principal propositions that go into forming a funny thought.

a) The thought flow, eternally, brings with it a famous principle that has a very special characteristic because it is one of the only principles about which one can be certain, and at the same time one can not see at all what it offers to us. It is certain, but it is empty. This famous principle is the principle of identity. The principle of identity has a classical formula, A is A. That is certain. If I say blue is blue or God [is] God, I am not saying with this that God exists, in a sense I am in certainty. Only there it is, do I think something when I say A is A, or am I not thinking? Let us nonetheless try to say what results from this principle of identity. It is presented in the form of a reciprocal proposition. A is A means: subject A, verb to be, A attribute or predicate. There is a reciprocity of subject and predicate. Blue is blue, a triangle is a triangle, these are empty and certain propositions. Is that all? An identical proposition is a proposition such that the attribute or the predicate is the same as the subject and reciprocates with the subject. There is a second case just a bit more complex, notably that the principle of identity can determine propositions which are not simply reciprocal propositions. There is no longer simply reciprocity of the predicate with the subject and subject with the predicate. Suppose that I say: "The triangle has tree sides," this is not the same thing as saying, "The triangle has three angles." "The triangle has three angles" is an identical proposition because it is reciprocal. "The triangle has three sides" is a little different, it is not reciprocal. There is no identity of subject and predicate. In fact, "three sides" is not the same thing as "three angles". And nonetheless, there is a supposed logical necessity. This logical necessity is that you cannot conceptualize three angles composing a single figure without this figure also having three sides. There is no reciprocity, but there is inclusion. Three sides are included in the triangle. Inherence or inclusion. Likewise, if I say that matter is matter, matter and matter is an identical proposition in the form of a reciprocal proposition. The subject is identical to the predicate. If I say that matter is in extension <étendue>, this is again an identical proposition because I cannot think of the concept matter without already introducing extension. Extension is in matter. This is all the more a reciprocal proposition since, inversely, perhaps I really can think of extension without anything filling it in, that is, without matter. This is therefore not a reciprocal proposition, but it is a proposition of inclusion; when I say "matter is in extension," this is an identical proposition by inclusion. I would say therefore that there are two kinds of identical propositions: there are reciprocal propositions in which the subject and predicate are one and the same, and propositions of inherence or inclusion in which the predicate is contained in the concept of the subject. If I say "this page has a front side and a back side," OK, let's leave that, I withdraw my example. If I am looking for a more interesting statement of the identity principle, I would say in Leibnizian fashion that the identity principle is stated as follows: every analytical proposition is true. What does analytical mean? According to the example we have just seen, an analytical proposition is one in which either the predicate or the attribute is identical with the subject, for example, "the triangle is triangular," reciprocal proposition, or proposition of inclusion such as "the triangle has three sides." The predicate is contained in the subject to the point that when you have conceived of the subject, the predicate was already there. It suffices therefore to have an analysis in order to find the predicate in the subject. Up to this point, Leibniz as original thinker has yet to emerge.

b) Leibniz emerges. He arises in the form of this very bizarre scream . I am going to give it a more complex expression than I did earlier. Everything that we're saying is not philosophy, but pre-philosophy. This is the terrain on which a very prodigious philosophy will be built. Leibniz arrives and says: OK, the identity principle gives us a certain model. Why a certain model? In its very statement <énoncé>, an analytical proposition is true, if you attribute to a subject something that constitutes a unity with the subject itself, or that is mixed up with or is already contained in the subject. You risk nothing in being wrong. Thus, every analytical proposition is true. Leibniz's stroke of pre-philosophical genius is to say: Let's consider reciprocity! Something absolutely new and nonetheless very simple starts there, since this had to be thought through. And what does it mean to say, "it had to be thought through"? It means that one had to have need of that, that had to relate to something quite urgent for him. What is the reciprocity of the identity principle in its complex statement, "every analytical proposition is true"? Reciprocity poses many more problems. Leibniz emerges and says: every true proposition is analytical. If it is true that the identity principle gives us a model of truth, why are we stumped by the following difficulty, notably: it is true, it doesn't make us think anything. The identity principle will force us to think something; it is going to be reversed, turned around. You will tell me that turning A is A around yields A is A. Yes and no. That yields A is A in the formal formulation which prevents the reversal of the principle. But in the philosophical formulation, which still amounts to exactly the same thing, "every analytical proposition is a true proposition", if you reverse the principle: "every true proposition is necessarily analytical," what does that mean? Each time that you formulate a true proposition, it must be analytical (and this is where there is the scream!), whether you want it or not, that is, it is reducible to a proposition of attribution or of predication, and not only is it reducible to a judgment of predication or attribution (the sky is blue), but it is analytical, that is the predicate is either reciprocal with the subject or contained in the concept of the subject? Does that go without saying? He throws himself into a strange undertaking , and it is not from preference that he says that, rather he needs it. But he undertakes an impossible task, in fact he needs some entirely crazy concepts in order to reach this task that he is in the process of giving himself. If every analytical proposition is true, every true proposition certainly must be analytical. It does not go without saying at all that every judgment is reducible to a judgment of attribution. It's not going to be easy to show. He throws himself into a combinatory analysis, as he himself says, that is fantastic. Why doesn't it go without saying? "The box of matches is on the table," I'd say that this is a judgment, you know? "On the table" is a spatial determination. I could say that the matchbox is "here." "Here," what's that? I'd say that it's a judgment of localization. Again I repeat very simple things, but they always have been fundamental problems of logic. It's only to suggest that in appearance, all judgments do not have as form predication or attribution. When I say, "the sky is blue," I have a subject, sky, and an attribute, blue. When I say "the sky is up there" or "I am here," is "here" - spatial localization - assimilable to a predicate? Can I formally link the judgment "I am here" to a judgment of the kind "I am blond"? It's not certain that spatial localization is a quality. And "2+2=4" is a judgment that we ordinarily call a relational judgment. Or if I say, "Pierre is smaller than Paul," this is a relation between two terms, Pierre and Paul. No doubt I orient this relation upon Pierre: if I say "Pierre is smaller than Paul," I can say "Paul is larger than Pierre." Where is the subject, where is the predicate? That is exactly the problem that has disturbed philosophy since its beginnings; ever since there was logic they have wondered to what extent the judgment of attribution could be considered as the universal form of any possible judgment, or rather one case of judgment among others. Can I treat "smaller than Paul" like an attribute of Pierre? It's not certain, not at all obvious. Perhaps we have to distinguish very different types of judgment from each other, notably: relational judgment, judgment of spatio-temporal localization, judgment of attribution, and still many more: judgment of existence. If I say "God exists," can I formally translate it into the form of "God is existent," existent being an attribute? Can I say that "God exists" is a judgment of the same form as "God is all-powerful"? Undoubtedly not, since I can only say "God is all-powerful" by adding "yes, if he exists". Does God exist? Is existence an attribute? Not certain. So you see that by proposing the idea that every true proposition must be in one way or another an analytical proposition, that is identical, Leibniz already gives himself a very hard task; he commits himself to showing in what way all propositions can be linked to the judgment of attribution, notably propositions that state relations, that state existences, that state localizations, and that, at the outside, exist, are in relation with, can be translated as the equivalent of the attribute of the subject. In your mind there must arise the idea of an infinite task. Let us assume that Leibniz reached it: what world is going to emerge from it? What very bizarre world? What kind of world is it in which I can say "every true proposition is analytical"? You recall certainly that ANALYTICAL is a proposition in which the predicate is identical to the subject or else is included in the subject. That kind of world is going to be pretty strange. What is the reciprocity of the identity principle? The identity principle is thus any true proposition is analytical; not the reverse, any analytical proposition is true. Leibniz said that another principle is necessary, reciprocity: every true proposition is necessarily analytical. He will give to it a very beautiful name: the principle of sufficient reason. Why sufficient reason? Why does he believe himself fully immersed in his very own scream? EVERYTHING MUST SURELY HAVE A REASON. The principle of sufficient reason can be expressed as follows: whatever happens to a subject, be it determinations of space and time, of relation, event, whatever happens to a subject, what happens, that is what one says of it with truth, everything that is said of a subject must be contained in the notion of the subject. Everything that happens to a subject must already be contained in the notion of the subject. The notion of "notion" is going to be essential. It is necessary for "blue" to be contained in the notion of sky. Why is this the principle of sufficient reason ? Because if it is this way, each thing with a reason, reason is precisely the notion itself in so far as it contains all that happens to the corresponding subject . Henceforth everything has a reason. Reason = the notion of the subject in so far as this notion contains everything said with truth about this subject. That is the principle of sufficient reason which is therefore justly the reciprocal of the identity principle. Rather than looking for abstract justifications I wonder what bizarre world is going to be born from all that? A world with very strange colors if I return to my metaphor of painting. A painting signed Leibniz. Every true proposition must be analytical or still more, everything that you say with truth about a subject must be contained in the notion of the subject. You sense that this is getting crazy, he's got a lifetime of work ahead of him. What does "notion" mean? It's signed Leibniz. Just as there is a Hegelian conception of the concept, there is a Leibnizian conception of the concept.

c) Again, my problem is what world is going to emerge, and in this sub-category c), I would like to begin to show that, from this point, Leibniz is going to create truly hallucinatory concepts. It's truly a hallucinatory world. If you want to think about relations between philosophy and madness, for example, there are some very weak pages by Freud on the intimate relation of metaphysics with delirium . One can only grasp the positivity of these relations through a theory of the concept, and the direction that I would like to take would be the relationship of the concept with the scream. I would like to make you feel this presence of a kind of conceptual madness in Leibniz's universe as we are going to see it be born. It is a gentle violence, let yourself go. It is not a question of arguing. Understand the stupidity of objections. I will add a parenthesis to complicate things. You know that there is a philosopher following Leibniz who said that truth is one of synthetic judgments. He is opposed to Leibniz. OK! How does that concern us? It's Kant. This is not to say that they do not agree with each other. When I say that, I credit Kant with a new concept which is synthetic judgment. This concept had to be invented, and it was Kant who did so. To say that philosophers contradict one another is a feeble formula, it's like saying that Velasquez did not agree with Giotto, right! It's not even true, it's nonsensical. Every true proposition must be analytical, that is such that it attributes something to a subject and that the attribute must be contained in the notion of the subject. Let us consider an example. I do not wonder if it is true, I wonder what it means. Let us take an example of a true proposition. A true proposition can be an elementary one concerning an event that took place. Let's take Leibniz's own example: "CAESAR CROSSED THE RUBICON". It's a proposition. It is true or we have strong reasons to assume it's true. Another proposition: "ADAM SINNED". There is a highly true proposition. What do you mean by that? You see that all these propositions chosen by Leibniz as fundamental examples are event-ual propositions , so he does not give himself an easy task. He is going to tell us this: since this proposition is true, it is necessary, whether you want it or not, that the predicate "crossed the Rubicon," if the proposition is true, but it is true, this predicate must be contained in the notion of Caesar. Not in Caesar himself, but in the notion of Caesar. The notion of the subject contains everything that happens to a subject, that is, everything that is said about the subject with truth. In "Adam sinned," sin at a particular moment belongs to the notion of Adam. Crossing the Rubicon belongs to the notion of Caesar. I would say that here, Leibniz proposes one of his greatest concepts, the concept of inherence. Everything that is said with truth about something is inherent in the notion of this something. This is the first aspect or development of sufficient reason.

d) When we say that, we can no longer stop. When one has started into the domain of the concept, one cannot stop. In the domain of screams, there is a famous scream from Aristotle. The great Aristotle -- who, let us note, exerted an extremely strong influence on Leibniz -- at one point proposed in the Metaphysics a very beautiful formula: it is indeed necessary to stop (anankstenai). This is a great scream. This is the philosopher in front of the chasm of the interconnection of concepts. Leibniz could care less, he does not stop. Why? If you refer to proposition c): everything that you attribute to a subject must be contained in the notion of this subject. But what you attribute with truth to any subject whatsoever in the world, if were it Caesar, it is sufficient for you to attribute to it a single thing with truth in order for you to notice with fright that, from that moment on, you are forced to cram into the notion of the subject not only the thing that you attribute to it with truth, but the totality of the world. Why? By virtue of a well-known principle that is not at all the same as that of sufficient reason. This is the simple principle of causality. For in the end, the causality principle stretches to infinity, that's it's very characteristic. And this is a very special infinite since, in fact, it stretches to the indefinite . Specifically, the causality principle states that everything has a cause, which is very different from every thing has a reason. But the cause is a thing, and in its turn, it has a cause, etc. etc. I can do the same thing, notably that every cause has an effect and this effect is in its turn the cause of effects. This is therefore an indefinite series of causes and effects. What difference is there between sufficient reason and cause? We understand very well. Cause is never sufficient. One must say that the causality principle poses a necessary cause, but never a sufficient one. We must distinguish between necessary cause and sufficient reason. What distinguishes them evidently is that the cause of a thing is always something else. The cause of A is B, the cause of B is C, etc..... An indefinite series of causes. Sufficient reason is not at all something other than the thing. The sufficient reason of a thing is the notion of the thing. Thus, sufficient reason expresses the relation of the thing with its own notion whereas cause expresses the relations of the thing with something else. It's limpid.

e) If you say that a particular event is encompassed in the notion of Caesar, "crossing the Rubicon" is encompassed in the notion of Caesar . You can't stop yourself in which sense? From cause to cause and effect to effect, it's at that moment the totality of the world that must be encompassed in the notion of a particular subject. That becomes very odd, there's the world passing by inside each subject, or each notion of subject. In fact, crossing the Rubicon has a cause, this cause itself has multiple causes, from cause to cause, into cause from cause and into cause from cause of cause. It's the whole series of the world that passes there, at least the antecedent series. And moreover, crossing the Rubicon has effects. If I limit myself to the largest ones: commencement of a Roman empire. The Roman empire in its turn has effects, we follow directly from the Roman empire. From cause to cause and effect to effect, you cannot say a particular event is encompassed in the notion of a particular subject without saying that, henceforth, the entire world is encompassed in the notion of a particular subject. There is indeed a trans-historical characteristic of philosophy. What does it mean to be Leibnizian in 1980? They exist, or at least it's possible that they exist. If you said, conforming to the principle of sufficient reason, that what happens to a particular subject, and which personally concerns it, then what you attribute it with truth, having blue eyes, crossing the Rubicon, etc. ... belongs to the notion of the subject, that is encompassed in this notion of the subject; you cannot stop, one must say that this subject contains the whole world. It is no longer the concept of inherence or inclusion, it's the concept of expression which, in Leibniz's work, is a fantastic concept. Leibniz expresses himself in this form: the notion of the subject expresses the totality of the world. His own "crossing the Rubicon" stretches to infinity backward and forward by the double play of causes and effects. But then, it is time to speak for ourselves, little matter what happens to us and the importance of what happens to us. We must say that it is each notion of subject that contains or expresses the totality of the world. That is, each of you, me, expresses or contains the totality of the world. Just like Caesar, no more, no less. That gets complicated, why? A great danger: if each individual notion, if each notion of the subject expresses the totality of the world, that means that there is only a single subject, a universal subject, and the you, me, Caesar, would only be appearances of this universal subject. It would be quite possible to say: there would be a single subject that would express the world. Why couldn't Leibniz say that? He had no choice. It would mean repudiating himself. All that he had done before that with the principle of sufficient reason would then make what sense? In my opinion, this was the first great reconciliation of the concept and the individual. Leibniz was in the process of constructing a concept of the concept such that the concept and the individual were finally becoming adequate to one another. Why? That the concept might extend into the individual, why is this new? Never had anyone dared that. The concept, what is it? It is defined by the order of generality. There is a concept when there is a representation which is applied to several things. But identifying the concept and the individual with each other, never had that been done. Never had a voice reverberated in the domain of thought to say that the concept and the individual were the same thing. What had always been distinguished was an order of the concept that referred to a generality and an order of the individual that referred to a singularity. Even more, it was always considered as going without saying that the individual as such was not comprehensible via the concept. It was always understood that the proper name was not a concept. Indeed, "dog" is certainly a concept, but "Fido" is not a concept. There is certainly a dogness about all dogs, as certain logicians say in a splendid language, but there is no Fido-ness about all Fidos. Leibniz is the first to say that concepts are proper names, that is, that concepts are individual notions. There is a concept of the individual as such. Thus you see that Leibniz cannot fall back on the proposition since every true proposition is analytical, the world is thus contained in a single and same subject which would be a universal subject. He cannot since his principle of sufficient reason implied that what was contained in a subject -- thus what was true, what was attributable to a subject -- was contained in a subject as an individual subject. Thus he cannot give himself a kind of universal mind. He has to remain fixed on the singularity, on the individual as such. And in fact, this will be one of the truly original points for Leibniz, the perpetual formula in his works: substance (no difference between substance and subject for him) is individual. It's the substance Caesar, it's the substance you, the substance me, etc. ... The urgent question in my sub-category d) since he forbids himself from invoking a universal mind in which the world will be included ... other philosophers will invoke a universal mind. There is even a very short text by Leibniz entitled "Considerations on universal mind," in which he goes on to show in what way there is indeed a universal mind, God, but that does not prevent substance from being individual. Thus irreducibility of individual substances. Since each substance expresses the world, or rather each substantial notion, each notion of a subject, since each one expresses the world, you express the world, for all times. We notice that, in fact, he has a lifetime of work because he faces the objection that's made to him immediately: but then, what about freedom? If everything that happens to Caesar is encompassed in the individual notion of Caesar, if the entire world is encompassed in the universal notion of Caesar, then Caesar crossing the Rubicon only acts to unroll --odd word, devolvere, which comes up all the time in Leibniz's works -- or explicate (the same thing), that is to say, literally to unfold , like you unfold a rug. It's the same thing: explicate, unfold, unroll. Thus crossing the Rubicon as event only acts to unroll something that was encompassed for all times in the notion of Caesar. You see that it's quite a real problem. Caesar crossed the Rubicon in a particular year, but even were he crossing the Rubicon in a particular year, it was encompassed for all time in his individual notion. Thus, where is this individual notion? It is eternal. There is an eternal truth of dated events. But then, how about freedom? Everyone jumps on him. Freedom is very dangerous under a Christian regime. So Leibniz will write a little work, "On freedom," in which he explains what freedom is. Freedom is going to be a pretty funny thing for him. But leave that aside for the moment. What distinguishes one subject from another? That, we can't leave aside for the moment, unless our flow were to be cut off. What is going to distinguish you from Caesar since just like him, you express the totality of the world, present, past, and future? It's odd, this concept of Expression. That's where he proposes a very rich notion.

f) What distinguishes an individual substance from another is not very difficult. In some way, it has to be irreducible. Each one, each subject, for each individual notion, each notion of subject has to encompass this totality of the world, express this total world, but from a certain point of view. And there begins a perspectivist philosophy. And it's not inconsiderable. You will tell me: what is more banal than the expression "a point of view"? If philosophy means creating concepts, what does create concepts mean? Generally speaking, these are banal formulae. Great philosophers each have banal formulae that they wink at. A wink from a philosopher is, at the outside limit, taking a banal formula and having a ball , you have no idea what I'm going to put inside it. To create a theory of point of view, what does that imply? Could that be done at any time at all? Is it by chance that it's Leibniz who created the first great theory at a particular moment? At the moment in which the same Leibniz created a particularly fruitful chapter in geometry, called projective geometry. Is it by chance that it's out of an era in which are elaborated, in architecture as in painting, all sorts of techniques of perspective? We retain simply these two domains that symbolize that: architecture-painting and perspective in painting on one hand, and on the other hand, projective geometry. Understand what Leibniz wants to develop from them. He is going to say that each individual notion expresses the totality of the world, yes, but from a certain point of view. What does that mean? Of so little import is it, banally, pre-philosophically, that it is henceforth as equally impossible for him to stop. That commits him to showing that what constitutes the individual notion as individual is point of view. And that therefore point of view is deeper that whosoever places himself there. At the basis of each individual notion, it will indeed be necessary for there to be a point of view that defines the individual notion. If you prefer, the subject is second in relation to the point of view. And after all, to say that is not a piece of cake, it's not inconsiderable. He established a philosophy that will find its name in the works of another philosopher who stretches out his hand to Leibniz across the centuries, to wit Nietzsche. Nietzsche will say: my philosophy is a perspectivism. You understand that it becomes idiotic or banal to whine about whether perspectivism consists in saying that everything is relative to the subject; or simply that everything is relative. Everyone says it, it belongs to propositions that hurt no one since it is meaningless. So long as I take the formula as signifying everything depends on the subject, that means nothing, I caused, as one says ...

. . . What makes me = me is a point of view on the world. Leibniz cannot stop. He has to go all the way to a theory of point of view such that the subject is constituted by the point of view and not the point of view constituted by the subject. Fully into the nineteenth century, when Henry James renews the techniques of the novel through a perspectivism, through a mobilization of points of view, there too in James's works, it's not points of view that are explained by the subjects, it's the opposite, subjects that are explained through points of view. An analysis of points of view as sufficient reason of subjects, that's the sufficient reason of the subject. The individual notion is the point of view under which the individual expresses the world. It's beautiful and it's even poetic. James has sufficient techniques in order for there to be no subject; what becomes one subject or another is the one who is determined to be in a particular point of view. It's the point of view that explains the subject and not the opposite. For Leibniz, every individual substance is like an entire world and like a mirror of God or of the whole universe that each substance expresses in its own way: kind of like an entire city is diversely represented depending on the different situations of the one who looks at it. Thus, the universe is seemingly multiplied as many times as there are substances, and the glory of God is redoubled equally by as many completely different representations of his/her/its . He speaks like a cardinal. One can even say that every substance bears in some ways the characteristic of infinite wisdom and of all of God's power, and limits as much as it is able to.

In all this, I maintain that the new concept of point of view is deeper than the concept of individual and individual substance. It is point of view which will define essence. Individual essence. One must believe that to each individual notion corresponds a point of view. But that gets complicated because this point of view would be in effect from birth to death for an individual. What would define us is a certain point of view on the world. I said that Nietzsche will rediscover this idea. He didn't like him , but that's what he took from him. The theory of point of view is an idea from the Renaissance. The Cardinal de Cuse , a very great Renaissance philosopher, referred to portraiture changing according to point of view. From the era of Italian fascism, one notices a very odd portrait almost everywhere: face on, it represented Mussolini, from the right side it represented his son-in-law, and if one stood to the left, it represented the king.

The analysis of points of view in mathematics -- and it's again Leibniz who caused this chapter of mathematics to make considerable progress under the name of analysis situs --, and it is evident that it is connected to projective geometry. There is a kind of essentiality, of objectity of the subject, and the objectity is the point of view. Concretely were everyone to express the world in his own point of view, what does that mean? Leibniz did not retreat from the strangest concepts. I can no longer say "from his own point of view." If I said "from his own point of view," I would make the point of view depend on a preceding subject , but it's the opposite. But what determines this point of view? Leibniz : understand, each of us expresses the totality of the world, only he expresses it in an obscure and confused way. Obscurely and confused means what in Leibniz's vocabulary? That means that the totality of the world is really in the individual, but in the form of minute perception. Minute perceptions. Is it by chance that Leibniz is one of the inventors of differential calculus? These are infinitely tiny perceptions, in other words, unconscious perceptions. I express everyone, but obscurely, confusedly, like a clamor.

Later we will see why this is linked to differential calculus, but notice that the minute perceptions of the unconscious are like differentials of consciousness, it's minute perceptions without consciousness. For conscious perceptions, Leibniz uses another word: apperception. Apperception, to perceive , is conscious perception, and minute perception is the differential of consciousness which is not given in consciousness. All individuals express the totality of the world obscurely and confusedly. So what distinguishes a point of view from another point of view? On the other hand, there is a small portion of the world that I express clearly and distinctly, and each subject, each individual has his/her own portion, but in what sense? In this very precise sense that this portion of the world that I express clearly and distinctly, all other subjects express it as well, but confusedly and obscurely.

What defines my point of view is like a kind of projector that, in the buzz of the obscure and confused world, keeps a limited zone of clear and distinct expression. However stupid you may be, however insignificant we all may be, we have our own little thing, even the pure vermin has its little world: it does not express much clearly and distinctly, but it has its little portion. Beckett's characters are individuals: everything is confused, an uproar , they understand nothing, they are in tatters ; there is the great uproar of the world. However pathetic they may be in their garbage can, they have their very own little zone. What the great Molloy calls "my properties." He no longer moves, he has his little hook and, in a strip of one meter, with his hook, he grabs things, his properties. It's a clear and distinct zone that he expresses. We are all the same. But our zone is more or less sizable, and even then it's not certain, but it is never the same. What is it that determines the point of view? It's the proportion of the region of the world expressed clearly and distinctly by an individual in relation to the totality of the world expressed obscurely and confusedly. That's what point of view is.

Leibniz has a metaphor that he likes: you are near the sea and you listen to waves. You listen to the sea and you hear the sound of a wave. I hear the sound of a wave, that is, I have an apperception: I distinguish a wave. And Leibniz says: you would not hear the wave if you did not have a minute unconscious perception of the sound of each drop of water that slides over and through another, and that makes up the object of minute perceptions. There is the roaringof all the drops of water, and you have your little zone of clarity, you clearly and distinctly grasp one partial result from this infinity of drops, from this infinity of roaring, and from it, you make your own little world, your own property.

Each individual notion has its point of view, that is from this point of view, it extracts from the aggregate of the world that it expresses a determined portion of clear and distinct expression. Given two individuals, you have two cases: either their zones do not communicate in the least, and create no symbols with one another -- there aren't merely direct communications, one can conceive of there being analogies -- and in that moment, they have nothing to say to each other; or it's like two circles that overlap: there is a little common zone, there we can do something together. Leibniz thus can say quite forcefully that no two individual substances have the same point of view or exactly the same clear and distinct zone of expression. And finally, Leibniz's stroke of genius: what will define the clear and distinct zone of expression that I have? I express the totality of the world, but I only express clearly and distinctly a reduced portion of it, a finite portion. What I express clearly and distinctly, Leibniz tells us, is what relates to my body. We will see what this body means, but what I express clearly and distinctly is that which affects my body.

Thus I obviously do not express clearly and distinctly the passage of the Rubicon, since that concerned Caesar's body. There is something that concerns my body and that only I express clearly and distinctly, in relation to this buzz that covers the entire universe.

f) In this story of the city, there is a problem. OK, there are different points of view. These points of view preexist the subject who is placed there, good. In this event, the secret of point of view is mathematical, geometrical, and not psychological. It's at the least psycho-geometrical. Leibniz is a man of notions, not a man of psychology. But everything urges me to say that the city exists outside points of view. But in my story of expressed world, in the way we started off, the world has no existence outside the point of view that expresses it; the world does not exist in itself. The world is uniquely the common expressed of all individual substances, but the expressed does not exist outside that which expresses it. The world does not exist in itself, the world is uniquely the expressed. The entire world is contained in each individual notion, but it exists only in this inclusion. It has no existence outside. It's in this sense that Leibniz will be, and not incorrectly, on the side of the idealists: there is no world in itself, the world exists only in the individual substances that express it. It's the common expressed of all individual substances. It's the expressed of all individual substances, but the expressed does not exist outside the substances that express it. It's a real problem!

What distinguishes these substances is that they all express the same world, but they don't express the same clear and distinct portion. It's like chess. The world does not exist. It's the complication of the concept of expression. Which is going to provide this final difficulty. Still it is necessary that all individual notions express the same world. So it's curious -- it's curious because by virtue of the principle of identity that permits us to determine what is contradictory, that is, what is impossible, it's A is not A. It's contradictory: example: the squared circle. A squared circle is a circle that is not a circle. So starting from the principle of identity, I can have a criterion of contradiction. According to Leibniz, I can demonstrate that 2 + 2 cannot make 5, I can demonstrate that a circle cannot be squared. Whereas, on the level of sufficient reason, it's much more complicated, why? Because Adam the non-sinner, Caesar not crossing the Rubicon, is not like the squared circle. Adam the non-sinner is not contradictory. Understand how he's going to try to save freedom, once he has placed himself in a bad situation for saving it. This is not at all impossible: Caesar could have not crossed the Rubicon, whereas a circle cannot be squared; here, there is no freedom.

So, again he's stuck, again Leibniz has to find another concept and, of all his crazy concepts, this will undoubtedly be the craziest. Adam could have not sinned, so in other words, the truths governed by the principle of sufficient reason are not the same type as the truths governed by the principle of identity, why? Because the truths governed by the principle of identity are such that their contradictory status is impossible, whereas the truths governed by the principle of sufficient reason have a contradictory status that is possible: Adam the non-sinner is possible.

It's even all that distinguishes, according to Leibniz, the truths called truths of essence and those called truths of existence. The truths of existence are such that their contradictory status is possible. How is Leibniz going to get out of this final difficulty? How is he going to be able to maintain at once that all that Adam did is contained forever in his individual notion, and nonetheless Adam the non-sinner was possible. He seems stuck, it's delicious because from this perspective, philosophers are somewhat like cats, it's when they are stuck that they get loose, or they're like fish, the concept becoming fish. He is going to tell us the following: that Adam the non-sinner is perfectly possible, like Caesar not having crossed the Rubicon, all that is possible, but it did not happen because, if it is possible in itself, it's incompossible. That's when he created the very strange logical concept of incompossibility. On the level of existences, it is not enough for a thing to be possible in order to exist, one must also know with what it is compossible. So Adam the non-sinner, though possible in himself, is incompossible with the world that exists. Adam could have not sinned, yes, but provided that there were another world. You see that the inclusion of the world in the individual notion, and the fact that something else is possible, he suddenly reconciles the notion of compossibility, Adam the non-sinner belongs to another world. Adam the non-sinner could have been possible, but this world was not chosen. It is incompossible with the existing world. It is only compossible with other possible worlds that have not passed into existence.

Why is it that world which passed into existence? Leibniz explains what is, for him, the creation of worlds by God, and we see well how this is a theory of games: God, in his understanding , conceives an infinity of possible worlds, only these possible worlds are not compossible with each other, and necessarily so since it's God who chooses the best. He chooses the best of possible worlds. And it happens that the best of possible worlds implies Adam as sinner. Why? That's going to be awful . What is interesting logically is the creation of a proper concept of compossiblity to designate a more limited logical sphere than that of logical possibility. In order to exist, it is not enough for something to be possible, this thing must also be compossible with others that constitute the real world. In a famous formula from the Monadology, Leibniz says that individual notions have neither doors nor windows. That arrives to correct the metaphor of the city. No doors or windows means that there is no opening. Why? Because there is no exterior. The world that individual notions express is interior, it is included in individual notions. Individual notions have no doors or windows, everything is included in each one, and yet there is a world common to all individual notions: for what each individual notion includes, to wit the totality of the world, the notion includes it necessarily as a form in which what it expresses is compossible with what the others express. It's a marvel. It's a world in which there is no direct communication between subjects. Between Caesar and you, between you and me, there is no direct communication, and as we'd say today, each individual notion is programmed in such a way that what it expresses forms a common world with what the other expresses. It's one of the last concepts from Leibniz: pre-established harmony. Pre-established, it's absolutely a programmed harmony. It's the idea of the spiritual automaton, and at the same time, it's the grand age of automatons at this end of the seventeenth century.

Each individual notion is like a spiritual automaton, that is what it expresses is interior to it, it's without doors or windows; it is programmed in such a way that what it expresses is in compossibility with what the other expresses. What I have done today was solely a description of the world of Leibniz, and even so, only one part of this world. Thus, the following notions have been successively laid out: sufficient reason, inherence and inclusion, expression or point of view, incompossibility.

Cours Vincennes - 22/04/1980

The last time, as we agreed, we had begun a series of studies on Leibniz that should be conceived as an introduction to a reading, yours, of Leibniz. To introduce a numerical clarification, I relied on numbering the paragraphs so that everything did not get mixed up. The last time, our first paragraph was a kind of presentation of Leibniz's principal concepts. As background to all this, there was a corresponding problem for Leibniz, but obviously much more general, to wit: what precisely does it mean to do philosophy. Starting from a very simple notion: to do philosophy is to create concepts, just as doing painting is to create lines and colors. Doing philosophy is creating concepts because concepts are not something that pre-exists, not something that is given ready made. In this sense, we must define philosophy through an activity of creation: creation of concepts. This definition seemed perfectly suitable for Leibniz who, precisely, in an apparently fundamentally rationalist philosophy, is engaged in a kind of exuberant creation of unusual concepts of which there are few such examples in the history of philosophy. If concepts are the object of a creation, then one must say that these concepts are signed. There is a signature, not that the signature establishes a link between the concept and the philosopher who created it. Rather the concepts themselves are signatures. The entire first paragraph caused a certain number of properly Leibnizian concepts to emerge. The two principal ones that we discerned were inclusion and compossibility. There are all kinds of things that are included in certain things, or enveloped in certain things. Inclusion, envelopment. Then, the completely different, very bizarre concept of compossibility: there are things which are possible in themselves, but that are not compossible with another. Today, I would like to give a title to this second paragraph, this second inquiry on Leibniz: Substance, World, and Continuity. The purpose of this second paragraph is to analyze more precisely these two major concepts of Leibniz: Inclusion and Compossibility. At the point where we ended the last time, we found ourselves faced with two problems: the first is that of inclusion. In what sense? We saw that if a proposition were true, it was necessary in one way or another that the predicate or attribute be contained or included -- not in the subject --, but in the notion of the subject. If a proposition is true, the predicate must be included in the notion of the subject. Let’s allow ourselves the freedom to accept that and, as Leibniz says, if Adam sinned, the sin had to be contained or included in the individual notion of Adam. Everything that happens, everything that can be attributed, everything that is predicated about a subject must be contained in the notion of the subject. This is a philosophy of predication. Faced with such a strange proposition, if one accepts this kind of Leibnizian gamble, one finds oneself immediately faced with problems. Specifically if any given event that concerns a specific individual notion, for example, Adam, or Caesar -- Caesar crossed the Rubicon, it is necessary that crossing the Rubicon be included in the individual notion of Caesar -- great, O.K., we are quite ready to support Leibniz. But if we say that, we cannot stop: if a single thing is contained in the individual notion of Caesar, like "crossing the Rubicon," then it is quite necessary that, from effect to cause and from cause to effect, the totality of the world be contained in this individual notion. Indeed, crossing the Rubicon itself has a cause that must also be contained in the individual notion, etc. etc. to infinity, both ascending and descending. At that point, the entire Roman empire -- which, grosso modo, results from the crossing of the Rubicon as well as all the consequences of the Roman empire -- in one way or another, all of this must be included in the individual notion of Caesar such that every individual notion will be inflated by the totality of the world that it expresses. It expresses the totality of the world. There we see the proposition becoming stranger and stranger. There are always delicious moments in the history of philosophy, and one of the most delicious of these came at the far extreme of reason -- that is, when rationalism, pushed all the way to the end of its consequences, engendered and coincided with a kind of delirium that was a delirium of madness. At that moment, we witness this kind of procession, a parade, in which the same thing that is rational pushed to the far end of reason is also delirium, but delirium of the purest madness. Thus, if it is true that the predicate is included in the notion of the subject, each individual notion must express the totality of the world, and the totality of the world must be included in each notion. We saw that this led Leibniz to an extraordinary theory that is the first great theory in philosophy of perspective or point of view since each individual notion will be said to express and contain the world. Yes, but from a certain point of view which is deeper, notably it is subjectivity that refers to the notion of point of view and not the notion of point of view that refers to subjectivity. This is going to have many consequences in philosophy, starting with the echo that this would have for Nietzsche in the creation of a perspectivist philosophy. The first problem is this: in saying that the predicate is contained in the subject, we assume that this brought up all sorts of difficulties, specifically: can relations be reduced to predicates, can events be considered as predicates? But let us accept that. We can find Leibniz wrong only starting from an aggregate of conceptual coordinates from Leibniz's. A true proposition is one for which the attribute is contained in the subject; we see quite well what that can mean on the level of truths of essences. Truths of essences, be they metaphysical truths (concerning God), or else mathematical truths. If I say 2+2=4, there is quite a bit to discuss about that, but I immediately understand what Leibniz meant, always independently of the question of whether he is right or wrong; we already have enough trouble knowing what someone is saying that if, on top of that, we wonder if he is right, then there is no end to it. 2+2=4 is an analytical proposition. I remind you that an analytical proposition is a proposition for which the predicate is contained in the subject or in the notion of the subject, specifically it is an identical proposition or is reducible to the identical.Identity of the predicate with the subject. Indeed, Leibniz tells us: I can demonstrate through a series of finite procedures, a finite number of operational procedures, I can demonstrate that 4, by virtue of its definition, and 2+2, by virtue of their definition, are identical. Can I really demonstrate it, and in what way? Obviously I do not pose the problem of how. We understand generally what that means: the predicate is encompassed in the subject, that means that, through a group of operations, I can demonstrate the identity of one and the other. Leibniz selects an example in a little text called "On Freedom." He proceeds to demonstrate that every number divisible by twelve is by this fact divisible by six. Every duodecimal number is sextuple . Notice that in the logistics of the nineteenth and twentieth centuries, you will again find proofs of this type that, notably, made Russell famous. Leibniz's proof is very convincing: he first demonstrates that every number divisible by twelve is identical to those divisible by two, multiplied by two, multiplied by three. It's not difficult. On the other hand, he proves that the number divisible by six is equal to that divisible by two multiplied by three. By that, what did he reveal? He revealed an inclusion since two multiplied by three is contained in two multiplied by two multiplied by three. It's an example that helps us understand on the level of mathematical truths that we can say that the corresponding proposition is analytical or identical. That is, the predicate is contained in the subject. That means, strictly speaking, that I can make into an aggregate, into a series of determinate operations, a finite series of determinate operations -- I insist on that -- I can demonstrate the identity of the predicate with the subject, or I can cause an inclusion of the predicate in the subject to emerge. And that boils down to the same thing. I can display this inclusion, I can show it. Either I can demonstrate the identity or I can show the inclusion. He showed the inclusion when he showed, for example... -- a pure identity would have been: any number divisible by twelve is divisible by twelve -- but with that, we reach another case of truth of essence: any number divisible by twelve is divisible by six, this time he does not stop at showing an identity, he shows an inclusion resulting from finite operations, quite determinate. That's what truths of essence are. I can say that inclusion of the predicate in the subject is proven by analysis and that this analysis responds to the condition of being finite, that is, it only includes a limited number of quite determinate operations. But when I say that Adam sinned, or that Caesar crossed the Rubicon, what is that? That no longer refers to a truth of essence, it's specifically dated, Caesar crossed the Rubicon here and now, with reference to existence, since Caesar crossed the Rubicon only if it existed. 2+2=4 occurs in all time and in all places. Thus, there are grounds to distinguish truths of essence from truths of existence. The truth of the proposition "Caesar crossed the Rubicon" is not the same type as 2+2=4. And yet, by virtue of the principles we saw the last time, no less for truths of existence than for truths of essence, the predicate must be in the subject and included in the notion of the subject; included therefore for all eternity in the notion of the subject, including for all eternity that Adam will sin in a particular place at a particular time. This is a truth of existence. No less than for truths of essence, for truths of existence, the predicate must be contained in the subject. Granted, but no less, that does not mean in the same way. And in fact, and this is our problem, what initial great difference is there between truth of essence and truth of existence? We sense it immediately. For the truths of existence, Leibniz tells us that even there, the predicate is contained in the subject. The "sinner" must be contained in the individual notion of Adam, just look: if the sinner is contained in the individual notion of Adam, it's the entire world that is contained in the individual notion of Adam, if we follow the causes back and if we track down the effects, as it's the entire world, you understand, that the proposition "Adam sinned" must be an analytical proposition, only in that case, the analysis is infinite. The analysis extends to infinity. What could that even mean? It seems to mean this: in order to demonstrate the identity of "sinner" and "Adam," or the identity of "who crossed the Rubicon" and "Caesar," this time an infinite series of operations is required. It goes without saying that we aren't capable of that, or it appears that we aren't. Are we capable of making an analysis to infinity? Leibniz is quite formal: [no], you, us, men, are not able to do so. Thus, in order to situate ourselves in the domain of truths of existence, we have to wait for the experience. So why does he present this whole story about analytical truths? He adds: yes, but infinite analysis, on the other hand, not only is possible, but created in the understanding of God. Does it suit us that God, he who is without limits, he who is infinite, can undertake infinite analysis? We're happy, we're happy for him, but at first glance, we wonder what Leibniz is talking about. I emphasize only that our initial difficulty is: what is infinite analysis? Any proposition is analytical, only there is an entire domain of our propositions that refers to an infinite analysis. We are hopeful: if Leibniz is one of the great creators of differential calculus or of infinitesimal analysis, undoubtedly this is in mathematics, and he always distinguished philosophical truths and mathematical truths, and so it's not a question for us of mixing up everything. But it's impossible to think that, when he discovers a certain idea of infinite analysis in metaphysics, that there aren't certain echoes in relation to a certain type of calculus that he himself invented, notably the calculus of infinitesimal analysis. So there is my initial difficulty: when analysis extends to infinity, what type or what is the mode of inclusion of the predicate in the subject? In what way is "sinner" contained in the notion of Adam, once it is stated that the identity of sinner and Adam can appear only in an infinite analysis? What does infinite analysis mean, then, when it seems that there is analysis only under conditions of a well-determined finitude? That's a tough problem. Second problem. I just exposed already a first difference between truths of essence and truths of existence. In truths of essence, the analysis is finite, in truths of existence, the analysis is infinite. That is not the only one, for there is a second difference: according to Leibniz, a truth of essence is such that its contradictory is impossible, that is, it is impossible for 2 and 2 not to make 4. Why? For the simple reason that I can prove the identity of 4 and of 2+2 through a series of finite procedures. Thus 2+2=5 can be proven to be contradictory and impossible. Adam non sinner, Adam who might not have sinned, I therefore seize the contradictory of sinner. It's possible. The proof is that, following the great criterion of classical logic -- and from this perspective Leibniz remains within classical logic -- I can think nothing when I say 2+2=5, I cannot think the impossible, no more than I think whatever it might be according to this logic when I say squared circle. But I can very well think of an Adam who might not have sinned.Truths of existence are called contingent truths. Caesar could have not crossed the Rubicon. Leibniz's answer is admirable: certainly, Adam could have not sinned, Caesar could have not crossed the Rubicon. Only here it is: this was not compossible with the existing world. An Adam non sinner enveloped another world. This world was possible in itself, a world in which the first man might not have sinned is a logically possible world, only it is not compossible with our world. That is, God chose a world such that Adam sinned. Adam non sinner implied another world, this world was possible, but it was not compossible with ours. Why did God choose this world? Leibniz goes on to explain it. Understand that at this level, the notion of compossibility becomes very strange: what is going to make me say that two things are compossible and that two other things are incompossible? Adam non sinner belongs to another world than ours, but suddenly Caesar might not have crossed the Rubicon either, that would have been another possible world. What is this very unusual relation of compossibility? Understand that perhaps this is the same question as what is infinite analysis, but it does not have the same outline. So we can draw a dream out of it, we can have this dream on several levels. You dream, and a kind of wizard is there who makes you enter a palace; this palace... it's the dream of Apollodorus told by Leibniz. Apollodorus is going to see a goddess, and this goddess leads him into the palace, and this palace is composed of several palaces. Leibniz loved that, boxes containing boxes. He explained, in a text that we will examine, he explained that in the water, there are many fish and that in the fish, there is water, and in the water of these fish, there are fish of fish. It's infinite analysis. The image of the labyrinth hounds him. He never stops talking about the labyrinth of continuity. This palace is in the form of a pyramid. Then, I look closer and, in the highest section of my pyramid, closest to the point, I see a character who is doing something. Right underneath, I see the same character who is doing something else in another location. Again underneath the same character is there in another situation, as if all sorts of theatrical productions were playing simultaneously, completely different, in each of the palaces, with characters that have common segments. It's a huge book by Leibniz called Theodicy , specifically divine justice. You understand, what he means is that at each level is a possible world. God chose to bring into existence the extreme world closest to the point of the pyramid. How was he guided in making that choice? We shall see, we must not hurry since this will be a tough problem, what the criteria are for God's choice. But once we've said that he chose a particular world, this world implicated Adam sinner; in another world, obviously all that is simultaneous, these are variants, one can conceive of something else, and each time, it's a world. Each of them is possible. They are incompossible with one another, only one can pass into existence. And all of them attempt with all their strength to pass into existence. The vision that Leibniz proposes of the creation of the world by God becomes very stimulating. There are all these worlds that are in God's understanding, and each of which on its own presses forward pretending to pass from the possible into the existent. They have a weight of reality, as a function of their essences. As a function of the essences they contain, they tend to pass into existence. And this is not possible for they are not compossible with each other: existence is like a dam. A single combination will pass through. Which one? You already sense Leibniz's splendid response: it will be the best one! And not the best one by virtue of a moral theory, but by virtue of a theory of games. And it's not by chance that Leibniz is one of the founders of statistics and of the calculus of games. And all that will get more complicated... What is this relation of compossibility? I just want to point out that a famous author today is Leibnizian. What does it mean to be Leibnizian today? I think that means two things, one not very interesting and one very interesting. The last time, I said that the concept is in a special relationship with the scream. There is an uninteresting way to be Leibnizian or to be Spinozist today, by job necessity, people working on an author, but there is another way to make use of a philosopher, one that is non-professional. These are people who are able not to be philosophers. What I find amazing in philosophy is when a non-philosopher discovers a kind of familiarity that I can no longer call conceptual, but immediately seizes upon a familiarity between his very own screams and the concepts of the philosopher. I think of Nietzsche, he had read Spinoza early on and, in this letter, he had just re-read him, and he exclaims: I can't get over it! I can't get over it! I have never had a relation with a philosopher like the one I have had with Spinoza. And that interests me all the more when it's from non-philosophers. When the British novelist Lawrence expresses in a few words the way Spinoza upset him completely. Thank God he did not become a philosopher over that. What did he grasp, what does that mean? When Kleist stumbles across Kant, he literally can't get over it. What is this kind of communication? Spinoza shook up many uncultivated readers ... Borges and Leibniz. Borges is an extremely knowledgeable author who read widely. He is always talking about two things: the book that does not exist...

...he really likes detective stories, Borges. In Ficciones, there is a short story, "The Garden of Forking Paths." As I summarize the story, keep in mind the famous dream of the Theodicy.

"The Garden of Forking Paths," what is it? It's the infinite book, the world of compossibilities. The idea of the Chinese philosopher being involved with the labyrinth is an idea of Leibniz's contemporaries, appearing in mid-17th century. There is a famous text by Malebranche that is a discussion with the Chinese philosopher, with some very odd things in it. Leibniz is fascinated by the Orient, and he often cites Confucius. Borges made a kind of copy that conformed to Leibniz's thought with an essential difference: for Leibniz, all the different worlds that might encompass an Adam sinning in a particular way, an Adam sinning in some other way, or an Adam not sinning at all, he excludes all this infinity of worlds from each other, they are incompossible with each other, such that he conserves a very classical principle of disjunction: it's either this world or some other one. Whereas Borges places all these incompossible series in the same world, allowing a multiplication of effects. Leibniz would never have allowed incompossibles to belong to a single world. Why? I only state our two difficulties: the first is, what is an infinite analysis? and second, what is this relationship of incompossibility?

The labyrinth of infinite analysis and the labyrinth of compossibility.

Most commentators on Leibniz, to my knowledge, try in the long run to situate compossibility in a simple principle of contradiction. They conclude that there would be a contradiction between Adam non sinner and our world. But, Leibniz's letter already appears to us such that this would not be possible.

It's not possible since Adam non sinner is not contradictory in itself and the relation of compossibility is absolutely irreducible to the simple relation of logical possibility.

So trying to discover a simple logical contradiction would be once again to situate truths of existence within truths of essence. Henceforth it's going to be very difficult to define compossibility.

Still remaining within this paragraph on substance, the world, and continuity, I would like to ask the question, what is infinite analysis? I ask you to remain extremely patient. We have to be wary of Leibniz's texts because they are always adapted to the correspondents within given audiences, and if I again take up his dream, I must change it, and a variant of the dream, even within the same world, would result in levels of clarity or obscurity such that the world might be presented from one point of view or another. So that for Leibniz's texts, we have to know to whom he addresses them in order to be able to judge them.

Here is a first kind of text by Leibniz in which he tells us that, in any proposition, the predicate is contained in the subject. Only it is contained either in act -- actually -- or virtually. The predicate is contained in the subject, but this inclusion, this inherence is either actual or virtual. We would like to say that that seems fine. Let us agree that in a proposition of existence of the type Caesar crossed the Rubicon, the inclusion is only virtual, specifically crossing the Rubicon is contained in the notion of Caesar, but is only virtually contained. Second kind of text: the infinite analysis in which sinner is contained in the notion of Adam is an indefinite analysis, that is, I can move back from sinner to another term, then to another term, etc... Exactly as if sinner = 1/2+1/4+1/8, etc., to infinity. This would result in a certain status: I would say that infinite analysis is virtual analysis, an analysis that goes toward the indefinite. There are texts by Leibniz saying that, notably in "The discourse on metaphysics," but in "The discourse on metaphysics," Leibniz presents and proposes the totality of his system for use by people with little philosophical background. I choose another text that seems to contradict the first; in a more scholarly text, "On Freedom," Leibniz uses the word "virtual," but quite strangely he does not use this word with reference to truths of existence, but to truths of essence.

This text suffices already for me to say that it is not possible for the distinction truths of essence/truths of existence be reduced to saying that in truths of existence, inclusion would only be virtual, since virtual inclusion is a case of truths of essence. In fact, you recall that truths of essence refer to two cases: the pure and simple identity in which we demonstrate the identity of the predicate and the subject, and the discovery of an inclusion of the type ‘every number divisible by 12 is divisible by 6,’ (I demonstrate the inclusion following a finite operation), and it is for the latter case that Leibniz says: I have discovered a virtual identity. Thus it is not enough to say that infinite analysis is virtual.

Can we say that this is an indefinite analysis? No, because an indefinite analysis would be the same as saying that it's an analysis that is infinite only through my lack of knowledge, that is, I cannot reach the end of it. Henceforth, God with his understanding would reach the end. Is that it? No, it's not possible for Leibniz to mean that because the indefinite never existed in his thinking. We have here notions that are incompatible, anachronistic. Indefinite is not one of Leibniz's gimmicks <

trucs

>. What is the indefinite, rigorously defined? What differences are there between

indefinite and infinite

The indefinite is the fact that I must always pass from one term to another term, always, without stopping, but without the following term at which I arrive pre-existing. It is my own procedure that consists in causing to exist. If I say 1=1/4+1/8, etc...., we must not believe that this "etc." pre-exists, it's my procedure that makes it appear each time, that is, the indefinite exists in a procedure through which I never stop pushing back the limit that I confront. Nothing pre-exists. It's Kant who will be the first philosopher to give a status to the indefinite, and this status will be precisely that the indefinite refers to an aggregate that is not separable from the successive synthesis that runs through it. That is, the terms of the indefinite series do not pre-exist the synthesis that goes from one term to another.

Leibniz does not know that. Moreover, the indefinite appears to him to be purely conventional or symbolic; why? There is an author who said quite well what creates the family resemblance of philosophers of the 17th century, it was Merleau-Ponty. He wrote a small text on so-called classical philosophers of the seventeenth century, and he tried to characterize them in a lively way, and said that what is so incredible in these philosophers is an innocent way of thinking starting from and as a function of the infinite. That's what the classical century is. This is much more intelligent than to tell us that it's an era in which philosophy is still confused with theology. That's stupid. One must say that if philosophy is still confused with theology in the 17th century, it's precisely because philosophy is not separable at that time from an innocent way of thinking as a function of infinity.

What differences are there between the infinite and the indefinite? It's this: the indefinite is virtual; in fact, the following term does not exist prior to my procedure having constituted it. What does that mean?

The infinite is actual, there is no infinite except in act .

So there can be all sorts of infinites. Think of Pascal. It's a century that will not stop distinguishing orders of infinities, and the thought of orders of infinity is fundamental throughout the 17th century. It will fall back on our heads, this thought, at the end of the 19th and 20th centuries precisely with the theory of so-called infinite aggregates. With infinite aggregates, we rediscover something that worked at the basis of classical philosophy, notably the distinction of orders of infinities: this obviously includes Pascal, Spinoza with the famous letter on infinity, and Leibniz who would subordinate an entire mathematical apparatus to the analysis of the infinite and orders of infinities. Specifically, in what sense can we say that an order of infinities is greater than another, what is an infinite that is greater than another infinite, etc...? An innocent way of thinking starting from the infinite, but not at all in a confused way since all sorts of distinctions are introduced.

In the case of truths of existence, Leibniz's analysis is obviously infinite. It is not indefinite. Thus, when he uses the words virtual, etc..., there is a formal text that supports this interpretation that I am trying to sketch, it's a text taken from "On Freedom" in which Leibniz says exactly this: "When it is a matter of analyzing the inclusion of the predicate sinner in the individual notion Adam, God certainly sees, not the end of the resolution, but the end that does not take place." Thus, in other words, even for God there is no end to this analysis. So, you will tell me that it's indefinite even for God? No, it's not indefinite since all the terms of the analysis are given. If it were indefinite, all the terms would not be given, they would be given little by little. They would not be given in a pre-existing manner. In other words, in an infinite analysis, we reach what result: you have a passage of infinitely small elements one to another, the infinity of infinitely small elements being given. Of such an infinity, we will say that it is actual since the totality of infinitely small elements is given. You will say to me that we can then reach the end! No, by its nature, you cannot reach the end since it's an infinite aggregate. The totality of elements is given, and you pass from one element to another, and thus you have an infinite aggregate of infinitely small elements. You pass from one element to another: you perform an infinite analysis, that is, an analysis without end, neither for you nor for God.

What do you see if you perform this analysis? Let us assume that there is only God that can do it, you make yourself the indefinite because your understanding is limited, but as for God, he makes infinity. He does not see the end of the analysis since there is no end of the analysis, but he performs the analysis. Furthermore, all the elements of the analysis are given to him in an actual infinity. So that means that sinner is connected to Adam. Sinner is an element, it is connected to the individual notion of Adam by an infinity of other elements actually given. Fine, it's the entire existing world, specifically all this whole compossible world that has passed into existence. We are getting at something quite profound here. When I perform the analysis, I pass from what to what? I pass from Adam sinner to Eve temptress, from Eve temptress to the evil Serpent, to the apple. It's an infinite analysis, and it's this infinite analysis that shows the inclusion of sinner in the individual notion Adam. What does that mean, the infinitely small element? Why is sin an infinitely small element? Why is the apple an infinitely small element? Why is crossing the Rubicon an infinitely small element? You understand what that means? There are no infinitely small elements, so an infinitely small elements means obviously, we don't need to say it, it means an infinitely small relation between two elements. It is a question of relations, not a question of elements. In other words, an infinitely small relation between elements, what can that be? What have we achieved in saying that it is not a question of infinitely small elements, but of infinitely small relations between two elements? And you understand that if I speak to someone who has no idea of differential calculus, you can tell him it's infinitely small elements. Leibniz was right. If it's someone who has a very vague knowledge, he has to understand that these are infinitely small relations between finite elements. If it's someone who is very knowledgeable in differential calculus, I can perhaps tell him something else.

Infinite analysis that goes on to demonstrate the inclusion of the predicate in the subject at the level of truths of existence, does not proceed by the demonstration of an identity, even a virtual one. It's not that. But Leibniz, in another drawer, has another formula to give you: identity governs truths of essence, but not truths of existence; all the time he says the opposite, but that has no importance. Ask yourself to whom he says it. So what is it? What interests him at the level of truths of existence is not identity of the predicate and the subject, it's rather that one passes from one predicate to another, from one to another, and again on from one to another, etc.... from the point of view of an infinite analysis, that is, from the maximum of continuity.

In other words, it's identity that governs truths of essence, but it's continuity that governs truths of existence. And what is a world? A world is defined by its continuity. What separates two incompossible worlds? It's the fact that there is discontinuity between the two worlds. What defines a compossible world? It's the compossibility of which it is capable. What defines the best of worlds? It's the most continuous world. The criterion of God's choice will be continuity. Of all the worlds incompossible with each other and possible in themselves, God will cause to pass into existence the one that realizes the maximum of continuity.

Why is Adam's sin included in the world that has the maximum of continuity? We have to believe that Adam's sin is a formidable connection, that it's a connection that assures continuities of series. There is a direct connection between Adam's sin and the Incarnation and the Redemption by Christ. There is continuity. There are something like series that are going to begin to fit into each other across the differences of time and space. In other words, in the case of truths of essence, I demonstrated an identity in which I revealed an inclusion; in the case of truths of existence, I am going to witness a continuity assured by the infinitely small relations between two elements. Two elements will be in continuity when I will be able to assign an infinitely small relation between these two elements.

I have passed from the idea of infinitely small element to the infinitely small relation between two elements, that's not enough. A greater effort is required. Since there are two elements, there is a difference between the two elements: between Adam's sin and the temptation of Eve, there is a difference, only what is the formula of the continuity? We will be able to define continuity as the act of a difference in so far as it tends to disappear.

Continuity is an evanescent difference.

What does it mean that there is continuity between the seduction of Even and Adam's sin? It's that the difference between the two is a difference that tends to disappear. I would say therefore that

truths of essence are governed by the principle of identity, truths are governed by the law of continuity, or evanescent differences, and that comes down to the same.

Thus between sinner and Adam you will never be able to demonstrate a logical identity, but you will be able to demonstrate -- and the word demonstration will change meaning --, you will be able to demonstrate a continuity, that is, one or several evanescent differences.

An infinite analysis is an analysis of the continuous operating through evanescent

differences.

That refers to a certain symbolic, a symbolic of differential calculus or of infinitesimal analysis. But it's at the same time that Newton and Leibniz develop differential calculus. And the interpretation of differential calculus by the evanescent categories is Leibniz's very own. In Newton's works, whereas both of them really invent it at the same time, the logical and theoretical armature is very different in Leibniz's works and Newton's, and the theme of the differential conceived as evanescent difference is proper to Leibniz. Moreover, he relies on it greatly, and there is a great polemic between Newtonians and Leibniz. Our story becomes more precise: what is this evanescent difference? . Differential equations today are fundamental. There is no physics without a differential equation. Mathematically, today, differential calculus has purged itself of any consideration of the infinite; the kind of axiomatic status of differential calculus in which it is absolutely no longer a question of the infinite dates from the end of the 19th century. But if we place ourselves at the time of Leibniz, put yourself in the place of a mathematician: what is he going to do when he finds himself faced with the magnitude and quantities of different powers, equations whose variables are to different powers, equations of the ax2+y type? You have a quantity to the second power and a quantity to the first power. How does one compare? You all know the story of non-commensurable quantities. Then, in the 17th century, the quantities of different powers received a neighboring term, incomparable quantities. The whole theory of equations collides in the 17th century with this problem that is a fundamental one, even in the simplest algebra; what is differential calculus for? Differential calculus allows you to proceed directly to compare quantities raised to different powers. Moreover, it is used only for that.

Differential calculus finds its level of application when you are faced with incomparables, that is, faced with quantities raised to different powers. Why? In ax2+y, let us assume that by various means, you extract dx and dy. What is that? We will define it verbally, conventionally, we will say that dx or dy is the infinitely small quantity assumed to be added or subtracted from x or from y. Now there is an invention! The infinitely small quantity... that is, it's the smallest variation of the quantity considered. It is unassignable by convention. Thus dx=0 in x, is the smallest quantity by which x can vary, so it equals zero. dy = 0 in relation to y. The notion of evanescent difference is beginning to take shape. It's a variation or a difference, dx or dy; it is smaller than any given or givable <

donnable

> quantity. It's a mathematical symbol. In a sense, it's crazy, in a sense it's operational. For what? Here is what is formidable in the symbolism of differential calculus: dx=0 in relation to x, the smallest different, the smallest increase of which the quantity x or the unassignable quantity y might be capable, it's infinitely small. The miracle dy/dx is not equal to zero, and furthermore: dy/dx has a perfectly expressible finite quantity.

These are relative , uniquely relative. dx is nothing in relation to y, dy is nothing in relation to y, but then dy/dx is something.

A stupefying, admirable, and great mathematical discovery.

It's something because in an example such as ax2-by+c, you have two powers in which you have incomparable quantities: y2 and x. If you consider the differential relation, it is not zero, it is determined, it is determinable.

The relation dy/dx gives you the means to compare two incomparable quantities that were raised to different powers since it operates a depotentialization of quantities. So it gives you a direct means to confront incomparable quantities raised to different powers. From that moment on, all mathematics, all algebra, all physics will be inscribed in the symbolism of differential calculus... It's the relation between dx and dy that made possible this kind of co-penetration of physical reality and mathematical calculus.

There is a small note of three pages called "Justification of the calculus of infinitesimals by the calculus of ordinary algebra." With that you will understand everything. Leibniz tries to explain that in a certain way, differential calculus already functioned before being discovered, and that it couldn't occur otherwise, even at the level of the most ordinary algebra.

x is not equal to y, neither in one case, nor another, since it would be contrary to the very givens of the construction of the problem. To the extent that, for this case, you can write x/y = c/e, c and e are zeros.

Like he says in his language, these are nothings, but they are not absolute nothings, that are nothings respectively.

Specifically, these are nothings but ones which conserve the relational difference. Thus c does not become equal to e since it remains proportional to x and x is not equal to y.

This is a justification of the old differential calculus, and the interest of this text is that it's a justification through the easiest or most ordinary algebra. This justification puts nothing into question about the specificity of differential calculus.

I read this very beautiful text:

"Thus, in the present case, there will be x-c=x. Let us assume that this case is included under the general rule, and nonetheless c and e will not at all be absolute nothings since they together maintain the reason of CX to XY, or that which is between the entire sine or radius and between the tangent that corresponds to the angle in c. We have assumed this angle always to remain the same. For if c, C and e were absolutely nothings in this calculus reduced to the case of coincidence of points c, e and a, as one nothing has the same value as the other, then c and e would be equal and the equations or analogy x/y = c/e would make x/y = 0/0 = 1. That is, we would have x=y which would be totally absurd."

"So we find in algebraic calculus the traces of the transcendent calculus of differences (i.e. differential calculus), and its same singularities that some scholars have fretted about, and even algebraic calculus could not do without it if it must conserve its advantages of which one of the most considerable is the generality that it must maintain so that it can encompass all cases."

It's exactly in this way that I can consider that rest is an infinitely small movement, or that the circle is the limit of an infinite series of polygons the sides of which increase to infinity. What is there to compare in all these examples? We have to consider the case in which there is a single triangle as the extreme case of two similar triangles opposed at the vertex. What Leibniz demonstrated in this text is how and in what circumstances a triangle can be considered as the extreme case of two similar triangles opposed at the vertex. There you sense that we are perhaps in the process of giving to "virtual" the sense that we were looking for. I could say that in the case of my second figure in which there is only one triangle, the other triangle is there, but it is only there virtually. It's there virtually since a contains virtually e and c distinct from a. Why do e and c remain distinct from a when they no longer exist? e and c remain distinct from a when they no longer exist because they intervene in a relation with it, continue to exist when the terms have vanished. It's in this way that rest will be considered as a special case of movement, specifically an infinitely small movement. In my second figure, xy, I would say it's not at all the triangle CEA, it's not at all the case that the triangle has disappeared in the common sense of the word, but we have to say both that it has become unassignable, and however that it is perfectly determined since in this case, c=0, e=0, but c/e is not equal to zero.

c/e is a perfectly determined relation equal to x/y.

Thus it is determinable and determined, but it is unassignable. Likewise, rest is a perfectly determined movement, but it's an unassignable movement. Likewise, the circle is an unassignable polygon, yet perfectly determined.

You see what virtual means. Virtual no longer means at all the indefinite, and there all Leibniz's texts can be revived. He undertook a diabolical operation: he took the word virtual, without saying anything -- it's his right -- he gave it a new meaning, completely rigorous, but without saying anything. He will only say it in other texts:

that no longer meant going toward the indefinite; rather, that meant unassignable, yet also determined.

It's a conception of the

virtual

that is both quite new and very rigorous. Yet the technique and concepts were required so that this rather mysterious expression might acquire a meaning at the beginning: unassignable, yet determined. It's unassignable since c became equal to zero, and since e became equal to zero. And yet it's completely determined since c/e, specifically 0/0 is not equal to zero, nor to 1, it's equal to x/y.

Moreover, he really had a professor-like genius. He succeeded in explaining to someone who never did anything but elementary algebra what differential calculus is. He assumed no a priori notion of differential calculus.

The idea that there is a continuity in the world -- it seems that there are too many commentators on Leibniz who make more theological pronouncements than Leibniz requires: they are content to say that infinite analysis is in God's understanding, and it is true according to the letter of his texts. But with differential calculus, it happens that we have the artifice not to make ourselves equal to God's understanding, that's impossible of course, but differential calculus gives us an artifice so that we can operate a well-founded approximation of what happens in God's understanding so that we can approach it thanks to this symbolism of differential calculus, since after all, God also operates by the symbolic, not the same way, certainly.

Thus this approximation of continuity is such that the maximum of continuity is assured when a case is given, the extreme case or contrary can be considered from a certain point of view as included in the case first defined.

You define the movement, it matters little, you define the polygon, it matters little, you consider the extreme case or the contrary: rest, the circle is stripped of any angle. Continuity is the institution of the path following which the extrinsic case -- rest contrary to movement, the circle contrary to the polygon -- can be considered as included in the notion of the intrinsic case.

There is continuity when the extrinsic case can be considered as included in the notion of the intrinsic case.

Leibniz just showed why. You find the formula of predication: the predicate is included in the subject.

Understand well. I call general, intrinsic case the concept of movement that encompasses all movements. In relation to this first case, I call extrinsic case rest or the circle in relation to all the polygons, or the unique triangle in relation to all the triangles combined. I undertake to construct a concept that implies all the differential symbolism, a concept that both corresponds to the general intrinsic case and which still includes the extrinsic case. If I succeed in that, I can say that in all truth, rest is an infinitely small movement, just as I say that my unique triangle is the opposition of two similar triangles opposed at the vertex, simply, by which one of the two triangles has become unassignable. At that moment, there is continuity from the polygon to the circle, there is continuity from rest to movement, there is continuity from two similar triangles opposed at the vertex to a single triangle.

In the mid-19th century, a very great mathematician named Poncelet will produce projective geometry in its most modern sense, it is completely Leibnizian. Projective geometry is entirely based on what Poncelet called a completely simple axiom of continuity: if you take an arc of a circle cut at two points by a right angle, if you cause the right angle to recede, there is a moment in which it leaves the circle, no longer touching it at any point. Poncelet's axiom of continuity claims the possibility of treating the case of the tangent as an extreme case, specifically it's not that one of the points has disappeared, both points are still there, but virtual. When they all leave, it's not that the two points have disappeared, they are still there, but both are virtual. This is the axiom of continuity that precisely allows any system of projection, any so-called projective system. Mathematics will keep that integrally, it's a formidable technique.

There is something desperately comical in all that, but that will not bother Leibniz at all. There again, commentators are very odd. From the start, we sink into a domain in which it's a question of showing that the truths of existence are not the same thing as truths of essence or mathematical truths. To show it, either it's with very general propositions full of genius in Leibniz's works, but that leave us like that, God's understanding, infinite analysis, and then what does that amount to? And finally when it's a question of showing in what way truths of existence are reducible to mathematical truths, when it's a question of showing it concretely, all that is convincing in what Leibniz says is mathematical. It's funny, no?

A professional objector would say to Leibniz: you announce to us, you talk to us of the irreducibility of truths of existence, and you can define this irreducibility concretely only by using purely mathematical notions. What would Leibniz answer? In all sorts of texts, people have always had me say that differential calculus designated a reality. I never said that, Leibniz answers, differential calculus is a well-founded convention. Leibniz relies enormously on differential calculus being only a symbolic system, and not sketching out a reality, but designating a way of treating reality. What is this well-founded convention? It's not in relation to reality that it's a convention, but in relation to mathematics. That's the misinterpretation not to make. Differential calculus is symbolism, but in relation to mathematical reality, not at all in relation to real reality. It's in relation to mathematical reality that the system of differential calculus is a fiction. He also used the expression "well founded fiction." It’s a well-founded fiction in relation to the mathematical reality. In other words, differential calculus mobilizes concepts that cannot be justified from the point of view of classical algebra, or from the point of view of arithmetic. It's obvious. Quantities that are not nothing and that equal zero, it's arithmetical nonsense, it has neither arithmetic reality, nor algebraic reality. It's a fiction. So, in my opinion, it does not mean at all that differential calculus does not designate anything real, it means that differential calculus is irreducible to mathematical reality. It's therefore a fiction in this sense, but precisely in so far as it's a fiction, it can cause us to think of existence.

In other words,

differential calculus is a kind of union of mathematics and the existent, specifically it's the symbolic of the existent.

It's because it's a well-founded fiction in relation to mathematical truth that it is henceforth a basic and real means of exploration of the reality of existence.

You see therefore what the words "evanescent" and "

evanescent difference

" mean.

It's when the relation continues when the terms of the relation have disappeared.

The relation c/e when C and E have disappeared, that is, coincide with A. You have therefore constructed a continuity through differential calculus.

Leibniz becomes much stronger in order to tell us: understand that in God's understanding, between the predicate sinner and the notion of Adam, well, there is continuity.

There is a continuity by evanescent difference

to the point that when he created the world, God was only doing calculus <

ne fait que calculer

>. And what a calculus! Obviously not an arithmetical calculus.

He will oscillate on this topic between two explanations.

Therefore God created the world by calculating . God calculates, the world is created.

The idea of God as player <

joueur

> can be found everywhere. We can always say that God created the world by playing, but everyone has said that. It's not very interesting. There is a text by Heraclitus in which it is a question of the player child who really constituted the world. He plays, at what? What do the Greeks and Greek children play? Different translations yield different games. But Leibniz would not say that, when he gives his explanation of games, he has two explanations. In problems of tiling , astride architectural and mathematical problems, a surface being given, with what figure is one to fill it completely? A more complicated problem: if you take a rectangular surface and you want to tile it with circles, you do not fill it completely. With squares, do you fill it completely? That depends on the measurement. With rectangles? Equal or unequal? Then, if you suppose two figures, which of them combine to fill a space completely? If you want to tile with circles, with which other figure will you fill in the empty spaces? Or you agree not to fill everything; you see that it's quite connected to the problem of continuity. If you decide not to fill it all, in what cases and with which figures and which combination of different figures will you succeed in filling the maximum possible? That puts incommensurables into play, and puts incomparables into play. Leibniz has a passion for tiling.

When Leibniz says that God causes to exist and chooses the best of all possible worlds, we have seen, one gets ahead of Leibniz before he has spoken. The best of all possible worlds was the crisis of Leibnizianism, that was the generalized anti-Leibnizianism of the 18th century. They could not stand the story of the best of all possible worlds.

Voltaire was right, these worlds had a philosophical requirement that obviously was not fulfilled by Leibniz, notably from the political point of view. So, he could not forgive Leibniz. But if one casts oneself into a pious approach, what does Leibniz mean by the statement that the world that exists is the best of possible worlds? Something very simple: since there are several worlds possible, only they are not compossible with each other, God chooses the best and the best is not the one in which suffering is the least. Rationalist optimism is at the same time an infinite cruelty, it's not at all a world in which no one suffers,

it's the world that realizes the maximum of circles.

If I dare use a non-human metaphor, it's obvious that the circle suffers when it is no more than an affection of the polygon. When rest is no more than an affection of movement, imagine the suffering of rest.

Simply it's the best of worlds because it realizes the maximum of continuity.

Other worlds were possible, but they would have realized less continuity. This world is the most beautiful, the most harmonious, uniquely under the weight of this pitiless phrase: because it effectuates the most continuity possible. So if that occurs at the price of your flesh and blood, it matters little. As God is not only just, that is, pursuing the maximum of continuity, but as he is at the same time quite stylish, he wants to vary the world. So God hides this continuity. He poses a segment that should be in continuity with that other segment that he places elsewhere to hide his tracks.

We run no risk of making sense of this. This world is created at our expense. So, obviously the 18th century does not receive Leibniz's story very favorably. You see henceforth the problem of tiling: the best of worlds will be the one in which figures and forms will fill the maximum of space time while leaving the least emptiness.

Second explanation by Leibniz, and there he is even stronger: the chess game. Such that between Heraclitus's phrase that alludes to a Greek game and Leibniz's allusion to chess, there is all the difference that there is between the two games at the same moment in which the common formula "God plays" could make us believe that it's a kind of beatitude. How does Leibniz conceive of chess: the chess board is a space, the pieces are notions. What is the best move in chess, or the best combination of moves? The best move or combination of moves is the one that results in a determinate number of pieces with determinate values holding or occupying the maximum space. The total space being contained on the chess board. One must place ones pawns in such a way that they command the maximum space.

Why are these only metaphors? Here as well there is a kind of principle of continuity: the maximum of continuity. What does not work just as well in the metaphor of chess as in the metaphor of tiling? In both cases, you have reference to a receptacle. The two things are presented as if the possible worlds were competing to be embodied in a determinate receptacle. In the case of tiling, it's the surface to be tiled; in the case of chess, it's the chess board. But in the conditions of the creation of the world, there is no a priori receptacle.

We have to say, therefore, that

the world that passes into existence is the one that realizes in itself the maximum of continuity, that is, which contains the greatest quantity of reality or of essence. I cannot speak of existence since there will come into existence the world that contains not the greatest quantity of existence, but the greatest quantity of essence from the point of view of continuity. Continuity is, in fact, precisely the means of containing the maximum quantity of reality.

Now that's a very beautiful vision, as philosophy. In this paragraph, I have answered the question: what is infinite analysis. I have not yet answered the question: what is compossibility. That's it.

Cours Vincennes - 29/04/1980

Today we must look at some amusing and recreational, but also quite delicate, things. Answer to a question on differential calculus: It seems to me that one cannot say that at the end of the seventeenth century and in the eighteenth century, there were people for whom differential calculus is something artificial and others for whom it represents something real. We cannot say that because the division is not there. Leibniz never stopped saying that differential calculus is pure artifice, that it’s a symbolic system. So, on this point, everyone is in strict agreement. Where the disagreement begins is in understanding what a symbolic system is, but as for the irreducibility of differential signs to any mathematical reality, that is to say to geometrical, arithmetical and algebraic reality, everyone agrees. A difference arises when some people think that, henceforth, differential calculus is only a convention, a rather suspect one, and others think that its artificial character in relation to mathematical reality, on the contrary, allows it to be adequate to certain aspects of physical reality. Leibniz never thought that his infinitesimal analysis, his differential calculus, as he conceived them sufficed to exhaust the domain of the infinite such as he, Leibniz, conceived it. For example, calculus. There is what Leibniz calls calculus of the minimum and of the maximum which does not at all depend on differential calculus. So differential calculus corresponds to a certain order of infinity. If it is true that a qualitative infinity cannot be grasped by differential calculus, Leibniz is, on the other hand, so conscious of it that he initiates other modes of calculus relative to other orders of infinity. What eliminated this direction of the qualitative infinity, or even simply of actual infinity tout court, Leibniz wasn’t the one who blocked it off. What blocked this direction was the Kantian revolution. This was what imposed a certain conception of the indefinite and directed the most absolute critique of actual infinity. We owe that to Kant and not to Leibniz.

In geometry, from the Greeks to the seventeenth century, you have two kinds of problems: those in which it’s a question of finding so-called straight lines and so-called rectilinear surfaces. Classical geometry and algebra were sufficient. You have problems and you get the necessary equations; it’s Euclidean geometry. Already with the Greeks, then in the Middle Ages of course, geometry will not cease to confront a type of problem of another sort: it’s when one must find and determine curves and curvilinear surfaces. Where all geometries are in agreement is in the fact that classical methods of geometry and algebra no longer sufficed. The Greeks already had to invent a special method called the method by exhaustion. It allowed them to determine curves and curvilinear surfaces in so far as it gave equations of variable degrees, to the infinite limit, an infinity of various degrees in the equation. These are the problems that are going to make necessary and inspire the discovery of differential calculus and the way in which differential calculus takes up where the old method by exhaustion left off. If you already connect a mathematical symbolism to a theory, if you don’t connect it to the problem for which it is created, then you can no longer understand anything. Differential calculus has sense only if you place yourself before an equation in which the terms are raised to different powers. If you don’t have that, then it’s non-sensical to speak of differential calculus. It’s very much about considering the theory that corresponds to a symbolism, but you must also completely consider the practice. In my opinion, as well, one can’t understand anything about infinitesimal analysis if one does not see that all physical equations are by nature differential equations. A physical phenomenon can only be studied ? and Leibniz will be very firm: Descartes only had geometry and algebra, and what Descartes himself had invented under the name of analytical geometry, but however far he went in that invention, it gave him at most the means to grasp figures and movement of a rectilinear kind; but with the aggregate of natural phenomena being after all phenomena of the curvilinear type, that doesn’t work at all. Descartes remained stuck on figures and movement. Leibniz will translate: it’s the same thing to say that nature proceeds in a curvilinear manner, or to say that beyond figures and movement, there is something that is the domain of forces. And on the very level of the laws of movement, Leibniz is going to change everything, thanks precisely to differential calculus. He will say that what is conserved is not MV, not mass and velocity, but MV2. The only difference in the formula is the extension of V to the second power. This is made possible by differential calculus because differential calculus allows the comparison of powers and of rejects . Descartes did not have the technical means to say MV2. >From the point of view of the language of geometry and of arithmetic and algebra, MV2 is pure and simple non-sense.

With what we know in science today, we can always explain that what is conserved is MV2 without appealing to any infinitesimal analysis. That happens in high school texts, but to prove it, and for the formula to make any sense, an entire apparatus of differential calculus is required.

< Intervention by Comptesse.>

Gilles: Differential calculus and the axiomatic certainly have a point of encounter, but this is one of perfect exclusion. Historically, the rigorous status of differential calculus arises quite belatedly. What does that mean? It means that everything that is convention is expelled from differential calculus. And, even for Leibniz, what is artifice? It’s an entire set of things: the idea of a becoming, the idea of a limit of becoming, the idea of a tendency to approach the limit, all these are considered by mathematicians to be absolutely metaphysical notions. The idea that there is a quantitative becoming, the idea of the limit of this becoming, the idea that an infinity of small quantities tends toward the limit, all these are considered as absolutely impure notions, thus as really non-axiomatic or non-axiomitizable. Thus, from the start, whether in Leibniz’s work or in Newton’s and the work of his successors, the idea of differential calculus is inseparable and not separated from a set of notions judged not to be rigorous or scientific. They themselves are quite prepared to recognize it. It happens that at the end of the nineteenth and the start of the twentieth century, differential calculus or infinitesimal analysis would receive a rigorously scientific status, but at what price? We hunt for any reference to the idea of infinity; we hunt for any reference to the idea of limit, we hunt for any reference to the idea of tendency toward the limit. Who does that? An interpretation and a rather strange status of calculus will be given because it stops operating with ordinary quantities, and its interpretation will be purely ordinal. Henceforth, that becomes a mode of exploring the finite, the finite as such. It’s a great mathematician, Weierstrass, who did that, but it came rather late. So, he creates an axiomatic of calculus, but at what price? He transformed it completely. Today, when we do differential calculus, there is no reference to the notions of infinity, of limit and of tendency toward the limit. There is a static interpretation. There is no longer any dynamism in differential calculus, but a static and ordinal interpretation of calculus. One must read Vuillemin’s book, La philosophie de l’algèbre [Paris: PUF, 1960, 1962]. This fact is very important for us because it must certainly show us that the differential relations ? Yes, but even before the axiomatization, all mathematicians agreed in saying that differential calculus interpreted as a method for exploring the infinite was an impure convention. Leibniz was the first to say that, but still in that case, one would have to know what the symbolic value was then. Axiomatic relations and differential relations, well no. They were in opposition. Infinity has completely changed meaning, nature, and, finally, is completely expelled. A differential relation of the type dy/dx is such that one extracts it from x and y. At the same time, dy is nothing in relation to y, it’s an infinitely small quantity; dx is nothing in relation to x, it’s an infinitely small quantity in relation to x. On the other hand, dy/dx is something else. But it’s something completely different from y/x. For example, if y/x designates a curve, dy/dx designates a tangent. And what’s more, it’s not just any tangent. I would say therefore that the differential relation is such that it signifies nothing concrete in relation to what it’s derived from, that is, in relation to x and to y, but it signifies something else concrete [autre chose de concret], and that is how it assures [the] passage to limits. It assures something else concrete, namely a z. It’s exactly as if I said that differential calculus is completely abstract in relation to a determination of the type a/b. But on the other hand, it determines a C. Whereas the axiomatic relation is completely formal from all points of view, if it is formal in relation to a and b, it does not determine a c that would be concrete for it. So it doesn’t assure a passage at all. This would be the whole classical opposition between genesis and structure. The axiomatic is really the structure common to a plurality of domains. Last time, we were considering my second topic heading, which dealt with Substance, World, and Compossibility. In the first past, I tried to state what Leibniz called infinite analysis. The answer was this: infinite analysis fulfills the following condition: it appears to the extent that continuity and tiny differences or vanishing differences are substituted for identity. It’s when we proceed by continuity and vanishing differences that analysis becomes properly infinite analysis. Then I arrive at the second aspect of the question. There would be infinite analysis and there would be material for infinite analysis when I find myself faced with a domain that is no longer directly governed by the identical, by identity, but a domain that is governed by continuity and vanishing differences. We reach a relatively clear answer. Hence the second aspect of the problem: what is compossibility? What does it mean for two things to be compossible or non compossible? Yet again, Leibniz tells us that Adam non-sinner is possible in itself, but not compossible with the existing world. So he maintains a relation of compossibility that he invents, and you sense that it’s entirely linked to the idea of infinite analysis. The problem is that the incompossible is not the same thing as the contradictory. It’s complicated. Adam non-sinner is incompossible with the existing world, another world would have been necessary. If we say that, I only see three possible solutions for trying to characterize the notion of incompossibility. First solution: we’ll say that one way or another, incompossibility has to imply a kind of logical contradiction. A contradiction would have to exist between Adam non-sinner and the existing world. Yet we could only bring out this contradiction at infinity; it would be an infinite contradiction. Whereas there is a finite contradiction between circle and square, there is only an infinite contradiction between Adam non-sinner and the world. Certain texts by Leibniz move in this direction. But yet again, we know that we have to be careful about the levels of Leibniz’s texts. In fact, everything we said previously implied that compossibility and incompossibility are truly an original relation, irreducible to identity and contradiction. Contradictory identity. Furthermore, we saw that infinite analysis, in accordance with our first part, was not an analysis that discovered the identical as a result of an infinite series of steps. The whole of our results the last time was that, far from discovering the identical at the end of a series, at the limit of an infinite series of steps, far from proceeding in this way, infinite analysis substituted the point of view of continuity for that of identity. Thus, it’s another domain than the identity/contradiction domain. Another solution that I will state rapidly because certain of Leibniz’s texts suggest it as well: it’s that the matter is beyond our understanding because our understanding is finite, and hence, compossibility would be an original relation, but we could not know what its roots are. Leibniz brings a new domain to us. There is not only the possible, the necessary and the real. There is the compossible and the incompossible. He was attempting to cover an entire region of being. Here is the hypothesis that I’d like to suggest: Leibniz is a busy man, he writes in all directions, all over the place, he does not publish at all or very little during his life. Leibniz has all the material, all the details to give a relatively precise answer to this problem. Necessarily so since he’s the one who invented it, so it’s him who has the solution. So what happened for him not to have put all of it together? I think that what will provide an answer to this problem, at once about infinite analysis and about compossibility, is a very curious theory that Leibniz was no doubt the first to introduce into philosophy, that we could call the theory of singularities. In Leibniz’s work, the theory of singularities is scattered, it’s everywhere. One even risks reading pages by Leibniz without seeing that one is fully in the midst of it, that’s how discreet he is. The theory of singularities appears to me to have two poles for Leibniz, and one would have to say that it’s a mathematical-psychological theory. And our work today is: what is a singularity on the mathematical level, and what does Leibniz create through that? Is it true that he creates the first great theory of singularities in mathematics? Second question: what is the Leibnizian theory of psychological singularities? And the last question: to what extent does the mathematical-psychological theory of singularities, as sketched out by Leibniz, help us answer the question: what is the incompossible, and thus the question what is infinite analysis? What is this mathematical notion of singularity? Why did it arrive [tomb?]? It’s often like that in philosophy: there is something that emerges at one moment and will be abandoned. That’s the case of a theory that was more than outlined by Leibniz, and then nothing came afterwards, the theory was unlucky, without follow-up. Wouldn’t it be interesting if we were to return to it? I am still divided about two things in philosophy: the idea that it does not require a special kind of knowledge, that really, in this sense, anyone is open to philosophy, and at the same time, that one can do philosophy only if one is sensitive to a certain terminology of philosophy, and that you can always create the terminology, but you cannot create it by doing just anything. You must know what terms like these are: categories, concept, idea, a priori, a posteriori, exactly like one cannot do mathematics if one does not know what a, b, xy, variables, constants, equation are. There is a minimum. So you have to attach some importance to those points. The singular has always existed in a certain logical vocabulary. "Singular" designates what is not difference, and at the same time, in relation to "universal." There is another pair of notions, it’s "particular" that is said with reference to "general." So the singular and the universal are in relation with each other; the particular and the general are in relation. What is a judgment of singularity? It’s not the same thing as a judgment called particular, nor the same thing as a judgment called general. I am only saying, formally, "singular" was thought, in classical logic, with reference to "universal." And that does not necessarily exhaust a notion: when mathematicians use the expression "singularity," with what do they place it into relation? One must be guided by words. There is a philosophical etymology, or even a philosophical philology. "Singular" in mathematics is distinct from or opposed to "regular." The singular is what is outside the rule. There is another pair of notions used by mathematicians, "remarkable" and "ordinary." Mathematicians tell us that there are remarkable singularities and singularities that aren’t remarkable. But for us, out of convenience, Leibniz does not yet make this distinction between the non-remarkable singular and the remarkable singular. Leibniz uses "singular," "remarkable," and "notable" as equivalents, such that when you find the word "notable" in Leibniz, tell yourself that necessarily there’s a wink, that it does not at all mean "well-known"; he enlarges the word with an unusual meaning. When he talks about a notable perception, tell yourself that he is in the process of saying something. What interest does this have for us? It’s that mathematics already represents a turning point in relation to logic. The mathematical use of the concept "singularity" orients singularity in relation to the ordinary or the regular, and no longer in relation to the universal. We are invited to distinguish what is singular and what is ordinary or regular. What interest does this have for us? Suppose someone says: philosophy isn’t doing too well because the theory of truth in thought has always been wrong. Above all, we’ve always asked what in thought was true, what was false. But you know, in thought, it’s not the true and the false that count, it’s the singular and the ordinary. What is singular, what is remarkable, what is ordinary in a thought? Or what is ordinary? I think of Kierkegaard, much later, who would say that philosophy has always ignored the importance of a category, that of the interesting! While it is perhaps not true that philosophy ignored it, there is at least a philosophical-mathematical concept of singularity that perhaps has something interesting to tell us about the concept "interesting." This great mathematical discovery is that singularity is no longer thought in relation to the universal, but is thought rather in relation to the ordinary or to the regular. The singular is what exceeds the ordinary and the regular. And saying that already takes us a great distance since saying it indicates that, henceforth, we wish to make singularity into a philosophical concept, even if it means finding reasons to do so in a favorable domain, namely mathematics. And in which case does mathematics speak to us of the singular and the ordinary? The answer is simple: concerning certain points plotted on a curve. Not necessarily on a curve, but occasionally, or more generally concerning a figure. A figure can be said quite naturally to include singular points and others that are regular or ordinary. Why a figure? Because a figure is something determined! So the singular and the ordinary would belong to the determination, and indeed, that would be interesting! You see that by dint of saying nothing and marking time, we make a lot of progress. Why not define determination in general, by saying that it’s a combination of singular and ordinary, and all determination would be like that? Perhaps? I take a very simple figure: a square. Your very legitimate requirement would be to ask me: what are the singular points of a square? There are four singular points in a square, the four vertices a, b, c, d. We are going to define singularity, but we remain with examples, and we are making a childish inquiry, we are talking mathematics, but we don’t know a word of it. We only know that a square has four sides, so there are four singular points that are the extremes. The points are markers, precisely that a straight line is finished/finite [finie], and that another begins, with a different orientation, at 90 degrees. What will the ordinary points be? This will be the infinity of points that compose each side of the square; but the four extremities will be called singular points. Question: how many singular points do you give to a cube? I see your vexed amazement! There are eight singular points in a cube. That is what we call singular points in the most elementary geometry: points that mark the extremity of a straight line. You sense that this is only a start. I would therefore oppose singular points and ordinary points. A curve, a rectilinear figure perhaps, can I say of them that singular points are necessarily the extremes? Maybe not, but let us assume that at first sight, I can say something like that. For a curve, it’s ruined. Let’s take the simplest example: an arc of a circle, concave or convex, as you wish. Underneath, I make a second arc, convex if the other is concave, concave if the other is convex. The two meet one another at a point. Underneath I trace a straight line that, in accordance with the order of things, I call the ordinate. I trace the ordinate. I draw a line perpendicular to the ordinate. It’s Leibniz’s example, in a text with the exquisite title, "Tantanem analogicum", a tiny little work seven pages long written in Latin, which means "analogical essays." Segment ab thus has two characteristics: it’s the only segment raised from the ordinate to be unique. Each of the others has, as Leibniz says, a double, its little twin. In fact, xy has its mirror, its image in x’y’, and you can get closer through vanishing differences of ab, there is only ab that remains unique, without twin. Second point: ab can also be considered a maximum or a minimum, maximum in relation to one of the arcs of the circle, minimum in relation to the other. Ouf, you’ve understood it all. I’d say that AB is a singularity. I have introduced the example of the simplest curve: an arc of a circle. It’s a bit more complicated: what I showed was that a singular point is not necessarily connected, is not limited to the *extremum*. It can very well be in the middle, and in that case, it is in the middle. And it’s either a minimum or a maximum, or both at once. Hence the importance of a calculus that Leibniz will contribute to extending quite far, that he will call calculus of maxima and of minima. And still today, this calculus has an immense importance, for example, in phenomena of symmetry, in physical and optical phenomena. I would say therefore that my point a is a singular point; all the others are ordinary or regular. They are ordinary and regular in two ways: first, they are below the maximum and above the minimum, and second, they exist doubly. Thus, we can clarify somewhat this notion of ordinary. It’s another case; it’s a singularity of another case. Another attempt: take a complex curve. What will we call its singularities? The singularities of a complex curve, in simplest terms, are neighboring points of which ? and you know that the notion of neighborhood, in mathematics, which is very different from contiguity, is a key notion in the whole domain of topology, and it’s the notion of singularity that is able to help us understand what neighborhood is. Thus, in the neighborhood of a singularity, something changes: the curve grows, or it decreases. These points of growth or decrease, I will call them singularities. The ordinary one is the series, that which is between two singularities, going from the neighborhood of one singularity to another’s neighborhood, of ordinary or regular character. We grasp some of these relations, some very strange nuptials: isn’t "classical" philosophy’s fate relatively linked, and inversely, to geometry, arithmetic, and classical algebra, that is, to rectilinear figures? You will tell me that rectilinear figures already include singular points, OK, but once I discovered and constructed the mathematical notion of singularity, I can say that it was already there in the simplest rectilinear figures. Never would the simplest rectilinear figures have given me a consistent occasion, a real necessity to construct the notion of singularity. It’s simply on the level of complex curves that this becomes necessary. Once I found it on the level of complex curves, now there, yes, I back up and can say: ah, it was already an arc of a circle, it was already in a simple figure like the rectilinear square, but before you couldn’t.

Intervention: xxx [missing from transcript].

Gilles groans: … Too bad [Piti?]… My God… He caught me. You know, speaking is a fragile thing. Too bad… ah, too bad … I’ll let you talk for an hour when you want, but not now … Too bad, oh l? l? … It’s the blank in memory [trou]. I will read to you a small, late text by Poincar? that deals extensively with the theory of singularities that will be developed during the entire eighteenth and nineteenth centuries. There are two kinds of undertaking by Poincar?, logical and philosophical projects, and mathematical ones. He is above all a mathematician. There is an essay by Poincar? on differential equations. I am reading a part of it on kinds of singular points in a curve referring to a function or to a differential equation. He tells us that there are four kinds of singular points: first, crests , which are points through which two curves defined by the equation pass, and only two. Here, the differential equation is such that, in the neighborhood of this point, the equation is going to define and going to cause two curves and only two to pass. The second type of singularity: knots, in which an infinity of curves defined by the equation come to intersect. The third type of singularity: foci , around which these curves turn while drawing closer to them in the form of a spiral. Finally, the fourth type of singularity: centers, around which curves appear in the form of a closed circle. And Poincar? explains in the sequel to the essay that, according to him, one great merit of mathematics is to have pushed the theory of singularities into relationship with the theory of functions or of differential equations. Why do I quote this example from Poincar?? You could find equivalent notions in Leibniz’s works. Here a very curious terrain appears, with crests, foci, centers, truly like a kind of astrology of mathematical geography. You see that we went from the simplest to the most complex: on the level of a simple square, of a rectilinear figure, singularities were extremum; on the level of a simple curve, you have singularities that are even easier to determine, for which the principle of determination was easy. The singularity was the unique case that had no twin, or else was the case in which the maximum and minimum were identified. There you have more complex singularities when you move into more complex curves. Therefore it’s as if the domain of singularities is infinite, strictly speaking. What is the formula going to be? As long as you are dealing with problems considered as rectilinear, that is, in which it’s a question of determining right angles or rectilinear surfaces, you don’t need differential calculus. You need differential calculus when you find yourself faced with the task of determining curves and curvilinear surfaces. What does that mean? In what way is the singularity linked to differential calculus? It’s that the singular point is the point in the neighborhood of which the differential relation dy/dx changes its sign . For example: vertex, relative vertex of a curve before it descends, so you will say that the differential relation changes its sign. It changes its sign at this spot, but to what extent? To the extent that it becomes equal; in the neighborhood of this point, it becomes equal to zero or to infinity. It’s the theme of the minimum and of the maximum that you again find there. All this together consists in saying: look at the kind of relationship between singular and ordinary, such that you are going to define the singular as a function of curvilinear problems in relation to differential calculus, and in this tension or opposition between singular point and ordinary point, or singular point and regular point. This is what mathematicians provide us with as basic material, and yet again if it is true that in the simplest cases, the singular is the extremity, in other simple cases, it’s the maximum or the minimum or even both at once. Singularities there develop more and more complex relations on the level of more and more complex curves. I hold onto the following formula: a singularity is a distinct or determined point on a curve, it’s a point in the neighborhood of which the differential relation changes its sign, and the singular point’s characteristic is to extend [prolonger] itself into the whole series of ordinary points that depend on it all the way to the neighborhood of subsequent singularities. So I maintain that the theory of singularities is inseparable from a theory or an activity of extension . Wouldn’t these be elements for a possible definition of continuity? I’d say that continuity or the continuous is the extension of a remarkable point onto an ordinary series all the way into the neighborhood of the subsequent singularity. With this, I’m very pleased because at last, I have an initial hypothetical definition of what the continuous is. It’s all the more bizarre since, in order to reach this definition of the continuous, I used what apparently introduces a discontinuity, notably a singularity in which something changes. And rather than being the opposite, it’s the discontinuity that provides me with this approximate definition. Leibniz tells us that we all know that we have perceptions, that for example, I see red, I hear the sea. These are perceptions; moreover, we should reserve a special word for them because they are conscious. It’s perception endowed with consciousness, that is, perception perceived as such by an "I" , we call it apperception, as a-perceiving. For, indeed, it’s perception that I perceive. Leibniz tells us that consequently there really have to be unconscious perceptions that we don’t perceive. These are called minute perceptions, that is, unconscious perception. Why is this necessary? Why necessary? Leibniz gives us two reasons: it’s that our a-perceptions, our conscious perceptions are always global. What we perceive is always a whole. What we grasp through conscious perception is relative totalities. And it is really necessary that parts exist since there is a whole. That’s a line of reasoning that Leibniz constantly follows: there has to be something simple if there is something composite , he builds this into a grand principle; and it doesn’t go without saying, do you understand what he means? He means that there is no indefinite, and that goes so little without saying that it implies the actual infinite. There has to be something simple since there is something composite. There are people who will think that everything is composite to infinity, and they will be partisans of the indefinite, but for other reasons, Leibniz thinks that the infinite is actual. Thus, there has to be something . Henceforth, since we perceive the global noise of the sea when we are seated on the beach, we have to have minute perceptions of each wave, as he says in summary form, and moreover, of each drop of water. Why? It’s a kind of logical requirement, and we shall see what he means. He pursues the same reasoning on the level of the whole and the parts yet again as well, not by invoking a principle of totality, but a principle of causality: what we perceive is always an effect, so there have to be causes. These causes themselves have to be perceived, otherwise the effect would not be perceived. In this case, the tiny drops are no longer the parts that make up the wave, nor the waves the parts that make up the sea, but they intervene as causes that produce an effect. You will tell me that there is no great difference here, but let me point out simply that in all of Leibniz’s texts, there are always two distinct arguments that he is perpetually trying to make coexist: an argument based on causality and an argument based on parts. Cause-effect relationship and part-whole relationship. So this is how our conscious perceptions bathe in a flow of unconscious minute perceptions. On the one hand, this has to be so logically, in accordance with the principles and their requirement, but the great moments occur when experience comes to confirm the requirement of great principles. When the very beautiful coincidence of principles and experience occurs, philosophy knows its moment of happiness, even if it’s personally the misfortune of the philosopher. And at that moment, the philosopher says: everything is fine, as it should be. So it is necessary for experience to show me that under certain conditions of disorganization in my consciousness, minute perceptions force open the door of my consciousness and invade me. When my consciousness relaxes, I am thus invaded by minute perceptions that do not become for all that conscious perceptions. They do not become apperceptions since I am invaded in my consciousness when my consciousness is disorganized. At that moment, a flow of minute unconscious perceptions invades me. It’s not that these minute perceptions stop being unconscious, but it’s me who ceases being conscious. But I live them, there is an unconscious lived experience . I do not represent them, I do not perceive them, but they are there, they swarm in these cases. I receive a huge blow on the head: dizziness is an example that recurs constantly in Leibniz’s work. I get dizzy, I faint, and a flow of minute unconscious perceptions arrives: a buzz in my head. Rousseau knew Leibniz, he will undergo the cruel experience of fainting after having received a huge blow, and he relates his recovery and the swarming of minute perceptions. It’s a very famous text by Rousseau in the Reveries of a Solitary Stroller , which is the return to consciousness. Let’s look for thought experiences: we don’t even need to pursue this thought experience, we know it’s like that, so through thought, we look for the kind of experience that corresponds to the principle: fainting. Leibniz goes much further and says: wouldn’t that be death? This will pose problems for theology. Death would be the state of a living person who would not cease living. Death would be catalepsy, straight out of Edgar Poe, one is simply reduced to minute perceptions. And yet again, it’s not that they invade my consciousness, but it’s my consciousness that is extended, that loses all of its own power, that becomes diluted because it loses self-consciousness, but very strangely it becomes an infinitely minute consciousness of minute unconscious perceptions. This would be death. In other words, death is nothing other than an envelopment, perceptions cease being developed into conscious perceptions, they are enveloped in an infinity of minute perceptions. Or yet again, he says, sleep without dreaming in which there are lots of minute perceptions. Do we have to say that only about perception? No. And there, once again, appears Leibniz’s genius. There is a psychology with Leibniz’s name on it, which was one of the first theories of the unconscious. I have already said almost enough about it for you to understand the extent to which it’s a conception of the unconscious that has absolutely nothing to do with Freud’s which is to say how much innovation one finds in Freud: it’s obviously not the hypothesis of an unconscious that has been proposed by numerous authors, but it’s the way in which Freud conceived the unconscious. And, in the lineage from Freud some very strange phenomena will be found, returning to a Leibnizian conception, but I will talk about that later. But understand that he simply cannot say that about perception since, according to Leibniz, the soul has two fundamental faculties: conscious apperception which is therefore composed of minute unconscious perceptions, and what he calls "appetition", appetite, desire. And we are composed of desires and perceptions. Moreover, appetition is conscious appetite. If global perceptions are made up of an infinity of minute perceptions, appetitions or gross appetites are made up of an infinity of minute appetitions. You see that appetitions are vectors corresponding to minute perceptions, and that becomes a very strange unconscious. The drop of sea water to which the droplet corresponds, to which a minute appetition corresponds for someone who is thirsty. And when I say, "my God, I’m thirsty, I’m thirsty," what do I do? I grossly express a global outcome of thousands of minute perceptions working within me, and thousands of minute appetitions that crisscross me. What does that mean? In the beginning of the twentieth century, a great Spanish biologist fell into oblivion; his name was Turro. He wrote a book entitled in French: The Origins of Knowledge (1914), and this book is extraordinary. Turro said that when we say "I am hungry" ? his background was entirely in biology -- and we might say that it’s Leibniz who has awakened-- and Turro said that when one says, "I am hungry," it’s really a global outcome, what he called a global sensation. He uses his concepts: global hunger and minute specific hungers. He said that hunger as a global phenomenon is a statistical effect. Of what is hunger composed as a global substance? Of thousands of minute hungers: salt hunger, protein substance hunger, grease hunger, mineral salts hunger, etc. . . . When I say, "I’m hungry," I am literally undertaking, says Turro, the integral or the integration of these thousands of minute specific hungers. The minute differentials are differentials of conscious perception; conscious perception is the integration of minute perceptions. Fine. You see that the thousand minute appetitions are the thousand specific hungers. And Turro continues since there is still something strange on the animal level: how does an animal know what it has to have? The animal sees sensible qualities , it leaps forward and eats it, they all eat minute qualities. The cow eats green, not grass, although it does not eat just any green since it recognizes the grass green and only eats grass green. The carnivore does not eat proteins, it eats something it saw, without seeing the proteins. The problem of instinct on the simplest level is: how does one explain that animals eat more or less anything that suits them? In fact, animals eat during a meal the quantity of fat, of salt, of proteins necessary for the balance of their internal milieu. And their internal milieu is what? It’s the milieu of all the minute perceptions and minute appetitions. What a strange communication between consciousness and the unconscious. Each species eats more or less what it needs, except for tragic or comic errors that enemies of instinct always invoke: cats, for example, who go eat precisely what will poison them, but quite rarely. That’s what the problem of instinct is. This Leibnizian psychology invokes minute appetitions that invest minute perceptions; the minute appetition makes the psychic investment of the minute perception, and what world does that create? We never cease passing from one minute perception to another, even without knowing it. Our consciousness remains there at global perceptions and gross appetites, "I am hungry," but when I say "I am hungry," there are all sorts of passages, metamorphoses. My minute salt hunger that passes into another hunger, a minute protein hunger; a minute protein hunger that passes into a minute fat hunger, or everything mixed up, quite heterogeneously. What causes children to be dirt eaters? By what miracle do they eat dirt when they need the vitamin that the earth contains? It has to be instinct! These are monsters! But God even made monsters in harmony. So what is the status of psychic unconscious life? It happened that Leibniz encountered Locke’s thought, and Locke had written a book called An Essay Concerning Human Understanding. Leibniz had been very interested in Locke, especially when he discovered that Locke was wrong in everything. Leibniz had fun preparing a huge book that he called New Essays on Human Understanding in which, chapter by chapter, he showed that Locke was an idiot . He was wrong, but it was a great critique. And then he didn’t publish it. He had a very honest moral reaction, because Locke had died in the meantime. His huge book was completely finished, and he put it aside, he sent it to some friends. I mention all this because Locke, in his best pages, constructs a concept for which I will use the English word, "uneasiness." To summarize, it’s unease , a state of unease. And Locke tries to explain that it’s the great principle of psychic life. You see that it’s very interesting because this removes us from the banalities about the search for pleasure or for happiness. Overall, Locke says that it’s quite possible to seek one’s pleasure, one’s happiness, perhaps it’s possible, but that’s not all; there is a kind of anxiety for a living person. This anxiety is not distress . He proposes the psychological concept of anxiety. One is neither thirsting for pleasure, nor for happiness, nor distressed; he seems to feel that we are, above all, anxious. We can’t sit still. And Leibniz, in a wonderful text, says that we can always try to translate this concept, but that finally, it’s very difficult to translate. This word works well in English, and an Englishman immediately sees what it is. For us, we’d say that someone is nervous. You see how he borrows it from Locke and how he is going to transform it: this unease of the living, what is it? It’s not at all the unhappiness of the living. Rather, it’s when he is immobile, when he has his conscious perception well framed, it all swarms: minute perceptions and minute appetitions invest the fluid minute perceptions, fluid perceptions and fluid appetites ceaselessly move, and that’s it. So, if there is a God, and Leibniz is persuaded that God exists, this ‘uneasiness’ is so little a kind of unhappiness that it is just the same as the tendency to develop the maximum perception. And the development of the maximum perception will define a kind of psychic continuity. We again find the theme of continuity, that is, an indefinite progress of consciousness. How is unhappiness possible? There can always be unfortunate encounters. It’s like when a stone is likely to fall: it is likely to fall along a path that is the right path , for example, and then it can meet a rock that crumbles it or splits it apart. It’s really an accident connected to the law of the greatest slope. That doesn’t prevent the law of the greatest slope from being the best. We can see what he means. So there is an unconscious defined by minute perceptions, and minute perceptions are at once infinitely small perceptions and the differentials of conscious perception. And minute appetites are at once unconscious appetites and differentials of conscious appetition. There is a genesis of psychic life starting from differentials of consciousness. Following from this, the Leibnizian unconscious is the set of differentials of consciousness. It’s the infinite totality of differentials of consciousness. There is a genesis of consciousness. The idea of differentials of consciousness is fundamental. The drop of water and the appetite for the drop of water, specific minute hungers, the world of fainting. All of that makes for a very funny world. I am going to open a very quick parenthesis. That unconscious has a very long history in philosophy. Overall, we can say that in fact, it’s the discovery and the theorizing of a properly differential unconscious. You see that this unconscious has many links to infinitesimal analysis, and that’s why I said a psycho-mathematical domain. Just as there are differentials for a curve, there are differentials for consciousness. The two domains, the psychic domain and the mathematical domain, project symbols . If I look for the lineage, it’s Leibniz who proposed this great idea, the first great theory of this differential unconscious, and from there it never stopped. There is a very long tradition of this differential conception of the unconscious based on minute perceptions and minute appetitions. It culminates in a very great author who, strangely, has always been poorly understood in France, a German post-Romantic named Fechner. He’s a disciple of Leibniz who developed the conception of differential unconscious. What was Freud’s contribution? Certainly not the unconscious, which already had a strong theoretical tradition. It’s not that, for Freud, there were no unconscious perceptions, [but] there were also unconscious desires. You recall that for Freud, there is the idea that representation can be unconscious, and in another sense, affect also can be unconscious. That corresponds to perception and appetition. But Freud’s innovation is that he conceived the unconscious ? and here, I am saying something very elementary to underscore a huge difference -- he conceived the unconscious in a conflictual or oppositional relationship with consciousness, and not in a differential relationship. This is completely different from conceiving an unconscious that expresses differentials of consciousness or conceiving an unconscious that expresses a force that is opposed to consciousness and that enters into conflict with it. In other words, for Leibniz, there is a relationship between consciousness and the unconscious, a relation of difference to vanishing differences, whereas for Freud, there is a relation of opposition of forces. I could say that the unconscious attracts representations, it tears them from consciousness, and it’s really two antagonistic forces. I could say that, philosophically, Freud depends on Kant and Hegel, that’s obvious. The ones who explicitly oriented the unconscious in the direction of a conflict of will, and no longer of differential of perception, were from the school of Schopenhauer that Freud knew very well and that descended from Kant. So we must safeguard Freud’s originality, except that in fact, he received his preparation in certain philosophies of the unconscious, but certainly not in the Leibnizian strain. Thus our conscious perception is composed of an infinity of minute perceptions. Our conscious appetite is composed of an infinity of minute appetites. Leibniz is in the process of preparing a strange operation, and were we not to restrain ourselves, we might want to protest immediately. We could say to him, fine, perception has causes, for example, my perception of green, or of any color, that implies all sorts of physical vibrations. And these physical vibrations are not themselves perceived. Even though there might be an infinity of elementary causes in a conscious perception, by what right does Leibniz conclude from this that these elementary causes are themselves objects of infinitely minute perceptions? Why? And what does he mean when he says that our conscious perception is composed of an infinity of minute perceptions, exactly like perception of the sound of the sea is composed of the perception of every drop of water? If you look at his texts closely, it’s very odd because these texts say two different things, one of which is manifestly expressed by simplification and the other expresses Leibniz’s true thought. There are two headings: some are under the Part-Whole heading, and in that case, it means that conscious perception is always one of a whole, this perception of a whole assuming not only infinitely minute parts, but assuming that these infinitely small parts are perceived. Hence the formula: conscious perception is made of minute perceptions, and I say that, in this case, "is made of" is the same as "to be composed of." Leibniz expresses himself in this way quite often. I select a text: "Otherwise we would not sense the whole at all". . . if there were none of these minute perceptions, we would have no consciousness at all. The organs of sense operate a totalization of minute perceptions. The eye is what totalizes an infinity of minute vibrations, and henceforth composes with these minute vibrations a global quality that I call green, or that I call red, etc. . . . The text is clear, it’s a question of the Whole-Parts relationship. When Leibniz wants to move rapidly, he has every interest in speaking like that, but when he really wants to explain things, he says something else, he says that conscious perception is derived from minute perceptions. It’s not the same thing, "is composed of" and "is derived from". In one case, you have the Whole-Parts relationship, in the other, you have a relationship of a completely different nature. What different nature? The relation of derivation, what we call a derivative. That also brings us back to infinitesimal calculus: conscious perception derives from the infinity of minute perceptions. At that point, I would no longer say that the organs of sense totalize. Notice that the mathematical notion of integral links the two: the integral is what derives from and is also what operates an integration, a kind of totalization, but it’s a very special totalization, not a totalization through additions. We can say without risk of error that although Leibniz doesn’t indicate it, it’s even the second texts that have the final word. When Leibniz tells us that conscious perception is composed of minute perceptions, this is not his true thinking. On the contrary, his true thinking is that conscious perception derives from minute perceptions. What does "derive from" mean? Here is another of Leibniz’s texts: "Perception of light or of color that we perceive, that is, conscious perception ? is composed of a quantity of minute perceptions that we do not perceive, and a noise that we do not perceive, and a noise that we do perceive but to which we give no attention becomes a-perceptible, i.e. passes into the state of conscious perception, through a minute addition or augmentation." We no longer pass minute perceptions into conscious perception via totalization as the first version of the text suggested; we pass minute perceptions into global conscious perception via a minute addition. We thought we understood, and suddenly, we no longer understand a thing. A minute addition is the addition of a minute perception; so we pass minute perceptions into global conscious perception via a minute perception? We tell ourselves that this isn’t right. Suddenly, we tend to fall back on the other version of the text, at least that was more clear. More clear, but insufficient. Sufficient texts are sufficient, but we no longer understand anything in them. A wonderful situation, except if we chance to encounter an adjoining text in which Leibniz tells us: "We must consider that we think a quantity of things all at once. But we pay attention only to thoughts that are the most distinct . . ." For what is "remarkable" must be composed of parts that are not remarkable ? there, Leibniz is in the process of mixing up everything, but on purpose. We who are no longer innocent can situate the word "remarkable," and we know that each time that he uses "notable", "remarkable", "distinct", it’s in a very technical sense, and at the same time, he creates a muddle everywhere. For the idea that there is something clear and distinct, since Descartes, was an idea that circulated all over. Leibniz slides in his little "distinct" , the most distinct thoughts. Understand "the distinct," "the remarkable," "the singular." So what does that mean? We pass from minute unconscious perception to global conscious perception through a minute addition. So obviously, this is not just any minute addition. This is neither another conscious perception, nor one more minute unconscious perception. So what does it mean? It means that your minute perceptions form a series of ordinaries, a series called regular: all the minute drops of water, elementary perceptions, infinitesimal perceptions. How do you pass into the global perception of the sound of the sea? First answer: via globalization-totalization. Commentators answer: Fine, it’s easy to say. One would never thinking of raising an objection. You have to like an author just enough to know that he’s not mistaken, that he speaks this way in order to proceed quickly. Second answer: I pass via a minute addition. This cannot be the addition of a minute ordinary or regular perception, nor can it be the addition of a conscious perception since at that point, consciousness would be presupposed. The answer is that I reach a neighborhood of a remarkable point, so I do not operate a totalization, but rather a singularization. It’s when the series of minute perceived drops of water approaches or enters into the neighborhood of a singular point, a remarkable point, that perception becomes conscious. It’s a completely different vision because at that moment, a great part of the objections made to the idea of a differential unconscious falls away. What does that mean? Here appear the texts by Leibniz that seem the most complete. From the start, we have dragged along the idea that with minute elements, it’s a manner of speaking because what is differential are not elements, not dx in relation to an x, because dx in relation to an x is nothing. What is differential is not a dy in relation to a y because dy in relation to a y is nothing. What is differential is dy/dx, this is the relation. That’s what is at work in the infinitely minute. You recall that on the level of singular points, the differential relation changes its sign. You recall that on the level of singular points, the differential relation changes its sign. Leibniz is in the process of impregnating Freud without knowing it. On the level of the singularity of increases or decreases, the differential relation changes it sign, that is, the sign is inverted. In this case of perception, which is the differential relation? Why is it that these are not elements, but indeed relations? What determines a relation is precisely a relationship between physical elements and my body. So you have dy and dx. It’s the relation of physical excitation to my biological body. You understand that on this level, we can no longer speak exactly of minute perceptions. We will speak of the differential relation between physical excitation and the physical state by assimilating it frankly to dy/dx, it matters little. And perception becomes conscious when the differential relation corresponds to a singularity, that is, changes its sign. For example, when excitation gets sufficiently closer. It’s the molecule of water closest to my body that is going to define the minute increase through which the infinity of minute perceptions becomes conscious perception. It’s no longer a relation of parts at all, it’s a relation of derivation. It’s the differential relation between that which excites and my biological body that is going to permit the definition of the singularity’s neighborhood. Notice in which sense Leibniz could say that inversions of signs, that is, passages from consciousness to the unconscious and from the unconscious to consciousness, the inversions of signs refer to a differential unconscious and not to an unconscious of opposition. When I alluded to Freud’s posterity, in Jung, for example, there is an entire Leibnizian side, and what he reintroduces, to Freud’s greatest anger, and it’s in this that Freud judges that Jung absolutely betrayed psychoanalysis, is an unconscious of the differential type. And he owes that to the tradition of German Romanticism which is closely linked also to the unconscious of Leibniz. So we pass from minute perceptions to unconscious perception via addition of something notable, that is, when the series of ordinaries reaches the neighborhood of the following singularity, such that psychic life, just like the mathematical curve, will be subject to a law which is that of the composition of the continuous. There is composition of the continuous since the continuous is a product: the product of the act by which a singularity is extended into the neighborhood of another singularity. And that this works not only upon the universe of the mathematical symbol, but also upon the universe of perception, of consciousness, and of the unconscious. From this point onward, we have but one question: what are the compossible and incompossible? These derive directly from the former. We possess the formula for compossibility. I return to my example of the square with its four singularities. You take a singularity, it’s a point; you take it as the center of a circle. Which circle? All the way into the neighborhood of the other singularity. In other words, in the square abcd, you take *a* as center of a circle that stops or whose periphery is in the neighborhood of singularity *b*. You do the same thing with *b*: you trace a circle that stops in the neighborhood of the singularity *a* and you trace another circle that stops in the neighborhood of singularity *c*. These circles intersect. You go on like that constructing, from one singularity to the next, what you will be able to call a continuity. The simplest case of a continuity is a straight line, but there is also precisely a continuity of non-straight lines. With your system of circles that intersect, you will say that there is continuity when the values of two ordinary series, those of *a* to *b*, those of *b* to *a*, coincide. When there is a coincidence of values of two ordinary series encompassed in the two circles, you have a continuity. Thus you can construct a continuity made from continuity. You can construct a continuity of continuity, for example, the square. If the series of ordinaries that derive from singularities diverge, then you have a discontinuity. You will say that a world is constituted by a continuity of continuity. It’s the composition of the continuous. A discontinuity is defined when the series of ordinaries or regulars that derive from two points diverge. Third definition: the existing world is the best? Why? Because it’s the world that assures the maximum of continuity. Fourth definition: what is the compossible? An set of composed continuities. Final definition: what is the incompossible? When the series diverge, when you can no longer compose the continuity of this world with the continuity of this other world. Divergence in the series of ordinaries that depend on singularities: at that moment, it can no longer belong to the same world. You have a law of composition of the continuous that is psycho-mathematical. Why isn’t that evident? Why is all this exploration of the unconscious necessary? Because, yet again, God is perverse. God’s perversity lies in having chosen the world that implicates the maximum of continuity, in composing the chosen world in this form, only by dispersing the continuities since these are continuities of continuities. God dispersed them. What does that mean? It seems, says Leibniz, that there are discontinuities in our world, leaps, ruptures. Using an admirable term, he says that it seems that there are musical descents . But in fact, there are none. To some among us, it seems that there is a gap between man and animal, a rupture. This is necessary because God, with extreme malice, conceived the world to be chosen in the form of the maximum of continuity, so there are all sorts of intermediary degrees between animal and man, but God held back from making these visible to us. If the need arose, God placed them on other planets of our world. Why? Because finally, it was good, it was good for us to be able to believe in the excellence of our domination of nature. If we had seen all the transitions between the worst animal and us, we would have been less vain, so this vanity is still quite good because it allows man to establish his power over nature. Finally it’s not a perversity of God, but that God did not stop breaking continuities that God had constructed in order to introduce variety in the chosen world, in order to hide the whole system of minute differences, of vanishing differences. So God proposed to our organs of sense and to our stupid thinking, presented on the contrary a very divided world

. We spend our time saying that animals have no soul (Descartes), or else that they do not speak. But not at all: there are all sorts of transitions, all sorts of minute definitions. In this, we grasp a specific relation that is compossibility or incompossibility. I would say yet again that compossibility is when series of ordinaries converge, series of regular points that derive from two singularities and when their values coincide, otherwise there is discontinuity. In one case, you have the definition of compossibility, in the other case, the definition of incompossibility.

Why did God choose this world rather than another, when another was possible? Leibniz’s answer becomes splendid: it’s because it is the world that mathematically implicates the maximum of continuity, and it’s uniquely in this sense that it is the best of all possible worlds. A concept is always something very complex. We can situate today’s meeting under the sign of the concept of singularity. And the concept of singularity has all sorts of languages that intersect within it. A concept is always necessarily polyvocal. You can grasp the concept of singularity only through a minimum of mathematical apparatus: singular points in opposition to ordinary or regular points, on the level of thought experiences of a psychological type: what is dizziness, what is a murmur, what is a hum , etc. And on the level of philosophy, in Leibniz’s case, the construction of this relation of compossibility. It’s not a mathematical philosophy, no more than mathematics becomes philosophy, but in a philosophical concept, there are all sorts of different orders that necessarily symbolize. It has a philosophical heading, it has a mathematical heading, and it has a heading for thought experience. And it’s true of all concepts. It was a great day for philosophy when someone brought this odd couple to general attention, and that’s what I call a creation in philosophy. When Leibniz proposed this topic, the singular, there precisely is the act of creation; when Leibniz tells us that there is no reason for you simply to oppose the singular to the universal. It’s much more interesting if you listen to what mathematicians say, who for their own reasons think of "singular" not in relation to "universal," but in relation to "ordinary" or "regular." Leibniz isn’t doing mathematics at that point. I would say that his inspiration is mathematical, and he goes on to create a philosophical theory, notably a whole conception of truth that is radically new since it’s going to consist in saying: don’t pay too much attention to the matter of true and false, don’t ask in your thinking what is true and what is false, because what is true and what is false in your thinking always results from something that is much deeper.

What counts in thinking are the remarkable points and the ordinary points. Both are necessary: if you only have singular points in thinking, you have no method of extension , it’s worthless; if you have only ordinary points, it’s in your interest to think something else. And the more you believe yourself [to be] remarkable (special), the less you think of remarkable points. In other words, the thought of the singular is the most modest thought in the world. It’s there that the thinker necessarily becomes modest, because the thinker is the extension onto the series of ordinaries, and thought itself explodes in the element of singularity, and the element of singularity is the concept.

Cours Vincennes - 06/05/1980

The last time, we ended with the question: what is compossibility and what is incompossibility? What are these two relationships, the relationship of compossibility and incompossibility? How do we define them?

We saw that these questions created all kinds of problems and led us necessarily to the exercise, however cursory, of infinitesimal analysis. Today, I would like to create a third major rubric that would consist in showing the extent to which Leibniz organizes in a new way and even creates some genuine principles. Creating principles is not a fashionable task of late. This third major introductory chapter for a possible reading of Leibniz is one I will call: Deduction of principles, precisely because principles are objects of a special kind of deduction, a philosophical deduction, which does not go without saying. There is such a rich abundance of principles in Leibniz's work. He constantly invokes principles while giving them, when necessary, names that did not previously exist. In order to situate oneself within his principles, one has to discover the progression [cheminement] of Leibnizian deduction.

The first principle that Leibniz creates with a rapid justification is the principle of identity. It is the minimum, the very least that he provides. What is the principle of identity? Every principle is a reason. A is A. A thing, it's a thing, that is what a thing is. I have already made some progress. A thing is what it is is better than A is A. Why? Because it shows what is the region governed by the principle of identity. If the principle of identity can be expressed in the form: a thing is what it is, this is because identity consists in manifesting the proper identity between the thing and what the thing is. If identity governs the relationship between the thing and what the thing is, namely what thing is identical to the thing, and the thing is identical to what it is, I can say: what is the thing? What the thing is, everyone has called it the essence of the thing. I would say that the principle of identity is the rule of essences or, what comes down to the same thing, the rule of the possible. In fact, the impossible is contradictory. The possible is the identical so that, to the extent that the principle of identity is a reason, a ratio, then which ratio? It is the ratio of essence or, as the Latins used to say, or the Middle Age terminology long before: ratio essendi. I choose that as a typical example because I think that it is very difficult to do philosophy if you do not have a kind of terminological certainty. Never tell yourself that you can do without it, but also never tell yourself that it is difficult to acquire. It is exactly the same as scales on the piano. If you do not know rather precisely the rigour of concepts, that is, the sense of major notions, then it is very difficult. One has to approach that like an exercise. It is normal for philosophers to have their own scales, it is their mental piano. One must change the tune of the categories. The history of philosophy can only be created by philosophers, yet alas, it has fallen into the hands of philosophy professors, and that's not good because they have turned philosophy into examination material and not material for study, or for scales.

Each time that I speak of a principle according to Lebiniz, I am going to give it two formulations: a vulgar formulation and a scholarly one. This is a beautiful procedure on the level of principles, the necessary relation between pre-philosophy and philosophy, this relationship of exteriority in which philosophy needs a pre-philosophy. The vulgar formulation of the principle of identity: the thing is what the thing is, the identity of the thing and of its essence. You see that, in the vulgar formulation, there are lots of things already implied.

The scholarly formulation of the principle of identity: every analytical proposition is true. What is an analytical proposition? It is a proposition in which the predicate and the subject are identical. An analytical proposition is true, A is A, is true. By going into the detail of Leibniz's formulae, one can even complete the scholarly formulation: every analytical proposition is true in two cases: either by reciprocity or by inclusion.

An example of a proposition of reciprocity: the triangle has three angles. Having three angles is what the triangle is. Second case: inclusion: the triangle has three sides. In fact, a closed figure having three angles envelopes, includes, implies having three sides. We will say that analytical propositions of reciprocity are objects of intuition, and we will say that analytical propositions of inclusion are objects of demonstration. Therefore, the principle of identity, the rule of essences, or of the possible, ratio essendi: what question does it answer? What cry does the principle of identity answer? The pathetic cry that constantly appears in Leibniz's works, corresponding to the principle of identity, why is there something rather than nothing? It is the cry of the ratio essendi, of the reason for being [raison d'être]. If there were no identity, no identity conceived as identity of the thing and what the thing is, then there would be nothing.

Second principle: principle of sufficient reason. This refers us back to the whole domain that we located as being the domain of existences. The ratio corresponding to the principle of sufficient reason is no longer the ratio essendi, the reason of essences or the reason for being, it is now the ratio existendi, the reason for existing. It is no longer the question: why something rather than nothing, since the principle of identity assured us that there was something, namely the identical. It is no longer: why something rather than nothing, but rather it is why this rather than that? What would its vulgar formulation be? We saw that every thing has a reason. Indeed, every thing must have a reason. What would the scholarly formulation be? You see that we apparently are completely outside the principle of identity. Why? Because the principle of identity concerns the identity of the thing and what it is, but it does not state whether the thing exists. The fact that the thing exists or does not exist is completely different from what it is. I can always define what a thing is independently of the question of knowing if it exists or not. For example, I know that the unicorn does not exist, but I can state what a unicorn is. Thus, a principle is indeed necessary that makes us think of the existent [lâexistant]. So just how does a principle, that appears to us as vague as "everything has a reason," make us think of the existent? It is precisely the scholarly formulation that will explain it to us. We find this scholarly formulation in Leibniz's works in the following statement: every predication (predication means the activity of judgment that attributes something to a subject; when I say "the sky is blue," I attribute blue to sky, and I operate a predication), every predication has a basis [fondement] in the nature of things. It is the ratio existendi.

Let us try to understand better how every predication has a basis in the nature of things. This means: everything said about a thing, the entirety of what is said about a thing, is the predication concerning this thing. Everything said about a thing is encompassed, contained, included in the notion of the thing. This is the principle of sufficient reason. You see that the formula which appeared innocent a short while ago - every predication has a basis in the nature of things, taking it literally - becomes much stranger: everything said about a thing must be encompassed, contained, included in the notion of the thing. So, what is everything said about a thing? First, it is the essence. In fact, the essence is said about the thing. Only one finds at that level that there would be no difference between sufficient reason and identity. And this is normal since sufficient reason includes all the properties [tout l'acquis] of the principle of identity, but is going to add something to it: what is said about a thing is not only the essence of the thing, it is the entirety of the affections, of the events that refer or belong to the thing.

Thus, not only will the essence be contained in the notion of the thing, but the slightest of events, of affections concerning the thing as well, that is, what is attributed truthfully to the thing is going to be contained in the notion of the thing. We have seen this: crossing the Rubicon, whether one likes it or not, must be contained in the notion of Caesar. Events, affections of the type "loving" and "hating" must be contained in the notion of that subject feeling these affections. In other words, each individual notion -- and the existent is precisely the object, the correlate of an individual notion -- each individual notion expresses the world. That is what the principle of sufficient reason is. "Everything has a reason" means that everything that happens to something must be contained forever in the individual notion of the thing. The definitive formulation of the principle of sufficient reason is quite simple: every true proposition is analytical, every true proposition, for example, every proposition that consists in attributing to something an event that really occurred and that concerns the something. So if it is indeed true, the event must be encompassed in the notion of the thing.

What is this domain? It is the domain of infinite analysis whereas, on the contrary, at the level of the principle of identity, we were only dealing with finite analyses. There will be an infinite analytical relationship between the event and the individual notion that encompasses the event. In short, the principle of sufficient reason is the reciprocal of the principle of identity. Only, what has occurred in the reciprocal? The reciprocal has taken over a radically new domain, the domain of existences. It was sufficient merely to reciprocate, to reverse the formula of identity in order to obtain the formula of sufficient reason; it was enough to reciprocate the formula of identity that concerns essences in order to obtain a new principle, the principle of sufficient reason concerning existences. You will tell me that this was not complicated. Yet it was enormously complicated, so why? The reciprocal, this reciprocation was only possible if one were able to extend the analysis to infinity. So the notion, the concept of infinite analysis is an absolutely original notion. Does that consist in saying that this takes place uniquely in the understanding [l'entendement] of God, which is infinite? Certainly not. This implies an entire technique, the technique of differential analysis or infinitesimal calculus.

Third principle: is it true that the reciprocal of the reciprocal would yield the first? It is not certain. Everything depends, there are so many viewpoints. Let us try to vary the formulation of the principle of sufficient reason. For sufficient reason, I left things off by saying that everything that happens to a thing must be encompassed, included in the notion of the thing, which implies infinite analysis. In other words, for everything that happens or for every thing there is a concept. I insisted earlier that what matters is not at all a way for Leibniz to recover a famous principle. On the contrary, he does not want that at all; this would be the principle of causality. When Leibniz says that everything has a reason, that does not at all mean that everything has a cause. Saying everything has a cause signifies A refers to B, B refers to C, etc. ... Everything has a reason means that one must account for reason in causality itself, namely that everything has a reason means that the relationship that A maintains with B must be encompassed in one way or another in the notion of A. Just like the relationship that B maintains with C must be encompassed one way or another in the notion of B. Thus, the principle of sufficient reason goes beyond the principle of causality. It is in this sense that the principle of causality states only the necessary cause, but not the sufficient reason. Causes are only necessities that themselves refer to and presuppose sufficient reasons.

Thus, I can state the principle of sufficient reason in the following way: for every thing there is a concept that takes account both of the thing and of its relations with other things, including its causes and its effects. For every thing, there is a concept, and that does not go without saying. Lots of people will think that not having a concept is the peculiarity [le propre] of existence. For every thing there is a concept, so what would the reciprocal be? Understand that the reciprocal does not at all have the same meaning. In Aristotle's work, there is a treatise of ancient logic that deals solely with the table of opposites. What is the contradictory, the contrary, the subaltern, etc. ... You cannot say the contradictory when it is the contrary, you cannot just say anything. Here I use the word reciprocal without specifying. When I say for every thing there is a concept (yet again, this is not at all certain), assume that you grant me that. There I cannot escape the reciprocal. What is the reciprocal ?

For a theory of the concept, we would have to start again from the bird song [chant dâoiseaux]. The great difference between cries and songs. The cries of alarm, of hunger, and then the bird songs. And we can explain acoustically what the difference is between cries and songs. In the same way, on the level of thought, there are cries of thought and songs of thought [chants de pensée]. How to distinguish these cries and these songs? One cannot understand how a philosophy as song or a philosophical song develops if one does not refer it to coordinates that are kinds of cries, continuous cries. These cries and songs are complex. If I return to music, the example that I recall again and again is the two great operas of [Alban] Berg; there are two great death cries, the cry of Marie and the cry of Lulu. [TN: cf. "N as in Neurology" in LâAbécédaire de Gilles Deleuze] When one dies, one does not sing, and yet there is someone who sings around death, the mourner. The one who loses the loved one sings. Or cries, I do not know. In Wozzeck, it is a si-, it is a siren. When you put sirens into music, you are placing a cry there. It is strange. And the two cries are not the same type, even acoustically: there is a cry that flits upward and there is a cry that skims along the earth. And then there is the song [chant]. Luluâs great woman friend sings death. It is fantastic. It is signed Berg. I would say that the signature of a great philosopher is the same. When a philosopher is great, although he writes very abstract pages, these are abstract only because you did not know how to locate the moment in which he cries. There is a cry underneath, a cry that is horrible.

Let us return to the song of sufficient reason. Everything has a reason is a song. It is a melody, we could harmonize. A harmony of concepts. But underneath there would be rhythmic cries: no, no, no. I return to my sung formulation of the principle of sufficient reason. One can sing off key in philosophy. People who sing off key in philosophy know it very well, but it [philosophy] is completely dead. They can talk interminably. The song of sufficient reason: for every thing there is a concept. What is the reciprocal ? In music, one would speak of retrograde series. Let us look for the reciprocal of "every thing has a concept." The reciprocal is: for every concept there is one thing alone.

Why is this the reciprocal of "for every thing a concept"? Suppose that a concept had two things that corresponded to it. There is a thing that has no concept and, in that case, sufficient reason is screwed [foutue]. I cannot say "for every thing a concept". As soon as I have said "for every thing a concept," I have necessarily said that a concept had necessarily one thing alone, since if a concept has two things, there is something that has no concept, and therefore already I could no longer say "for every thing a concept." Thus, the true reciprocal of the principle of sufficient reason in Leibniz will be stated like this: for every concept, one thing alone. It is a reciprocal in a very funny sense. But in this case of reciprocation, sufficient reason and the other principle, notably "for every thing, a concept" and "for every concept, one thing alone," I cannot say one without saying the other. Reciprocation is absolutely necessary. If I do not recognize the second, I destroy the first.

When I said that sufficient reason was the reciprocal of the principle of identity, it was not in the same sense since, if you recall the statement [énoncé] of the principle of identity ö namely, every true proposition is analytical, there is in this no necessity. I can say that every analytical proposition is true without necessarily preventing any true proposition from being analytical. I could very well say that there are true propositions that are something other than analytical. Thus, when Leibniz created his reciprocation of identity, he made a master stroke because he had the means to make this master stroke, that is, he let out a cry. He had himself created an entire method of infinite analysis. Otherwise, he could not have done so.

Whereas in the case of the passage from sufficient reason to the third principle that I have not yet baptized, there reciprocation is absolutely necessary. It had to be discovered. What does it mean that for every concept there is a thing and only one thing? Here it gets strange, you have to understand. It means that there are no two absolutely identical things, or every difference is conceptual in the last instance. If you have two things, there must be two concepts, otherwise there would not be two things. Does that mean that there are no two absolutely identical things as far as the concept goes? It means that there are no two identical drops of water, no two identical leaves. In this, Leibniz is perfect, he gets delirious with this principle. He says that obviously you, you believe that two drops of water are identical, but this is because you do not go far enough in your analysis. They cannot have the same concept. Here this is very odd because all of classical logic tends rather to tell us that the concept, by its very nature, encompasses an infinite plurality of things.

The concept of drops of water is applicable to all drops of water. Leibniz says, of course, if you have blocked off analysis of the concept at a certain point, at a finite moment. But if you push the analysis forward, there will be a moment in which the concepts are no longer the same. This is why the ewe recognizes its lamb, one of Leibniz's examples: how does the ewe recognize its little lamb? They [Eux] think it is via the concept. A little lamb does not have the same concept as the same individual concept, it is in this manner that the concept extends to the individual, another little lamb. What is this principle? There is but a single thing; there is necessarily one thing per concept and only one. Leibniz names it the principle of indiscernibles. We can state it this way: there is one thing and only one thing per concept, or every difference is conceptual in the final instance.

There is only conceptual difference. In other words, if you assign a difference between two things, there is necessarily a difference in the concept. Leibniz names this the principle of indiscernibles. And if I make it correspond to a ratio, what is this? You sense correctly that it consists in saying that we only gain knowledge through the concept. In other words, the principle of indiscernibles seems to me to correspond to the third ratio, the ratio as ratio cognoscendi, the reason as reason for knowing [raison de connaitre].

Let us look at the consequences of such a principle. If this principle of indiscernibles were true, namely that every difference is conceptual, there would be no difference except the conceptual. Here Leibniz asks us to accept something that is quite huge. Let us proceed in order: what other kind of difference is there other than conceptual? We see it immediately: there are numerical differences. For example, I say a drop of water, two drops, three drops. I distinguish the drops by the number alone [solo numero, that Deleuze translates as par le nombre seulement]. I count the elements of a set [ensemble], one two three four, I neglect their individuality, I distinguish them by the number. This constitutes a first type of very classic distinction, the numerical distinction. Second type of distinction: I say "take this chair"; some obliging person takes a chair, and I say, "not that one, but this one." This time, it is a spatio-temporal distinction of the here-now type. The thing that is here at a particular moment, and this other thing that is there at a particular moment. Finally, there are distinctions of figure and of movement: roof that has three angles, or something else. I would say that these are distinctions by extension and movement. Extension and movement.

Understand that this commits Leibniz to a strange undertaking, merely with his principle of indiscernibles. He has to show that all these types of non-conceptual distinctions - and in fact, all of these distinctions are non-conceptual since two things can be distinguished by the number even though they have the same concept. You focus on the concept of a drop of water, and you say: first drop, second drop. It is the same concept. There is the first and there is the second. There is one that is here, and another that is there. There is one that goes fast, and another that goes slowly. We have now nearly completed the set of non-conceptual distinctions.

Leibniz arrives and calmly tells us, no no. These are pure appearances, that is, these are only provisional ways of expressing a difference of another nature, and this difference is always conceptual. If there are two drops of water, they do not have the same concept. What of any great import does this mean? It is very important in problems of individuation. It is very well known, for example, that Descartes tells us that bodies are distinguished from one another by figure and by movement. Lots of thinkers have appreciated that. Notice that in the Cartesian formula, what is conserved in movement (mv) (the product of mass times movement) depends strictly on a vision of the world in which bodies are distinguished by the figure and movement. What does Leibniz commit himself to when he tells us no? It is absolutely necessary that to all these non-conceptual differences there correspond conceptual differences; they only cause it to be imperfectly translated. All non-conceptual differences only cause a basic conceptual difference to be imperfectly translated. Leibniz commits himself to a task of physics. He has to find a reason for which a body is either in a particular number, or in a particular here and now, or has a particular figure and a particular velocity. He will translate that quite well in his critique of Descartes when he says that velocity is a pure relative. Descartes was wrong, he took something that was purely relative for a principle. It is therefore necessary that figure and movement be surpassed [se dépassent] toward something deeper. This means something quite enormous for philosophy in the seventeenth century.

Specifically, that there is no extended substance or that extension [l'étendue] cannot be a substance. That extension is a pure phenomenon. That it refers to something deeper. That there is no concept of extension, that the concept is of another nature. It is therefore necessary that figure and movement find their reason in something deeper. Henceforth, extension has no sufficiency. It is not by chance that this is precisely what makes a new physics, he completely recreates the physics of forces. He opposes force, on one hand, to figure and extension, on the other, figure and extension being only manifestations of force. It is force that is the true concept. There is no concept of extension because the true concept is force. Force is the reason of figure and movement in extension. Hence the importance of this operation that appeared purely technical when he said that what is conserved in movement is not mv, but mv2. Squaring velocity is the translation of the concept of force, which is to say that everything changes. It is physics that corresponds to the principle of indiscernibles. There are no two similar or identical forces, and forces are the true concepts that must take account of or justify everything that is figure or movement in extension.

Force is not a movement, it is the reason for movement. Hence the complete renewal of the physics of forces, and also of geometry, of kinematics [la cinématique]. Everything passes through this, merely by the squaring of velocity. MV2 is a formula of forces, not a formula of movement. You see that this is essential.

To sum up generally, I can also say that figure and movement must move forward toward force. Number must move forward toward the concept. Space and time must also move forward toward the concept.

But this is how a fourth principle develops quite slowly, one that Leibniz names the law of continuity. Why did he say law? That is a problem. When Leibniz speaks of continuity that he considers to be a fundamental principle and one of his very own great discoveries, he no longer uses the term "principle," but uses the term "law." We have to explain that. If I look for a vulgar formulation of the law of continuity, it is quite simple: nature does not make a jump [la nature ne fait pas de saut]. There is no discontinuity. But there are two scholarly formulations. If two causes get as close as one would like, to the point of only differing by a difference decreasing to infinity, the effects must differ in like manner. I immediately say what Leibniz is thinking about because he has it in for Descartes so much. What are we told in the laws of the communication of movement? Here are two cases: two bodies of the same mass and velocity meet each other; one of the two bodies has a greater mass or a greater velocity, so it carries off the other. Leibniz says that this cannot be. Why? You have two states of the cause. First state of the cause: two bodies of the same mass and velocity. Second state of the cause: two bodies of different masses. Leibniz says that you can cause difference to decrease to infinity, you can act so these two states approach one another in the causes. And we are told that the two effects are completely different: in one case, there is a repulsion [rebondissement] of the two bodies, in the other case, the second body is dragged off by the first, in the direction of the first. There is a discontinuity in the effect whereas one can conceive of a continuity in the causes. It is in a continuous manner that we can pass from different masses to equal masses. Thus, it is not possible for there to be discontinuity in the facts/acts [faits] if there is possible continuity in the cause. That leads him again into a whole, very important physical study of movement that will be centered on the substitution of a physics of forces for a physics of movement. I was citing this to refresh our memory. But the other scholarly formulation of the same principle, and you will understand that it is the same thing as the preceding one: in a given case, the concept of the case ends in the opposite case.

This is the pure statement of continuity. Example: a given case is movement, the concept of movement ends in the opposite case, that is in rest. Rest is infinitely small movement. This is what we saw from the infinitesimal principle of continuity. Or I might say that the last possible scholarly formulation of continuity is: a given singularity extends itself [se prolonge] into a whole series of ordinaries all the way to the neighborhood of the following singularity. This time it is the law of the composition of the continuous. We worked on that the last time. But right when we thought we had finished there arises a very important problem. Something impels me to say that, between principle three and principle four, there is a contradiction, that is between the principle of indiscernibles and the principle of continuity, there is a contradiction. First question: in what way is there a contradiction? Second question: the fact is that Leibniz never considered there to be the slightest contradiction. Here we are in that situation of liking and profoundly admiring a philosopher, yet of being disturbed because some texts seem contradictory to us, and he did not even see what we might tell him. Where would the contradiction be if there was one? I return to the principle of indiscernibles, every difference is conceptual, there are no two things having the same concept. At the limit I might say that to every thing corresponds a determined difference, not only determined but assignable in the concept. The difference is not only determined or determinable, it is assignable in the very concept. There are no two drops of water having the same concept, that is the difference one, two must be encompassed in the concept. It must be assigned in the concept. Thus every difference is an assignable difference in the concept. What does the principle of continuity tell us? It tells us that things proceed by vanishing differences [différences évanouissantes], infinitely small differences, that is unassignable differences. That gets really awful. Can one say that every thing proceeds by unassignable difference and say at the same time that every difference is assigned and must be assigned in the concept? Ah! Doesn't Leibniz contradict himself? We can move forward a small bit by looking at the ratio of the principle of continuity since I found a ratio for each of the first three principles. Identity is the reason of essence or ratio essendi, sufficient reason is the reason of existence or the ratio existendi, the indiscernibles are the reason for knowing or the ratio cognoscendi, and the principle of continuity is the ratio fiendi, that is, the reason for becoming. Things become through continuity. Movement becomes rest, rest becomes movement, etc. The polygon becomes a circle by muliplying its sides, etc·. This is a very different reason for becoming from the reasons of being or of existing. The ratio fiendi needed a principle, and it is the principle of continuity.

How do we reconcile continuity and indiscernibles? Moreover, we have to show that the way in which we will reconcile them must take account of this at the same time: that Leibniz was right to see no contradiction at all between them. In this we have the experience of thought. I return to the proposition: each individual notion expresses the whole world. Adam expresses the world, Caesar expresses the world, each of you expresses the world. This formula is very strange. Concepts in philosophy are not a single word. A great philosophical concept is a complex, a proposition, or a prepositional function. One would have to do exercises in philosophical grammar. Philosophical grammar would consist of this: with a given concept, find the verb. If you have not found the verb, you have not rendered the verb dynamic, you cannot live it. The concept is always subject to a movement, a movement of thought. A single thing counts: movement. When you do philosophy, you are looking only at movement, only it is a particular kind of movement, the movement of thought. What is the verb? Sometimes the philosopher states it explicitly, sometimes he does not state it. Is Leibniz going to state it? In each individual notion that expresses the world, there is a verb, this is expressing. But what does that mean? It means two things at once, as if two movements coexisted.

Leibniz tells us at the same time: God does not create Adam the sinner, but creates the world in which Adam sinned. God does not create Caesar crossing the Rubicon, but creates the world in which Caesar crosses the Rubicon. Thus, what God creates is the world and not the individual notions that express the world. Second proposition by Leibniz: the world exists only in the individual notions that express it. If you privilege one individual notion over the other . . . If you accept that, what results is like two readings or two complementary and simultaneous ways of understanding, but two understandings of what? You can consider the world, but yet again the world does not exist in itself, it exists only in the notions that express it. But you can make this abstraction, you consider the world. How do you consider it? You consider it as a complex curve. A complex curve has singular points and ordinary points. A singular point extends itself into the ordinary points that depend on it all the way to the neighborhood of another singularity, etc. etc. . . . and you compose the curve in a continuous manner like that, by extending singularities into series of ordinaries. For Leibniz, that is what the world is. The continuous world is the distribution of singularities and regularities, or singularities and ordinaries that constitute precisely the set chosen by God, that is the set that unites the maximum of continuity. If you remain in this vision, the world is governed by the law of continuity since continuity is precisely this composition of singulars insofar as they extend into the series of ordinaries that depend on them. You have your world that is literally laid out [déployé] in the form of a curve in which singularities and regularities are distributed. This is the first point of view that is completely subject to the law of continuity.

Only here we are, this world does not exist in itself, it exists only in the individual notions that express this world. That means that an individual notion, a monad, that each one encompasses a small determined number of singularities. It encloses a small number of singularities. It is the small number of singularities·. You recall that individual notions or monads are points of view on the world. It is not the subject that explains [explique] the point of view, it is the point of view that explains the subject. Hence the need to ask oneself, what is this point of view? A point of view is defined by this: a small number of singularities drawn from the curve of the world. This is what is at the basis of an individual notion. What makes the difference between you and me is that you are, on this kind of fictional curve, you are constructed around such and such singularities, and me around such and such singularities. And what you call individuality is a complex of singularities insofar as they form a point of view. There are two states of the world. It has a developed state . . .

(end of the tape).

Cours Vincennes - 20/05/1980

I would like to finish these meetings on Leibniz by presenting the problem that I wanted to consider. I return to this question that I asked from the start, specifically: what does this image mean that good sense often creates about philosophy, what does this image mean that good sense sometimes produces about philosophy, like a kind of locus of discussion in which philosophers are fundamentally not in agreement? A kind of philosophical atmosphere in which people dispute, fight among themselves, whereas at least in science, they know what they are talking about. We are told as well that all philosophers say the same thing, they all agree or all hold opposite views. It’s in relation to Leibniz that I would like to select some very precise examples. What does it mean that two philosophies do not agree? Polemics, like a certain state of things that traverses certain disciplines, I do not find that there are more polemics in philosophy than there are in science or in art. What is a philosopher who critiques another philosopher? What is the function of critique? Leibniz offers us this example: what does the opposition between Kant and Leibniz mean, once we have said that it was a fundamental opposition in the history of philosophy? What does it mean for Kant to undertake a critique of Leibniz? I would like to number what I want to tell you. An initial task: to localize the oppositions. There are two fundamental oppositions from the point of view of knowledge. They function like thesis and antithesis. When we manage to trace the great philosophical oppositions, on the level of the concepts used by one philosopher or another, we also have to evaluate their relations to these oppositions. They [the oppositions] are not of equal value. Perhaps one does happen to have greater weight than another, to be more decisive. If you fail to organize the oppositions, I think that you are no longer able to understand what the subject is in a polemic.

First opposition between Leibniz and Kant, from the point of view of knowledge. I will let Leibniz speak. A Leibnizian proposition: all propositions are analytical, and knowledge can proceed only by analytical propositions. You recall that we call “analytical proposition” a proposition in which one of the two terms of the proposition is contained in the concept of the other. It’s a philosophical formula. We can already sense that there is no point in arguing at this level. Why? Because there is already something implied, specifically that there is a certain model of knowledge. What is presupposed, but in science as well, there are also presuppositions; what is presupposed is a certain ideal of knowledge, specifically knowing is discovering what is included in the concept. It’s a definition of knowledge. We are pleased to have a definition of knowledge, but why this one rather that something else? From the other side, Kant arises and says: there are synthetic propositions. You see what a synthetic proposition is: it’s a proposition in which one of the terms is not contained in the concept of the other. Is this a cry? Is this a proposition? Against Leibniz, he says, “no”; he says that there are synthetic propositions and that knowledge exists only through synthetic propositions. The opposition seems perfect. At this point, a thousand questions assail me: What would that mean to argue, to argue about who is right, who is right about what? Is this provable, are we in the domain of decidable propositions? I say simply that the Kantian definition must interest you because, if you consider it closely, it also implies a certain conception of knowledge, and it happens that this conception of knowledge is very different from Leibniz’s. When one says that knowledge proceeds only through synthetic propositions, that is, a proposition such that one of its terms is not contained in the concept of the other, there is therefore a synthesis between the two terms. Someone who says this can no longer base knowledge on the Leibnizian conception. He will tell us, on the contrary, that to know is not at all to discover what is included in a concept, that knowledge necessarily means leaving behind one concept in order to affirm something else. We call “synthesis” the act through which one leaves a concept behind in order to attribute to it or to affirm something else. In other words, to know is always to go beyond the concept. Knowing is to go beyond [connaître c’est dépasser]. Understand all that is in play here. In the first conception, to know is to have a concept and discover what is contained in the concept. I would say about that knowledge that it is based on a particular model which is one of passion or of perception. To know is finally to perceive something, to know is to apprehend, a passive model of knowledge, even if many activities depend on it. In the other case, to the contrary, it means leaving the concept behind in order to affirm something, and is a model of the knowledge-act [un modèle de la connaissance acte].

I return to my two propositions. Let us suppose that we are referees. We find ourselves faced with these two propositions, and we say: what do I choose? First when I say: is it decidable? What would that mean? It could mean that it’s a question of fact. One has to find the facts that allow one to say that one or the other is right. Obviously, it’s not that. Philosophical propositions, to some extent, aren’t justifiable on the basis of a verification of facts. That is why philosophy has always distinguished two questions, and Kant especially will take this distinction up again. This distinction was formulated in Latin: quid facti, what is derived from fact [qu'en est-il du fait], and quid juris, what is derived from principle [qu'en est-il du droit]. And if philosophy is concerned with principle, it is precisely because it poses questions that are called de jure questions [questions de droit]. What does it mean that my two paradoxical propositions, Leibniz’s and Kant’s, are not justifiable on the basis of a factual response? It means that in fact, there is no problem because all the time we encounter phenomena that are synthetic phenomena. Indeed, in my simplest judgments, I pass my time operating syntheses. I say, for example, that this straight line is white.

It is quite obvious that with this, I am affirming about a straight line something that is not contained in the concept of straight line. Why? Every straight line is not white. That this straight line is white is obviously an encounter in experience; I could not have made such a statement beforehand. I therefore encounter in experience straight lines that are white. It’s a synthesis, and we call this kind of synthesis *a posteriori*, that is, given in experience. Thus, there are syntheses of fact, but that does not resolve the problem. Why? For a very simple reason: this straight line [that] is white does not constitute knowledge. It’s a protocol of experience. Knowledge is something other than tracing protocols of experience. When does one know? One knows when a proposition appeals to a principle [se réclame d’un droit]. What defines a proposition’s principle is the universal and the necessary. When I say that a straight line is the shortest path from one point to another, I maintain a proposition in principle (une proposition de droit). Why? Because I don’t need to measure each straight line to know that, if it’s straight, it’s the shortest path. Every straight line, beforehand, a priori, that is, independently of experience, is the shortest path from one point to another, otherwise it would not be a straight line. Thus, I would say that the proposition “a straight line is the shortest path” constitutes indeed a proposition of knowledge. I do not await experience to discover that a straight line is the shortest path; to the contrary, I determine the experience since the shortest path from one point to another is my way of tracing a straight line experientially. Any straight line is necessarily the shortest path from one point to another. This is a proposition of knowledge and not a protocol proposition. Let us take this proposition, it’s an a priori proposition. In this, are we going to be able finally to pose the question of separation between Leibniz and Kant, specifically is it an analytical proposition or is it a synthetic proposition?

Kant says something very simple: it’s necessarily, a priori, a synthetic proposition. Why? Because when you say that the straight line is the shortest path from one point to another, you are leaving behind the concept “straight line.” Isn’t it the content in a straight line to be the shortest path from one point to another? It goes without saying that Leibniz would say that it is the content in “straight line.” Kant says no, the concept “straight line”, according to the Euclidian definition is: line ex aequo in all of its points. You won’t draw from this the shortest path between one point and another. You have to leave the concept behind to affirm something else about it. We’re not convinced. Why does Kant say that? Kant would answer, I suppose, that the shortest path to another is a concept that implies a comparison, the comparison of the shortest line with other lines that are either broken lines or curvilinear lines, that is, curves. I cannot say that the straight line is the shortest path from one point to another without implying a comparison, the relation of the straight line to curved lines. For Kant this suffices to say that a synthesis lies therein; you are forced to leave the “straight line” concept in order to reach the “curved line” concept, and it’s in the relation of straight lines to curved lines that you say the straight line is the shortest path from one point to another. . . It’s a synthesis, thus knowledge is a synthetic operation. Would Leibniz be disturbed by that? No, he would say that obviously you have to keep in mind the “curved line” concept when you say that the straight line is the shortest path from one point to another, but Leibniz is the creator of a differential calculus through which the straight line is going to be considered as the limit of curves. There is a process to the limit. Hence Leibniz’s theme: it’s an analytical relation, only it’s an infinite analysis. The straight line is the limit of the curve, just as rest is the limit of movement. Does this advance us? So either one can no longer resolve this, or they mean the same thing. [If] they say the same thing, what would this be? It would mean that what Leibniz calls infinite analysis is the same thing as what Kant calls finite synthesis. Henceforth, it’s only a question of words. In this perspective, at that point, we would say that they agree in order to establish a difference in nature, one of them between finite analysis and infinite analysis, the other between analysis and synthesis. It comes down to the same thing: what Leibniz calls infinite analysis, Kant will call finite synthesis.

You see the good sense idea that, simultaneously, a philosophical dispute is inextricable since we cannot decide who is right, and at the same time, knowing who is right is without any importance since they both say the same thing. Good sense can conclude just as well: the only good philosophy is me. Tragic situation. Because if good sense achieves the goals of philosophy, better than philosophy itself does it, then there is no reason to wear yourself out doing philosophy. So? Let’s look for a kind of bifurcation since this first great opposition between Leibniz and Kant, even if it now seems obvious too us, isn’t this because, in fact, this opposition moves well beyond itself toward a deeper opposition, and if we don’t see the deeper opposition, we can understand nothing. What would this second, deeper opposition be? We saw that there was a great Leibnizian proposition, called the principle of indiscernibles, notably that any difference, in the final instance, is conceptual. Any difference is in the concept. If two things differ, they cannot simply differ by number, by figure, by movement, but rather their concept must not be the same. Every difference is conceptual. See how this proposition is truly the presupposition of Leibniz’s preceding proposition. If he is right on this point, if every difference is conceptual, it is quite obvious that it’s by analyzing concepts that we know, since knowing is knowing through differences. Thus, if every difference, in the final instance, is conceptual, the analysis of the concept will make us know the difference, and will therefore cause us quite simply to know. We see into which quite advanced mathematical task this drew Leibniz, [a task] which consisted in showing the differences between figures, the differences between numbers, referring to differences in the concepts. Ok, what is Kant’s proposition in opposition to the second Leibnizian proposition? Here again, this is going to be pretty odd [un drôle de truc]. Kant maintains a very strange proposition: if you look closely at the world presented to you, you will see that it is composed of two sorts of irreducible determinations: you have conceptual determinations that always correspond to what a thing is, I can even say that a concept is the representation of what the thing is. You have determinations of this sort, for example, the lion is an animal that roars; that’s a conceptual determination. And then you have another kind of determination altogether. Kant proposes his great thing [son grand truc]: he says that it’s no longer conceptual determinations, but spatio-temporal determinations. What are these spatio-temporal determinations? It’s the fact that the thing is here and now, that it is to the right or to the left, that it occupies one kind of space or another, that it describes a space, that it lasts a certain time. And so, however far you push the analysis of concepts, you will never arrive at this domain of spatio-temporal determinations by analyzing concepts. Although you might push your analysis of the concept to infinity, you will never find a determination in the concept that takes this into account for you: that this thing is on the right or on the left.

What does he mean? He selects examples for himself that initially seem very convincing. Consider two hands. Everyone knows that two hands don’t have exactly the same traits, nor the same distribution of pores. In fact, there are no two hands that are identical. And this is a point for Leibniz: if there are two things, they must differ through the concept, it’s his principle of indiscernibles. Kant says that, in fact, it is indeed possible, but that’s not important. He says that it’s without interest. Discussions never pass through the true and the false, they pass through: does it have any interest whatsoever, or is it a platitude? A madman is not a question of fact, he’s also a question quid juris. It’s not someone who says things that are false. There are loads of mathematicians who completely invent absolutely crazy theories. Why are they crazy? Because they are false or contradictory? No, they are determined by the fact that they manipulate an enormous conceptual and mathematical apparatus [appareillage], for example, for propositions stripped of all interest. Kant would dare to tell Leibniz that what you are saying about the two hands with their different skin features [différences de pores] has no interest since you can conceive quid juris, in principle but not in fact, you can conceive of two hands belonging to the same person, having exactly the same distribution of pores, the same outline of traits. This is not logically contradictory, even if it does not exist in fact. But, says Kant, there is something nonetheless that is very odd: however far you push your analysis, these two hands are identical, but admire the fact that they cannot be superposed. You have your two absolutely identical hands, you cut them in order to have a radical degree of mobility. You cannot cause them to coincide; you cannot superpose them. Why? You cannot superpose them, says Kant, because there is a right and a left. They can be absolutely identical in everything else, there is still one that is the right hand and the other the left hand. That means that there is a spatial determination irreducible to the order of the concept. The concept of your two hands can be strictly identical, however far you push the analysis, there will still be one of them that is my right hand and one that is my left hand. You cannot cause them to be superposed. Under what condition can you cause two figures to be superposed? On the condition of having access to a dimension supplementary to that of the figures . . . It’s because there is a third dimension of space that you can cause two flat figures to be superposed. You could cause two volumes to be superposed if you have access to a fourth dimension. There is an irreducibility in the order of space. The same thing holds for time: there is an irreducibility in the order of time. Thus, however far you push the analysis of conceptual differences, an order of difference will always remain outside of the concepts and the conceptual differences. This will be spatio-temporal differences.

Does Kant again gain the stronger position? Let’s go back to the straight line. [Regarding] the idea of synthesis, we are going to recognize that it was not a matter of mere words for Leibniz. If we stopped at the analysis-synthesis difference, we didn’t have the means of finding [more]. We are in the process of discovering the extent to which this is something more than a matter of words. Kant is saying: as far as you go in your analysis, you will have an irreducible order of time and space, irreducible to the order of the concept. In other words, space and time are not concepts. There are two sorts of determinations: determinations of concepts and spatio-temporal determinations. What does Kant mean when he says that the straight line is the shortest path from one point to another, that it’s a synthetic proposition? What he means is this: [the] straight line is indeed a conceptual determination, but the shortest path from one point to another is not a conceptual determination, but a spatio-temporal determination. The two are irreducible. You will never be able to deduce one from the other. There is a synthesis between them. And what is knowing? Knowing is creating the synthesis of conceptual determinations and spatio-temporal determinations. And so he is in the process of tearing space and time from the concept, from the logical concept. Is it by chance that he himself will name this operation Aesthetics? Even on the most vulgar level of aesthetics, the best known word – the theory of art --, won’t this liberation of space and time in relation to logical concepts be the basis of any discipline called aesthetics? You see now how it is that, at this second level, Kant would define synthesis. He would say that synthesis is the act through which I leave behind all concepts in order to affirm something irreducible to concepts. Knowing is creating a synthesis because it necessarily means leaving behind all concepts in order to affirm something extra-conceptual in it. The straight line, concept, I leave it behind, it’s the shortest path from one point to another, a spatio-temporal, extra-conceptual determination. What is the difference between this second Kantian proposition and the first? Just admire the progress Kant made. Kant’s first definition – when he was saying that knowing means operating through synthesis – this is issuing synthetic propositions, Kant’s first proposition amounted to this: knowing means leaving behind a concept in order to affirm about it something that was not contained in it. But at this level, I could not know if he was right. Leibniz arrived and said that, in the name of an infinite analysis, what I affirm about a concept will always be contained in the concept. A second, deeper level: Kant no longer tells us that knowing means leaving a concept behind in order to affirm something that would be like another concept. Rather [he says that] knowing means leaving one concept in order to leave behind all concepts, and to affirm something about it that is irreducible to the order of the concept in general. This is a much more interesting proposition.

Yet again, they react [on rebondit]. Is this decidable? One of them tells us that every difference is conceptual in the last instance, and therefore you can affirm nothing about a concept that might go outside the order of the concept in general; the other one tells us that there are two kinds of differences, conceptual differences and spatio-temporal differences such that knowing necessarily means leaving behind the concept in order to affirm something about it that is irreducible to all concepts in general, specifically something that concerns space and time. At this point, we realize that we haven’t left all that behind because we realize that Kant, quietly – and he wasn’t obligated to say it, even since he could say it a hundred pages later – Kant can only maintain the proposition he just suggested about the irreducibility of spatio-temporal determinations in relation to conceptual determination, he can only affirm this irreducibility because he dealt a master stroke [coup de force]. For his proposition to make sense, he had to change radically the traditional definition of space and time. I hope that you are becoming more sensitive [to this]. He gives a completely innovative determination of space and time. What does that mean? We arrive at a third level of the Kant-Leibniz opposition. This opposition is stripped of any interest if we do not see that the Leibnizian propositions and the Kantian propositions are distributed in two completely different space-times. In other words, it’s not even the same space-time about which Leibniz said: all of these determinations of space and time are reducible to conceptual determinations; and this other one about which Kant told us that the determinations [of space-time] are absolutely irreducible to the order of the concept. This is what we have to show in a simple way; take note that this is a moment in which thought reels. For a very, very long time, space was defined as, to some extent, the order of coexistences, or the order of simultaneities. And time was defined as the order of successions. So, is it by chance that Leibniz is the one who pushes this very ancient conception to its limit, all the way to a kind of absolute formulation? Leibniz adds and states it formally: space is the order of possible coexistences and time is the order of possible successions. By adding “possible,” why does he push this to the absolute? Because it refers to his theory of compossibility and of the world. Thus, he captures in this way the old conception of space and time, and he uses it for his own system. At first glance, that seems rather good. In fact, it’s always delicate when someone tells me: define space, define time; if I don’t say by reflex that space is the order of successions and space is the order of coexistences, at least that’s something [c’est quand même un petit quelque chose]. What bothers Kant can be found in his most beautiful pages. He says: but not at all. Kant says that this just won’t do, he says that, on the one hand, I cannot define space as the order of coexistences, on the other hand, I cannot define time as the order of successions. Why? Because “coexistences,” after all, belong to time. Coexistence means, literally, at the same time. In other words, it’s a modality of time. Time is a form in which occur not only that which succeeds something, but also that which is at the same time. In other words, coexistence or simultaneity is a modality of time. At some far distant date when there will be a famous theory called the theory of simultaneity, of which one of the fundamental aspects will be to think simultaneity in terms of time, I don’t at all say that Kant invented relativity, but that such a formula, particularly what we already found comprehensible in it, would not have had this comprehensible element if Kant hadn’t been there centuries before. Kant is the first one to tell us that simultaneity does not belong to space, but belongs to time.

This is already a revolution in the order of concepts. In other words, Kant will say that time has three modalities: what lasts through it is called permanence; what follows after something else within it is called succession; and what coexists within it is called simultaneity of coexistence. I cannot define time through the order of successions since succession is only a modality of time, and I have no reason to privilege this modality over the others. And another conclusion at the same time: I cannot define space through the order of coexistences since coexistence does not belong to space. If Kant had maintained the classical definition of time and space, order of coexistences and of successions, he couldn’t have, or at least there wouldn’t have been any interest in doing so, he couldn’t have criticized Leibniz since if I define space through the order of coexistences and time through the order of successions, it goes without saying, whereas space and time refer in the last instance to that which follows something else and to that which coexists, that is, to something that one can enunciate within the order of the concept. There is no longer any difference between spatio-temporal differences and conceptual differences. In fact, the order of successions receives its raison d’être from that which follows, the order of coexistences receives it raison d’être from that which coexists. At that point, it’s conceptual difference that is the last word, on all differences. Kant couldn’t break with classical concepts, pushed to the absolute by Leibniz, if he didn’t propose to us another conception of space and time. This conception is the most unusual and the most familiar. What is space? Space is a form. That means that it’s not a substance and that it does not refer to substances. When I say that space is the order of possible coexistences, the order of possible coexistences is clarified in the last instance by things that coexist. In other words, the spatial order must find its reason in the order of things that fill space. When Kant says that space is a form, that is, is not a substance, that means that it does not refer to things that fill it. It’s a form, and how must we define it? He tells us that it’s the form of exteriority. It’s the form through which everything that is exterior to us reaches us, OK, but that’s not all it is; it’s also the form through which everything that is exterior to itself occurs. In this, he can again jump back into tradition. Tradition had always defined space as partes extra partes, one part of space is exterior to another part. But here we find that Kant takes what was only a characteristic of space in order to make it the essence of space. Space is the form of exteriority, that is the form through which what is exterior to us reaches us, and through which what remains exterior to itself occurs. If there were no space, there would be no exteriority.

Let’s jump to time. Kant is going to provide the symmetrical definition, he hits us with time as form of interiority. What does that mean? First, that time is the form of that which happens to us as interior, interior to ourselves. But it does not mean only that. Things are in time, which implies that they have an interiority. Time is the way in which the thing is interior to itself. If we jump and if we make some connections [rapprochements], much later there will be philosophies of time, and much later time will become the principal problem of philosophy. For a long time, things were not like that. If you take classical philosophy, certainly there are philosophies greatly interested in the problem of time, and they appeared unusual. Why are the so-called “unforgettable” pages on time by Saint Augustine always shown to us? The principal problem of classical philosophy is the problem of extension [étendue], and notably what the relation is between thought and extension, once it is said that thought is not part of extension. And it is well known that so-called classical philosophy attaches a great importance to the corresponding problem, the union of thought and extension, in the particular relation of the union of soul and body. It is therefore the relation of thought to that which appears most opaque to thought, specifically extension [l’étendue]. In some ways, some people find the source of modern philosophy in a kind of change of problematic, in which thought commences to confront time and no longer extension. The problem of the relationship between thought and time has never ceased to cause difficulties for philosophy, as if the real thing that philosophy confronted was the form of time and not the form of space. Kant created this kind of revolution: he ripped space and time from the order of the concept because he gave two absolutely new determinations of space and time: the form of exteriority and the form of interiority. Leibniz is the end of the seventeenth century, start of the eighteenth, while Kant is the eighteenth century. There is not much time between them. So what happened? We must see how everything intervenes: scientific mutations, so-called Newtonian science, political events. We cannot accept that when there was such a change in the order of concepts that nothing happened in the social order. Among other things, the French revolution occurred. Whether it implied another space-time, we don’t know. Mutations occurred in daily life. Let us say that the order of philosophical concepts expressed it [the revolution] in its own way, even if [this order] comes beforehand.

Yet again, we have started from an initial Leibniz-Kant opposition, and we have said that it is undecidable. I cannot decide between the proposition “every proposition is analytical,” and the other proposition in which knowledge proceeds by synthetic propositions. We had to step back. First step back, I have again two antithetical propositions: every determination is conceptual in the last instance, and the Kantian proposition: there are spatio-temporal determinations that are irreducible to the order of the concept. We had to step back again in order to discover a kind of presupposition, notably [that] the Leibniz-Kant opposition is valid only to the extent that we consider that space and time are not at all defined in the same way. It’s odd, this idea that space is that which opens us to an outside; never would someone from the Classical period have said that. It is already an existential relationship with space. Space is the form of what comes to us from outside.

If, for example, I look for the relationship between poetry and philosophy, what does that imply? It implies an open space. If you define space as a milieu of exteriority, it is an open space, not an enclosed space [espace bouclé]. Leibnizian space is an enclosed space, the order of coexistences. Kant’s form is a form that open us up, opens us to an x, it is the form of eruptions. It is already a Romantic space. It is an aesthetic space since it is emancipated from the logical order of the concept. It is a Romantic space because it is the space of overflows. It is the space of the open [l’ouvert]. And when you see in works of certain philosophers who came much later, like Heidegger, a kind of grand song on the theme of the open, you will see that Heidegger calls on Rilke who himself owes this notion of the Open to German Romanticism. You will better understand why Heidegger feels the need to write a book about Kant. He will deeply valorize the theme of the Open. At the same time, poets are inventing it as a rhythmic value or aesthetic value. At the same time, researchers are inventing it as a scientific species.

At this point of my thinking about it, it is very difficult to say who is right and who is wrong. One might like to say that Kant corresponds better to us, goes better with our way of being in space, space as my form of opening. Can we say that Leibniz has been left behind? It is not that simple. A fourth point. It is perhaps at the farthest extreme of what is new that, in philosophy, occurs what we call the return to [le retour à]. After all, it is never up to an author to push himself as far as he can. It is not Kant who is going as far as is possible for Kant; there will always be post-Kantians who are the great philosophers of German Romanticism. They are the ones who, having pushed Kant as far as possible, experience this strange thing: making a return to Leibniz. [end of the tape] ... I am looking for the deep changes that Kantian philosophy was to bring about both in relation to so-called Classical philosophy and in relation to the philosophy of Leibniz. We have seen a first change concerning space-time. There is a second change, this time concerning the concept of the phenomenon. You are going to see why one results from the other. For quite a long time, the phenomenon was opposed to what, and what did it mean? Very often phenomenon is translated as appearance, appearances. And appearances, let’s say that it is the sensible [le sensible]. The sensible appearance. And appearance is distinguished from what? It forms a doublet, a couple with the correlative of essence. Appearance is opposed to essence. And Platonism will develop a duality of appearance and essence, sensible appearances and intelligible essences. A famous conception results from this: the conception of two worlds. Are there two worlds, the sensible world and the intelligible world? Are we prisoners, through our senses and through our bodies, of a world of appearances? Kant uses the word “phenomenon,” and the reader gets the impression that when he [the reader] tries to situate the old notion of appearances under the Kantian word, it doesn’t work. Isn’t there going to be as important a revolution as for time and space, on the level of the phenomenon? When Kant uses the word “phenomenon,” he loads it with a much more violent meaning: it is not appearance that separates us from essence, it is apparition, that which appears insofar as it appears. The phenomenon in Kant’s work is not appearance, but apparition. Apparition is the manifestation of that which appears insofar as it appears. Why is it immediately linked to the preceding revolution? Because when I say that what appears insofar as it appears, what does the “insofar” [en tant que] mean? It means that that which appears does so necessarily in space and time. This is immediately united to the preceding theses. Phenomenon means: that which appears in space and in time. It no longer means sensible appearance, it means spatio-temporal apparition. What reveals the extent to which this is not the same thing? If I look for the doublet with which apparition is in relation. We have seen that appearance is related to essence, to the point that there are perhaps two worlds, the world of appearances and the world of essences. But apparition is related to what? Apparition is in relation to condition. Something that appears, appears under conditions that are the conditions of its apparition. Conditions are the making-appear of apparition. These are the conditions according to which what appears, appears. Apparition refers to the conditions of the apparition, just as appearance refers to essence. Others will say that apparition refers to meaning [sens]. The doublet is: apparition and meaning of the apparition. Phenomenon is no longer thought as an appearance in relation to its essence, but as an apparition in relation to its condition or its meaning. Yet another thunderclap: there is no longer only one world constituted by that which appears and the meaning of that which appears. What appears no longer refers to essences that would be behind the appearance; that which appears refers to conditions that condition the apparition of what appears. Essence yields to meaning. The concept is no longer the essence of the thing, it is the meaning of the apparition. Understand that this is an entirely new concept in philosophy from which will unfold philosophy’s determination under the name of a new discipline, that of phenomenology. Phenomenology will be the discipline that considers phenomena as apparitions, referring to conditions or to a meaning, instead of considering them as appearances referring to essences. Phenomenology will take as much meaning as you want, but it will at least have this unity, specifically its first great moment will be with Kant who pretends to undertake a phenomenology, precisely because he changes the concept of the phenomenon, making it the object of a phenomenology instead of the object of a discipline of appearances. The first great moment in which phenomenology will be developed as an autonomous discipline will be in Hegel’s famous text, Phenomenology of Spirit. And the word is very peculiar. The Phenomenology of Spirit being precisely the great book that announces the disappearance of the two worlds, there is no more than a single world. Hegel’s formula is: behind the curtain, there is nothing to see. Philosophically that means that the phenomenon is not a mere appearance behind which an essence is located; the phenomenon is an apparition that refers to the conditions of its apparition. There is but one single world. That is the moment when philosophy breaks its final links to theology. Phenomenology’s second moment will be the one in which Husserl renews phenomenology through a theory of apparition and meaning. He will invent a form of logic proper to phenomenology. Things are obviously more complex than that.

I will offer you an extremely simple schema. Kant is the one who broke with the simple opposition between appearance and essence in order to establish a correlation [between] the apparition and conditions of apparition, or apparition-meaning [apparition-sens]. But separating oneself from something is very difficult. Kant preserves something from the former opposition. In Kant, there is a strange thing, the distinction between the phenomenon and the thing in itself. Phenomenon-thing in itself, for Kant, preserves something from the former apparition. But the really innovative aspect of Kant is the conversion of another set of notions, apparition-conditions of the apparition. And the thing in itself is not at all a condition of apparition, but something completely different. And a second correction is this: from Plato to Leibniz, we were not simply told that there are appearances and essences. Moreover, already with Plato there appears a very curious notion that he calls well-founded appearance, that is, essence is hidden from us, but in some ways, appearance expresses it as well. The relation between appearance and essence is a very complex one that Leibniz will try to push in a very strange direction, specifically: he will create from it a theory of symbolization. The Leibnizian theory of symbolization quite singularly prepares the Kantian revolution. The phenomenon symbolizes with essence. This relation of symbolization is no longer that of appearance with essence.

I am trying to continue: there occurs a new disturbance at the level of the conception of the phenomenon. You will see just how it immediately links up with the disturbance of space-time. Finally there is a fundamental disturbance at the level of subjectivity. There again it’s a strange story. When does this notion of subjectivity take off? Leibniz pushes the presuppositions of classical philosophy as far as he can, down the paths of genius and delirium. From a perspective like that of Leibniz, one really has very little choice. These are philosophies of creation. What does a philosophy of creation mean? These are philosophies that have maintained a certain alliance with theology, to the point that even atheists, if indeed they are that, will pass by way of God. Obviously, that does not take place on the level of the word. As a result of this alliance that they have with theology, they pass by way of God to some extent. That is, their point of view is fundamentally creationist. And even philosophers who do something other than creationism, that is, who are not interested or who replace the concept of creation with something else, they fight against creation according to the concept of creation. In all cases, the point that they start from is infinity. Philosophers have an innocent way of thinking starting from infinity, and they give themselves to infinity. There was infinity everywhere, in God and in the world. That let them undertake things like infinitesimal analysis. An innocent way of thinking starting from infinity means a world of creation. They could go quite far, but not all the way. Subjectivity. To move in this direction, a completely different aggregate was necessary. Why couldn’t they go all the way toward a discovery of subjectivity? Still they went very far.

Descartes invents his own concept, the famous “I think, therefore I am,” notably the discovery of subjectivity or the thinking subject. The discovery that thought refers to a subject. A Greek would not even have understood what was being said with the idea of a thinking subject. Leibniz will not forget it, for there is a Leibnizian subjectivity. And generally we define modern philosophy with the discovery of subjectivity. They could not go all the way through this discovery of subjectivity for a very simple reason: however far they might go in their explorations, this subjectivity can only be posited as created, precisely because they have an innocent way of thinking starting from infinity. The thinking subject, insofar as the finite subject can be thought of as created, created by God. Thought referring to the subject can only be thought as created: what does that mean? It means that the thinking subject is substance, is a thing. Res. It is not an extended thing, as Descartes says it’s a thinking thing. It is an unextended thing, but it is a thing, a substance, and it has the status of created things, it is a created thing, a created substance. Does that block them? You will tell me that it’s not difficult, they had only to put the thinking subject in the place of God, no interest in exchanging places. In that event, one has to speak of an infinite thinking subject in relation to which finite thinking subjects would themselves be created substances. Nothing would be gained. Thus, their strength, specifically this innocent way of thinking according to infinity, leads them to the threshold of subjectivity and prevents them from crossing through.

What does Kant’s rupture with Descartes consist in? What is the difference between the Kantian cogito and the Cartesian cogito? For Kant, the thinking subject is not a substance, not determined as a thinking thing. It is going to be pure form, form of the apparition of everything that appears. In other words, it is the condition of apparition of all that appears in space and in time. Yet another thunderclap. Kant undertakes to find a new relation of thought with space and time. Pure form, empty form, there Kant becomes splendid. He goes so far as to say of the “I think” that it is the poorest thought. Only, it is the condition of any thought about any one thing. “I think” is the condition of all thought about any one thing that appears in space and in time, but itself is an empty form that conditions every apparition. That becomes a severe world, a desert world. The desert grows. What has disappeared is the world inhabited by the divine, the infinite, and it became the world of men. What disappeared is the problem of creation, replaced by an completely different problem that will be the problem of Romanticism, specifically the problem of founding [fondement]. The problem of founding or of foundation [fondation]. Now there arises a clever thought, puritanical, desert-like, that wonders, once it’s admitted that the world exists and that it appears, how to found it? The question of creation has been rejected, but now the problem of founding arrives. If there is really a philosopher who spoke the discourse of God, it was Leibniz. Now the model philosopher has become the hero, the founding hero. He is the one who founds within an existing world, not the one who creates the world. What is foundational [fondateur] is that which conditions the condition of what appears in space and in time. Everything is linked there. A change in the notion of space-time, a change in the notion of the subject. The thinking subject as pure form will only be the act of founding the world such as it appears and knowledge of the world such as it appears. This is an entirely new undertaking.

A year ago, I tried to distinguish the Classical artist from the Romantic artist. The Classical and the Baroque are two poles of the same enterprise. I was saying that the Classical artist is one who organized milieus and who, to some extent, is in the situation of God, this is creation. The Classical artist never stops undertaking creation anew, by organizing milieus, and never ceases to pass from one milieu to another. He passes from water to earth, he separates the earth and the waters, exactly God’s task in creation. He poses a kind of challenge to God: they are going to do just as much, and that is what the Classical artist is. The Romantic at first glance would be less crazy; his problem is that of founding. It is no longer the problem of the world, but one of the earth. It is no longer the problem of milieu, but one of territory. To leave one’s territory in order to find the center of the earth, that’s what founding is. The Romantic artist renounced creating because there is a much more heroic task, and this heroic task is foundation. It is no longer creation and milieu; it’s: I am leaving my territory. Empedocles. The founding is in the bottomless [Le fondement est dans le sans fond]. All post-Kantian philosophy from Schelling on will arise around this kind of abundant concept or the bottom, the fundament founding, the bottomless. That is always what the lied is, the tracing of a territory haunted by the hero, and the hero leaves, departs for the center of the earth, he deserts. The song of the earth. Mahler. The opposition maintained between the tune about the territory and the song of the earth.

The musical doublet territory-earth corresponds exactly to what in philosophy is the phenomenon apparition and the condition of apparition. Why do they abandon the point of view of creation? Why is the hero not someone who creates, but someone who founds, and why isn’t it the final word? If there were a moment in which Western thought was a bit tired of taking itself for God and of thinking in terms of creation, the seed must be here. Does the image of heroic thought suit us still? All that is finished. Understand the enormous importance of this substitution of the form of the ego [forme du moi] by the thinking subject. The thinking substance was still the point of view of God, it’s a finite substance, but created according to the infinite, created by God. Whereas when Kant tells us that the thinking subject is not a thing, he well understands a created thing, a form that conditions the apparition of all that appears in space and in time, that is, it is the form of founding. What is he in the process of doing? He institutes the finite ego [le moi fini] as first principle. Doing that is frightening. Kant’s history depends greatly on the reform. The finite ego is the true founding. Thus the first principle becomes finitude. For the Classics, finitude is a consequence, the limitation of something infinite. The created world is finite, the Classics tell us, because it is limited. The finite ego founds the world and knowledge of the world because the finite ego is itself the constitutive founding of what appears. In other words, it is finitude that is the founding of the world. The relations of the infinite to the finite shift completely. The finite will no longer be a limitation of the infinite; rather, the infinite will be an overcoming [dépassement] of the finite. Moreover, it is a property of the finite to surpass and go beyond itself. The notion of self-overcoming [auto-dépassement] begins to be developed in philosophy. It will traverse all of Hegel and will reach into Nietzsche. The infinite is no longer separable from an act of overcoming finitude because only finitude can overcome itself. Everything called dialectic and the operation of the infinite to be transformed therein, the infinite becoming and become the act through which finitude overcomes itself by constituting or by founding the world. In that way, the infinite is subordinated to the act of the finite. What results from this? Fichte has an exemplary page for the Kantian polemic with Leibniz. Here is what Fichte tells us: I can say A is A, but this is only a hypothetical proposition. Why? Because it presupposes “if there is A.” If A is, A is A, but if there is nothing, A is not A. This is very interesting because he is in the act of overthrowing the principle of identity. He says that the principle of identity is a hypothetical rule. Hence he launches his great theme: to overcome hypothetical judgment to go toward what he calls “thetic” judgment (le jugement thétique]. To go beyond hypothesis toward thesis. Why is it that A is A, if A does exist because finally the proposition A is A is not at all a final principle or a first principle? It refers to something deeper, specifically that one must say that A is A because it is thought. Specifically, what founds the identity of things that are thought is the identity of the thinking subject. Moreover, the identity of the thinking subject is the identity of the finite ego. Thus the first principle is not that A is A, but that ego equals ego. German philosophy will encumber its books with the magic formula: ego equals ego. Why is this formula so bizarre? It is a synthetic identity because ego equals ego marks the identity of the ego that thinks itself as the condition of all that appears in space and in time, and [illegible] that appears in space and in time itself. In this there is a synthesis that is the synthesis of finitude, notably the thinking subject, primary ego, form of all that appears in space and time, must also appear in space and in time, that is ego equals ego. Hence the synthetic identity of the finite ego replaces the infinite analytic identity of God.

I will finish with two things: what could it mean to be Leibnizian today? It’s that Kant absolutely created a kind of radically new conceptual aggregate. These are completely new philosophical conceptual coordinates. But in the case of these new coordinates, Kant in one sense renews everything, but there are all sorts of things that are not elucidated in what he proposes. An example: what exact relation is there between the condition of the phenomenon itself insofar as it appears? I will review: The thinking ego, the finite ego, conditions, founds the phenomenal apparition. The phenomenon appears in space and in time. How is this possible? What does this relation of conditioning mean? In other words, the “I think” is a form of knowledge that conditions the apparition of all that appears. How is this possible, what is the relation between the conditioned and the condition? The condition is the form of “I think.” Kant is quite annoyed. He says that this is a fact of reason, he who had so demanded that the question be elevated to the state quid juris, now he invokes what he himself call a factum: the finite ego is so constituted that what appears for it, what appears to it, conforms to the conditions of the apparition such that its very own thought determines it. Kant will say that this agreement of the conditioned and the condition can only be explained by a harmony of our faculties, specifically our passive sensibility and our active thought. What Kant does is pathetic; he is in the process of sneaking God in behind our backs. What guarantees this harmony? He will say it himself: the idea of God. What will the post-Kantians do? They are philosophers who say above all that Kant is inspired [genial], but still, we cannot remain in an exterior relation of the condition and conditioned because if we remain in this relation of fact, specifically that there is a harmony between the conditioned and the condition and that’s that, then we are obliged to resuscitate God as a guarantee of harmony. Kant still remains in a viewpoint which is that of exterior conditioning, yet he does not reach a true viewpoint of genesis. It would require showing how conditions of apparition are at the same time genetic elements of what appears. What is necessary to show that? One has to take seriously one of the Kantian revolutions that Kant left aside, notably that the infinite is truly the act of finitude insofar as it overcomes itself. Kant had left that aside because he was content with a reduction of the infinite to the indefinite. To return to a strong conception of the infinite, but in the manner of the Classics, one has to show that the infinite is an infinite in the strong sense, but as such, it is the act of finitude insofar as it overcomes itself, and in so doing, it constitutes the world of apparitions. This is to substitute the viewpoint of genesis for the viewpoint of the condition. Moreover, doing that means returning to Leibniz, but on bases other than Leibniz’s. All the elements to create a genesis such as the post-Kantians demand it, all the elements are virtually in Leibniz. The idea of a differential of consciousness, at that point the “I think” of consciousness must bathe in an unconscious, and there must be an unconscious of thought as such. The Classics would have said that there is only God who goes beyond thought. Kant would say that there is thought as a form of the finite ego. In this, one must almost summon an unconscious to thought that would contain the differentials of what appears in thought. In other words, which performs the genesis of the conditioned as a function of the condition. That will be Fichte’s great task, taken up again by Hegel on other bases.

You see henceforth that at the limit, they can rediscover all of Leibniz. And us? A lot has taken place. So I define philosophy as an activity that consists in creating concepts. To create concepts is as creative as art. But like all things, the creation of concepts occurs in correspondence with other modes of creation. In which sense [do] we need concepts? It’s a material existence, and concepts are spiritual animals [bêtes spirituelles). How do these kinds of appeals to concepts occur? The old concepts will serve, provided that they are taken up within new conceptual coordinates. There is a philosophical sensibility which is the art of evaluating the consistency of an aggregate of concepts. Does it work? How does it function? Philosophy does not have a history separate from the rest. Nothing, never is anyone overcome [dépassé]. We are never left behind in what we create. We are always left behind in what we do not create, by definition. What happened in our contemporary philosophy? I believe that the philosopher ceased taking himself for a founding hero, in the Romantic manner. What was fundamental in what we can call, generally, our modernity, was this kind of bankruptcy of Romanticism in our estimation. Hölderlin and Novalis no longer work for us and only work for us within the framework of new coordinates. We are finished taking ourselves for heroes. The model of the philosopher and artist is no longer God at all insofar as he [or she] proposes to create the equivalent of a world. This is no longer the hero insofar as he [or she] proposes to found a world, for it has become something else. There is a small text by Paul Klee in which he tries to say how he sees his own difference even from earlier painters. One can no longer go towards the motif. There is a kind of continuous flow, and this flow has twists and turns. Then the flow no longer passes in that direction. The coordinates of painting have changed.

Leibniz is infinite analysis, Kant is the grand synthesis of finitude. Assuming that today we are in the age of the synthesizer, that is something else entirely.

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