## Sur Leibniz

Cours Vincennes - St Denis
Cours du 06/05/1980
Charles J. Stivale, cstival@cms.cc.wayne.edu

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).