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The Graph of Desire

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The 'graph of desire' is one of the principal points of reference in Lacanian psychoanalysis. In this book the graph is analyzed in its multiple aspects and relations. Step by step, the author reveals and considers formulations from the simplest to the most complex. The treatment of this issue does not deal only with the development and explanation of its logical, mathematical and topological aspects but also goes through the psychoanalytical theory and practice. The author has immersed himself in Lacan's text "The Subversion of the Subject and the Dialectic of Desire in the Freudian Unconscious" to uncover and bring this fascinating subject to light.

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CHAPTER ONE: Graph of desire and topology

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Ishall dedicate this class to the introduction of the subject of the course, beginning with some points that we will need to master if we want to benefit from what Lacan proposes through the graph of desire.1

In Lacan’s teaching, the series built with models, schemata, graphs, topologic surfaces and knots takes an exclusive place and significance. There is no other psychoanalyst who has given such importance, given so much time and consideration to this problem of representations in psychoanalysis. This seems to be however very reasonable, taking into account that Lacan was the psychoanalyst who, more than anyone, studied and developed a theory of the representation of the human being.2

Within that series, graphs represent the first systematic inclusion of topology into psychoanalysis. I am careful and I say “the first‘systematic’ inclusion of topology” because, strictly speaking, there are topological issues already involved in the models and schemata; but systematically speaking, the graph of desire constitutes the first entrance of topology in Lacan’s teaching. This point has not been evident and it will be clarified and developed in later chapters.I will start with a very important historical issue which can be related to a structural dimension: the first study on graphs was carried out by Euler (1707–1783), one of the most prolific mathematicians in history; that study on graphs by Euler is the basis of topology. This means that topology not only enters psychoanalysis via the graphs, but it enters mathematics by the same route.

 

CHAPTER TWO: Object a and mathematical graph and nets theory

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Today we will refer specifically to the object a. The first thing to be considered when we say “object a” is that it fulfils the same function as the value “x” in mathematics: it is an unknown variable.

The letter “a” corresponds to an algebraic maneuver, according a name to something that cannot be said. That is why it is hard to tell you what I am going to talk about today; for you to know I must start talking. That is the reason why it is called object a, without any attribute or value, just object a.

There are several dimensions of the object a. I believe it is convenient (I am not saying it is necessary) to distinguish at least three dimensions of the object a: spatial, temporal and logical.

Strictly speaking, these are artificial cuts with regards to the notion of the object a; they allow us to see more clearly from which perspective we are facing the problem. There is no possibility of working on the spatial dimension of the object a without considering the other two dimensions, and vice versa.

 

CHAPTER THREE: The structure of language: Need, demand and desire

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We shall work today on the articulation between linguistics and psychoanalysis. In order to elaborate that articulation I shall profusely quote “The subversion of the subject and the dialectic of desire in the Freudian unconscious”. This writing by Lacan will be, from now on, our main reference.

My work today will turn around two categorical statements by Lacan; we will make use of them for progressing in relation to the point we reached last week. The first statement says that “the unconscious is structured like a language” and the second one that “since Freud the unconscious has been a chain of signifiers that somewhere (on another stage, in another scene, he says) is repeated, and insists on interfering in the breaks offered by the effective discourse and the cogitation that it informs”.1

As the structure of the “graph of desire” is supported by those two phrases, we will advance considerably today in its investigation. From next class on we will introduce clinical articulations. We have been working on the structural foundations, and this will allow the clinical articulations to be more that mere clinical descriptions.In both quotations Lacan affirms that the signifier is a fundamental notion. In “The subversion of the subject …” he says that “signifier” is a word that modern linguistics borrowed from ancient rhetoric. Lacan proposes to limit that modern linguistic: he call the inferior level “the dawn of modern linguistics” and he refers it to Ferdinand de Saussure. And he calls the superior level “modern linguistics’ culminating point”, referencing Roman Jakobson. What we do not know is whether Jakobson’s work will continue to be this culminating point, or whether it will have to be changed with the passage of time. You know that when the superior level is changed and for reasons that are intrinsic to the theory of the signifier, the inferior level might have to be changed too. Anyhow, it was like this for Lacan, in Lacan’s times.

 

CHAPTER FOUR: Graph one

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Today’s subject is graph number one. In order to exhaustively work on the graph we are going to articulate it with the following quotation from “Subversion of the subject …”, with which we ended last class:

“[…] It is precisely because desire is articulated that it is not articulable” (p. 335).

The fact that desire is not articulable may be clear to us because we already worked on the idea of desire being that effect of the demand that demand itself cannot recapture. Necessarily, desire will always imply a field that is beyond any demand. This justifies the fact that in the analytic practice with neurotics it is not possible for desire not to be there. Lacan is particularly subtle when he states that, regarding desire’s rejection, a neurotic subject can only go as far as “to desire not to desire”. We call desire then, the structural effect of demand over need, which is not recoverable through demand, but which has to be distinguished from any “I desire x object”.

We must keep in mind that in lacanian algebra, “demand” is written with a capital D, and “desire” with a small d. If you pay attentionXT to the logic according to which Lacan distributes small and capital letters (at least at the beginning of his teaching), you will find a surprise. When referring to the Symbolic, Lacan uses upper-case letters, and he uses lower-case letters when referring to the Imaginary (cf. for instance schema Lambda in Seminar 2).

 

CHAPTER FIVE: Questions and answers: The impossible-neurosis and psychosis

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Ishall begin with some questions or issues posed by you. The first question I was asked by one of you was about the type of relation existing between “absolute condition” and “unconditional”, for both terms are linked to desire and demand respectively.

The terms “absolute condition” and “unconditional” account for the relation between the terms “need-demand-desire” themselves. The problem with this triad is that for one of its terms, need, the subject is mythic. That is why, as we advance and in order to be more precise from a psychoanalytic perspective, we will substitute the triad need-demand-desire with jouissance-demand-desire. We could say that we are now in a mid-point in our way towards that substitution.

We have to be able, with the triad “need-demand-desire”, to make an equivalent maneuver to that which exists in Freudian topography. This implies that each of its elements acquires the status of a topos, a non-metric place—that is, a place defined by its position in relation to the others, and not by its autonomous placement in relation to any measure scale whatsoever. Thus, demand is for instance,between need and desire; demand breaks the continuity need-desire and introduces the structural discontinuity in that trio. And if demand produces such an effect due to being “between”, what has to be considered then are the relations between need and demand on one hand (unconditional) and the relation between demand and desire, on the other (absolute condition).

 

CHAPTER SIX: Ideal (I)-ego (m)-ideal (i): Graph 2

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Today we shall work on the articulation between the ego Ideal and the Ideal ego considering how Lacan elaborated these notions in relation to the notion of the Other. In order to do that we shall analyze some paragraphs from “Subversion of the subject …” in which Lacan presents the logic of graph 2.

Observe, in parentheses, that this Other, which is distinguished as the locus of Speech,1 imposes itself no less at witness to the Truth (p. 337).

The Other, then, is not only the locus of Speech; it is also witness to the Truth.

At this stage in our pathway, it would be convenient for us to apply the notion of‘signifier’, as we have developed it, to the signifiers of psychoanalysis. And although they require a conceptual structure, that is, a precise system of articulation, which we are allowed to elaborate within transmission, we should not forget that because these concepts are sustained by signifiers, they structurally imply ambiguity. I say this because a new way of understanding the Other results, precisely,from Lacan changing the context of this notion. We are considering the Other as a signifier—which it is—and therefore, it will only derive its signification from the other signifiers from which it differentiates itself in each case. And those other signifiers, within diachrony and synchrony, are the context of the notion that it is at issue. The Other will be locus of Speech or the witness to the Truth, or something else, according to the context that is chosen to define its meaning.

 

CHAPTER SEVEN: Graph 3: The question

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In this chapter we shall see how to get out, in the neuroses, of the infernal circle of demand, meaning by it the repetition effect of demand as such.

To begin our consideration of this problem we will make use of graph 3 of the graph of desire.

Perhaps it is better to pose the problem, regarding the direction of the cure,1 as follows: how does one access the new?

This is, in my view, one of the kernels of the psychoanalytical question. According to Freud, the absolutely new is not possible for the human being; and because structurally this possibility does not exist, it does not exist by means of psychoanalysis either. The ideal end at which an analysis may arrive, according to Freud, is the limit of castration anguish2 for men and penis envy for women.

What I am trying to introduce here, is the idea that graph 3 gives us a first elaboration which allows us to conceive the possibility of the absolutely new for the human being (obviously, within the field of neuroses). And also from this graph we will deduce how to operate in the direction of the cure in order to achieve this.

 

CHAPTER EIGHT: Desire and fantasme: A pathway (I)-the symptom

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While preparing this class the first thing I concluded was: to give a class on the fantasme1 makes no sense. It is completely incoherent to say that one is going to give a class on the fantasme. But after that I realized that is also impossible to give a class on the desire, for similar impossibilities appear. If one wants to give a class on desire and fantasme then, it would be necessary to articulate them; that is, to talk about the articulation between desire and fantasme. So we will approach the theme: desire and fantasme, emphasizing the “and”. I propose to add to that title an indication that will organize our work: the idea of a pathway or (as Freud would put it): a way. So we will begin this class, number 8, by entitling it: Desire and fantasme: a pathway.

I believe what I just said is clearly articulated by Lacan in his graph, for what characterizes graph 3 is the simultaneous, articulated entrance of desire (d), the question Che vuoi? and the fantasme (◊a).

The idea is thus that the question of desire and fantasme cannot be worked on or worked through except via a certain route, a certain diachrony. Actually, the entire graph supposes the idea of apathway; this is expressed by the fact that it is an oriented graph. Its edges have an orientation, a direction. Thus, the graph of desire inscribes the logic of the discourse “ways”, and that of the “defiles” of the signifier. In turn, I shall also posit “a pathway” in order to approach in this class, the pathway from fantasme to desire.

 

CHAPTER NINE: Desire and fantasme: A pathway (II)

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According to Lacan, the fundamental idea that reveals the nature of the relationship between desire and fantasme is that the neurotic expects desire to become “I desire this”, and the fantasme’s maneuver has to do with this purpose. There is no neurotic subject (as such) able to go beyond the question posed to the Other (which is in turn an answer to the Other’s question: “Che vuoi?”): “What do you want of me? It is a structural limitation.

Through the formula “What do you want of me?”, Lacan is telling us two things: first of all, that desire does not belong to the subject, it is not “the subject’s”. And secondly, that in so far as the subject is desired by the Other (since the desire of the Other is also unconscious) “it (the Other) does not know it”. The Other “does not know” what the subject is for it. And if the Other does not know it, the subject is most unlikely to know it.

In the human world—as it is established for the neurotic subject— desire, as a psychoanalytical concept, inscribes the function of lack both at the level of the desiring subject and at that of the desired object.

 

CHAPTER TEN: The formula of the fantasme: Introduction to the drive

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Today we shall reconsider some aspects of desire and the fan-tasme. Afterwards we shall approach the notion of the drive. The fact that we posit that there are no types of desire does not imply that no sort of attribution may be given with regard to desire. It is not that nothing can be said about desire; it is not that desire is by itself ineffable.

If I had to choose the most structural attributes of desire, those able to circumscribe it theoretically, within the logic of the case by case, I would propose two: desire is indestructible and desire is unconscious. For every case it can be posited that desire is indestructible and unconscious, whereas “prevented”, “impossible”, “unsatisfied”, etc., are reserved in order to account for the different clinical structures.

If desire is the field, which, as an abyss, is opened up (that is why it implies anguish) beyond any demand for which the function of the limit operates (psychosis is therefore excluded), then it [desire] is indestructible. Therefore, there is no demand that does not carry its “beyond”, and the neurotic subject will not be able, when refusing itsown desire, to go beyond “to desire not to desire”. It is unconscious because there is no demand able to say, to know, about desire. The dialectic between demand and desire always supposes, as we have seen, this “beyond”. This is what Lacan’s phrase teaches us: “to put it elliptically: it is precisely because desire is articulated that it is not articulable”, which we commented on in Chapter Four.

 

CHAPTER ELEVEN: The drive (I)

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In order to continue working on the notion of the drive, as Lacan does in his Seminar 11, I think it is very convenient to depart from the following question: what is Seminar 11 about? It seems to me that the function of this seminar is not clear yet. Seminar 11 is Lacan’s response to his expulsion from the International Psychoanalytical Association. A peculiar expulsion, for it was formally established that, according to the Association, his teaching and his analytic practice would be considered forever null in relation to the formation of analysts ever since.

In the first class of this seminar, Lacan makes a diagnosis of the IPA, taking the opportunity that, by chance; he was expelled from the IPA on the same date that Spinoza had been excommunicated from the Jewish faith. He says: “I have been also excommunicated”. Lacan’s diagnosis is the following: the current structure of psychoanalysis is equivalent to that of a church. I—says Lacan—have been punished, like a heretic; I am a heretic according to the international organization of psychoanalysts.

 

CHAPTER TWELVE: The drive (II)

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Today we shall resume our elaboration of the notion of the drive. We shall also return to its articulation with the concept of perversion, as you seemed particularly interested in it. This, however, is not unusual: perversion is always an interesting theme. At this point, there exists a fantasy: that the perverse enjoys (jouit). Departing from Seminar 11 we are going to put into question the idea—neurotic idea par excellence—that the perverse subject enjoys. We shall see that nobody else is as limited, regarding jouissance, by the fantasme, as the perverse subject is.

Last class we said (following Lacan) that the subject is “headless” in the drive. “Headless subjectivity” means that, in the drive, the subject is not yet placed. Let us stop for a moment in this “yet”. It is a complex notion which Lacan studied and to which he even dedicated the title of his seminar: Encore.1 What is Lacan trying to tell us through this “yet”? It is by no means an evolutionary or developmental notion, it is not “not yet, maybe later”.

 

CHAPTER THIRTEEN: S(A/): Being, jouissance and desire

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The subject for this class—and the following—will be S(); an arduous, an extremely difficult theme to work on. I propose to you that we begin by entitling it: “Being, jouissance and desire” (this title could make the bravest back down).

Let us start by departing from this quotation from “Subversion of the subject …”:

What the graph now offers us is situated at the point at which every signifying chain prides itself on looping its signification (p. 349).

Once again we have the code (C) and the message (M), but elaborated as treasure of the signifier, A, and the signified of the Other, s(A). Lacan states that the last floor of the graph posits again a circle: the circle of the completed graph. And he also posits that this circle closes itself (loops itself) upon a signification which, passing by S(), flows into s(A), which—actually—is the closing of signification.

Schema 1.

More radically, Lacan states that it is at S(A) that the signification closes itself at the unconscious level; thus, S(A) has the function of s(A) at the level of the unconscious. This seems to be, at first sight, contradictory.

 

CHAPTER FOURTEEN: S(A/): “Being (Res), jouissance and desire” (II)

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Today I will propose to revisit the logic—rather than the quotations—of what we discussed in our last class. In this sense and regarding the suggested title: “Being, desire and jouissance”, I shall propose a slight variation: “Being (res), desire and jouissance”. Without doubt I am thus introducing the Cartesian opposition res cogitans/res extensa.

Despite what I have just said, I will present to you some statements (as few as possible), taken from Lacan’s texts, and which I will use as the steps for my argument—except the first one, which has the structure of an axiom-, they can all be found in “Subversion of the subject …”

[…] every signifying chain prides itself on looping its signification (p. 349).

Every signifying chain—from the moral perspective of values— prides itself on looping its signification. And, obviously, every chain honoured with that pride will as a result, be finite, for it is honoured precisely in so far as its loop [circle] is closed. This is what we call “message”: when a chain loops on its signification. However, thepoint is that, in the context of Lacan’s teaching, that signification is of the Other, s(A). Nevertheless, we tend to conceive signifying chains as being infinite. I believe that almost all of us think that‘’S1-S2” is a formalized reduction of‘’S1-S2-S3…Sn”. So we must go slowly through this statement that I am proposing to you as an axiom.

 

CHAPTER FIFTEEN: The castration complex in Lacan's teaching

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Ishall dedicate this last chapter, predictably, to the final pages of “Subversion of the subject …”. The title I propose to you as a framework for our work is “The castration complex in Lacan’s teaching”.

This outline will be supported, as has been the case during this course, by a series of quotations. The first one has already been presented to you during the last class:

But it is not the Law itself that bars the subject’s access to jouissance—rather it creates out of an almost natural barrier a barred subject. For it is pleasure that sets the limits on jouissance, pleasure as that which binds incoherent life together,1 until another, unchallengeable prohibition arises from the regulation that Freud discovered as the primary process and appropriate law of pleasure.

It has been said that in this discovery Freud merely followed the course already being pursued by the science of his time, indeed, that it belonged to a long-standing tradition. To appreciate the true audacity of his step, we have only to consider hisrecompense, which was not slow in coming: failure over the heteroclite nature of the castration complex (pp. 352–353).

 

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