In response to my post “Deleuze and Guattari avec Lacan“, Reid asks “What is the Borromean Clinic?” I confess that I am working through this myself, so I do not have a completely adequate answer. In many respects, this is the most and dense and difficult period of Lacan’s teaching, but it is also a period where he completely exceeds what he had developed in prior years, developing both an entirely new diagnostic system and new possibilities for the end of analysis.

In his Borromean period, Lacan shifts to a topology of the subject based on the borromean knot:

The first thing to notice with this curious knot is that no two of the rings are directly tied together as in the case of a Hopf chain:

Consequently, in the borromean knot, if any one of the rings are severed the other two rings fall away as well. In short, the consistence of the borromean knot arises only from the knotting of the three and the manner in which the strings pass over and under one another in the proper way. Lacan equated each of the three rings with one of his three orders– the real, the symbolic, and the imaginary (RSI) –corresponding to the order of ex-sistence (the real) or that which exists outside the symbolic, the order of the hole or lack introduced into being (the symbolic), and the order of consistency (the imaginary). However, it will be noted that each of the rings overlaps with the others forming points of intersection with the other rings like a Venn diagram:

Consequently, we can think the different orders together getting various combinations between the elements. Thus, for example, there can be a hole in the real, just as there is an ex-sistence in the symbolic (the letter as opposed to the signifier). Likewise, there can be a consistence in the symbolic (meaning), just as there can be a hole in the imaginary. And so on. As I said, I am still working through this myself, so I have not yet worked out the implications of all this.

One of the major ways in which Lacan’s theory of the subject in terms of the Borromean knot transforms his prior theory is that each of the three orders are now on equal footing with one another. In his prior teaching Lacan had focused on in each period on one of the three orders. Thus, in the earliest work the order of the imaginary and the mirror stage holds the most eminent position. Here the aim of analysis centers around working through alienation in the mirror stage produced as a result of specular identifications. Beginning with Seminar 1 and up through about Seminar 6, it is the symbolic that holds center stage. Here the thesis is that the symptom can be entirely resolved through the activity of interpretation and so-called “full speech”. Between Seminars 7 and 18, the real comes to be the most important order and the aim of analysis now becomes traversing the fantasy and undergoing subjective destitution through the discovery that the big Other does not exist. With the introduction of the Borromean knot, all of this begins to change. No longer does one order hold pride of place among the others, overdetermining all of the others, but now they are all equivalent or on the same level, knotting themselves together in a variety of ways, producing different structures of subjectivity as well as new possibilities for the end of analysis.

In addition to this equivalence of the orders, the borromean knot also allows us to more precisely situate various phenomena that appear in the clinic and the life of the analysand:

Thus, when the symbolic is shifted in the direction of the real, we get the symptom. When the real is shifted in the direction of the imaginary, we get anxiety. And when the imaginary is shifted in the direction, we get inhibition. From a clinical standpoint, this helps to guide the analyst’s interventions and also determine where to look, what relationships to look for, when encounter symptoms, inhibitions, or anxiety. Moreover, it becomes possible to determine what structurations predominate in the subject-structure of the analysand based on the sort of jouissance that is encountered in the clinic (phallic jouissance, Other-jouissance, or surplus-jouissance).

Henceforth, subject-structure is to be understood as a particular way in which borromean knot is tied and analysis is understood as the practice of untying and retying knots so as to produce a new subject-structure. Insofar as the subject is understood to be a particular type of knot, we can imagine different ways in which the three orders are tied together generating very different types of structures of subjectivity. Thus we can imagine cases such as those of Joyce, where two of the orders are tied together as a Hopf chain, with one of the orders unbound to the other two. In Joyce’s case, this sort of knot can be detected in the writings of Dubliners, where the snippets of speech found in the epiphany, characterized as they are by the status of enigma or meaninglessness, indicate that the symbolic is bound to the real but not the imaginary (the imaginary being the source of effects of meaning. Likewise, Joyce’s various descriptions of depersonalization and his body found in texts such as Portrait of an Artist as a Young Man indicates that the dimension of the imaginary (which also pertains to the post-mirror stage body) were unmoored from the symbolic and the real, such that the anchor of nomination was not at work in his subjective structure. What is remarkable and of interest in Joyce is that he did not fall into psychosis. How is it that he managed to mend his knot? I’ll have more to say on that in a moment.

From a diagnostic perspective, all sorts of rich possibilities emerge that have been barely touched in the secondary literature. What would a structure of subjectivity look like where the real had slipped away from the symbolic and the imaginary (where the symbolic and imaginary formed a Hopf chain)? What would a structure of subjectivity look like where the symbolic had slipped away from the imaginary and the real? Are the structures of subjectivity that are organized around a three circle Hopf chain rather than a borromean knot? Presuming that neurosis is a matter of the three orders being tied together, how are we to distinguish hysteria from obsession? Are there different varieties of hysteria and obsession depending on how the different orders are shifted in the direction of one another? Are there different and entirely unheard of orders? These questions need to be worked through systematically.

Here already we see a significant transformation of Lacan’s earlier teaching. Where, in prior years, Lacan had argued that subject-positions are invariant, such that one is either a neurotic (hysteria/obsession), a pervert, or a psychotic and where the question was one of relating to the symptom in a new and different way, the notion of untying and retying implies the emergence of entirely new subject-structures over the course of analysis (and also the danger, perhaps, of falling into psychosis through inept untying and retying).

This possibility of confirmed in the case of Lacan’s reading of Joyce. As I mentioned a moment ago, Joyce somehow managed to mend the slip that occurred in the way his three orders were knotted together. This is significant for two reasons. On the one hand, according to Lacan Joyce managed to do this without the intervention in analysis on his own. Lacan contends that Joyce went as far as one can go through a process of analysis. Most excitingly, Joyce’s solution to the slip in his borromean knot took place through invention. That is, Joyce invented a new type of knot that allowed him to mend this slip. In order to get a sense of what I have in mind by a “slip” or “fault” in the tying of the three orders, attend carefully to the following diagram of the three orders:

Ignoring the brackets labeled “ego”, observe the manner in which the different rings pass over and under one another. It will be noted that in the case of the imaginary, the imaginary is not knotted to either of the other two orders, which is what allows it to slip away. It is this that accounts for the strange and senseless effect of the epiphanies which have the characteristic of begin engimas (signifiers in search of a signification), and the various bodily disturbances Joyce experiences. Insofar as the dimension of the imaginary is responsible for effects of meaning and the integrity of bodily experience, the fault in Joyce’s knotting is responsible for the production of these phenomena.

However, argues Lacan, Joyce manages to surmount this fault or slip by inventing a new knot that links the three orders together. This fourth knot is the sinthome:

The sinthome, introduced in Seminar 23, is a fourth knot irreducible to the three orders, that allows the three orders to be stitched together. For Joyce, according to Lacan, the sinthome was Joyce’s writing or literature. In each case, the sinthome of the subject will be absolutely unique and singular, outside of any order of the particular and the general. Moreover, the sinthome is something invented by the subject, thereby indicating the productive nature of a particular jouissance. Lacan will call this singular form of jouissance opaque jouissance, because it is purely singular and beyond or outside of any structures of meaning or interpretation.

However, Lacan’s proposal is more radical yet. We might suspect that the sinthome is something that is restricted to Joyce or is a solution that only applies in cases of psychosis where the issue is one of producing a sinthome that would once again tie the three orders together where the slip is produced as a result of the foreclosure of the name-of-the-father. After all, in Seminar 22, RSI, Lacan had argued that there are only three orders or three rings. However, by the time of Seminar 23, Sinthome, Lacan argues that the sinthome, the fourth ring, is indispensable for any and all borromean knots. Here I am not entirely sure I follow Lacan’s reasoning, but the line of thought seems to be that insofar as the three orders have been placed in a relation of equivalence in the borromean knot, it is necessary to have a fourth ring to distinguish the different orders.

This introduction of a fourth ring or the sinthome has a number of significant consequences. Once again, look carefully at the following diagram of what I will here call the “Lacanian Knot”:

Examine the manner in which the fourth knot, the sinthome, or Σ, passes underneath and above the other three rings. There are eight points where the fourth ring passes either over or under the other rings. What we begin to see here is the means for making diagnostic differentiations based on how it might become possible to make diagnostic differentiations based on the manner in which the rings are knotted together. In this particular instance, it will be noted that RSI are not knotted directly together at all, but either lie above or below one another, without forming any particular direct links to one another. It is only through the fourth ring, Σ, that they are attached to one another. What psychic structure, we might ask, would this be? I have not myself worked out the mathematics yet, but how many different ways are there of linking these four rings and how might the different ways in which the rings pass over and under one another be used to form a differential diagnosis? What forms of jouissance, desire, relations to the real, and relations to the Other would we find in all of these different ways of tying the knot? And what are we to make of the different “holes” that occur in this complex knot like a Venn diagram?

Here’s it’s worthwhile to recall the earlier diagram with inhibitions, symptoms, and anxiety as well as the different jouissances, where the points of intersection among the different orders were also different sites of jouissance.

What, then, is the significance of all this? The introduction of the borromean knot along with the idea of the process of analysis as a process of untying and retying suggests an entirely different aim for the end of analysis… An aim that would be post-neurotic. In this thesis I am deeply indebted to Roberto Harari’s How James Joyce Made His Name: A Reading of the Final Lacan. Most students of Lacan will be familiar with the Lacanian thesis that the end of analysis consists in traversing the fantasy and undergoing subjective destitution. It will be recalled that fantasy masks or veils castration. Consequently, the aim of traversing the fantasy would entail an acceptance of constitutive castration. If this would also involve subjective destitution, then this would be because it is discovered 1) that it is not you, in the dimension of your conscious ego, that has knowledge, but the unconscious that knows (as Lacan puts it in Seminar 17, “…it is not at all self-evident that all knowledge, by virtue of being knowledge, is known as knowledge” (30).), 2) because the drives as partial drives not unified in a subject reach their jouissance or satisfaction independent of any aim of a unified subject, and 3) because it is discovered that the big Other does not exist or that there is no guarantee of the subject’s identity to be found in the symbolic order.

Yet by the time of Seminar 23, Lacan has proposed a new aim of analysis: the invention and identification with the subject’s sinthome. And here is what is most surprising: In and through the invention of the sinthome, the analysand also reaches a beyond of neurosis. Compare, for a moment, the neurotic subject, with, for lack of a better word, the “sinthomatic” subject. The neurotic subject is phallic in relation to the symptom. That is to say, the neurotic subject believes in his symptom. Here the symptom is a message directed to the Other as in the case of Dora’s symptom as a message to her father. The neurotic subject ultimately searches for nomination in the Other, for a master, that could guarantee the subject’s identity. This is why it is possible for the neurotic subject to enter into transference with the analyst. To say that the neurotic subject believes in his symptom is to say that the neurotic believes that, in Peircian terms, there is a final interpretant or signifier that the analysand could finally attain, that the set can be completed, and that the subject’s being can be guaranteed in the symbolic. It is for this reason that the world of the neurotic is a world pervaded by meaning. All things the neurotic relates to are metaphorical substitutes for the missing phallus that would complete the subjects being (here is one of the reasons for Deleuze and Guattari’s careful hostility to metaphor).

Identification with the sinthome is something entirely different. Where the symptom is directed or addressed at the Other and is transitive, the sinthome is intransitive and belongs to the One. Where the symptom ex-sists in the unconscious, the sinthome is disinvested from the unconscious, exiled, outside of discourse. Where the symptom is premised in the belief in meaning (the phallus), the sinthome is another mode of credibility, pertaining to “j’ouis-sense“, the hearing of sense in the letter (not the signifier), and believes in being and S1. Where the symptom pertains to speaking-being or the divided subject, the sinthome pertains to the individual or that which cannot be divided (this is perhaps the most surprising and radical of Lacan’s theses on the sinthome). Where the symptom seeks meaning in an S1 or master (think of Deleuze and Guattari’s discussion of transcendence and the despotic machine), the sinthome undoes meaning, produces enigmas and seeks S2 or an endless metonymy (not unlike Deleuze and Guattari’s desiring-machines). Where the symptom is premised on a rotten, phallic, bodily jouissance, the sinthome revolves around an opaque mental jouissance of the Other. Where the symptom results from the name-of-the-father or Oedipalization as a vain attempt to name the desire of the mother, the sinthome is unconditioned and an exit from this metaphorization. Where the symptom is premised on metaphorical substitution endlessly searching for the phallus, the sinthome is premised on nomination. (This summary is based on Harari, page 241). In short, the sinthome marks an exit from the unconscious and the neurotic search for the phallus. It marks an entirely different way of relating to jouissance that is beyond the Oedipus.

In a very Deleuzian spirit, it can thus be said that Lacan’s account of the end of analysis as identification with the sinthome, as an exit from the unconscious, marks a shift from desiring the Oedipus, willing our own oppression, or paranoid, fascist desire, to a form of desire that is beyond neurosis. Could it be said that there was a bi-directional influence that took place between Deleuze and Guattari and Lacan? Is it the case that just as Deleuze and Guattari were deeply influenced by Lacan such that they made explicit many of the implications of his own teaching, Lacan, in turn, was deeply influenced by Deleuze and Guattari’s Anti-Oedipus, with their affirmative account of desire and critique of the Oedipus and paranoia, such that Lacan, in turn, was able to discover a beyond to neurosis? The fact that Seminar 23 was given three years after the publication of Anti-Oedipus suggests something very much along these lines. It is as if Lacan’s psychoanalysis began to approach something far closer to schizoanalysis, where terms like castration and lack seem to fall away, where the tragic picture of the subject as inherently destitute begins to disappear, and where the emphasis comes to land on creation or productivity (invention of the sinthome) rather than the endless backward tracing of metaphorical substitutions premised on the search for the elusive phallus. The aim no longer becomes the acceptance of the fact that the phallus will never be had, but instead becomes nomination, where nomination is a singular term, the same in all languages (we do not translate names), and a productive principle of endless metonymy wherein jouissance is drawn for its own sake.

I realize my remarks in this post have been extremely schematic and that I haven’t said a whole lot that is concrete or that would indicate just how the borromean knots are to be used. However, hopefully simply outlining these structures and their relationships will partially open the door to posing such questions and exploring the Lacanian quadruple knot.