In this episode, William Gomes explores Lacan’s late work, the period when his thinking shifted from linguistic models toward topology and the mathematics of knots. Far from being merely abstract or obscure, late Lacan represents a profound reconsideration of how the psyche is structured, moving beyond the primacy of language toward understanding how Real, Symbolic, and Imaginary are knotted together in ways that resist simple linearisation. By examining the Borromean knot, sinthome, and new conceptions of jouissance, this episode reveals why late Lacan remains essential for contemporary psychoanalytic theory and practice.
The Turn to Topology
From Linguistics to Mathematics
Lacan’s early and middle work was dominated by linguistic models. The unconscious structured like a language, the signifying chain, metaphor and metonymy: these concepts positioned language as the fundamental organising principle of psychic life. The subject was constituted through the symbolic order, structured by signifiers, determined by linguistic mechanisms.
Yet in his late work, beginning in the 1970s, Lacan increasingly turned toward topology and mathematical formalisation. This shift was not a rejection of earlier insights but rather a recognition of their limits. Language, despite its power to structure the psyche, cannot capture everything. There remains something about psychic structure that resists linguistic representation, that requires different modes of formalisation.
Topology, the mathematical study of spatial relationships and transformations, offered Lacan tools for thinking about psychic structure in non-linguistic terms. Topological objects like the torus, Möbius strip, and cross-cap had already appeared in his middle work. Yet in late Lacan, topology becomes central, particularly through the figure of the knot.
This turn to mathematics was not merely theoretical abstraction. Rather, it reflected Lacan’s clinical experience, his recognition that certain psychic structures could not be adequately described through linguistic models alone. The topology of knots provided ways of thinking about how psychic registers relate to each other, how psychosis differs from neurosis, how analysis works to restructure the psyche.
The Borromean Knot
The Borromean knot became the central figure in late Lacan’s thinking. This knot consists of three rings linked in such a way that cutting any one ring causes all three to separate. No two rings are directly linked; rather, all three hold together through their collective configuration.
Lacan uses the Borromean knot to represent the relationship between Real, Symbolic, and Imaginary. These three registers are not layered hierarchically, not reducible to one another, not explicable as combinations of more fundamental elements. Rather, they are irreducibly three, linked in such a way that all three are necessary for psychic functioning.
The Borromean structure has important implications. It means that none of the three registers is primary or foundational. Earlier Lacan had sometimes suggested the primacy of the Symbolic, the structuring power of language. Yet the Borromean model insists on the equal necessity of all three registers. The Real is not merely what resists symbolisation; it is an essential component without which Symbolic and Imaginary could not function.
Moreover, the Borromean knot demonstrates that psychic structure is fundamentally three-dimensional, that it cannot be reduced to binary oppositions or linear sequences. Understanding the psyche requires grasping how three heterogeneous registers are knotted together, how they hold each other in place whilst remaining irreducible to one another.
The Failure of the Knot
Lacan uses the Borromean structure to think about psychotic structure. In psychosis, the Borromean knot fails to hold. One ring slips out, causing the other two to separate. This is what Lacan calls foreclosure: not merely repression of particular contents but rather a failure in the fundamental structure that links the three registers.
In neurosis, the knot holds, though it might be strained or distorted. The neurotic subject has access to all three registers, can move between them, can use symbolic resources to manage encounters with the Real. Yet in psychosis, this basic structure has failed. The psychotic subject lacks the fundamental knotting that would allow Symbolic, Imaginary, and Real to function together.
This understanding of psychosis has clinical implications. The psychoanalytic approach to psychosis cannot simply be an application of techniques developed for neurosis. If the fundamental structure is different, if the knot has failed rather than merely being distorted, then the work must be different.
Rather than interpretation aimed at revealing unconscious meaning, work with psychosis might involve helping to establish or stabilise a knotting, helping the subject develop ways of linking the three registers when the Borromean structure has failed. This is where the concept of sinthome becomes crucial.
The Sinthome
In his seminar on James Joyce, Lacan introduces the concept of sinthome. This neologism, an archaic spelling of “symptom,” represents something different from the symptom as discussed in earlier work. The sinthome is not a compromise formation expressing unconscious conflict. Rather, it is a fourth ring that can stabilise a failed Borromean knot.
When the Borromean structure fails, when foreclosure has occurred, the subject might develop a sinthome that holds the remaining rings together. This sinthome is not pathological in the usual sense. Rather, it is a creative solution, a way of maintaining psychic functioning despite the failure of fundamental structure.
Lacan argues that Joyce’s writing functioned as sinthome, that Joyce’s literary work served to stabilise a psychic structure that would otherwise have collapsed into psychosis. The writing was not merely expressing unconscious conflicts; rather, it was performing essential structural work, knotting together registers that would otherwise have separated.
This concept has profound implications. It suggests that what appears pathological might actually be a necessary stabilisation, that certain symptoms or peculiarities might be serving crucial structural functions. Clinical work must therefore be careful not to simply eliminate symptoms without understanding what structural work they might be performing.
New Concepts in Late Lacan
Jouissance Revisited
Late Lacan develops increasingly complex theorisation of jouissance. Rather than a single concept, jouissance becomes differentiated into multiple forms: phallic jouissance, jouissance of the Other, jouissance of the body, surplus jouissance.
Phallic jouissance is the jouissance available within the symbolic order, structured through the phallic function and castration. It is limited, regulated, organised according to the logic of the signifier. This is the jouissance that the neurotic subject can access, that operates within the constraints of the symbolic order.
Yet there is also jouissance beyond the phallus, particularly what Lacan calls jouissance of the Other. This is jouissance that exceeds phallic organisation, that is not structured through castration or the symbolic order. Lacan associates this particularly with feminine jouissance, though not exclusively.
This differentiation of jouissance reflects late Lacan’s recognition that the phallic function does not exhaust the possibilities of enjoyment, that there are forms of jouissance that operate differently, that the symbolic order does not fully contain or regulate all forms of bodily or psychic satisfaction.
Feminine Jouissance and Sexual Difference
Late Lacan’s thinking about sexual difference becomes increasingly complex. Rather than simply positioning subjects as having or lacking the phallus, late Lacan suggests that there are different relationships to jouissance that are not reducible to this binary.
Feminine jouissance is characterised as supplementary, as something beyond phallic jouissance that cannot be fully spoken or symbolised. It is not the opposite of masculine jouissance but rather something additional, something that exceeds the logic of castration and the phallus.
This has important political and ethical implications. It suggests that the phallic organisation of the symbolic order, whilst dominant, does not exhaust the possibilities of human experience. There are forms of jouissance, modes of being, that escape phallic logic, that operate according to different principles.
Yet Lacan is careful to emphasise that feminine jouissance is not simply the property of anatomical women. Rather, it is a structural possibility, a relationship to jouissance that is available regardless of biological sex. The question is not anatomy but rather the subject’s particular relationship to the phallic function and to jouissance.
The Real as Consistency
In late Lacan, the Real takes on new significance. Rather than being merely what resists symbolisation or what remains outside the symbolic order, the Real becomes conceived as having its own consistency, its own logic.
The Real is what does not stop not being written. This enigmatic formulation captures the Real’s persistence, its insistence beyond symbolic representation. The Real is what continues despite our attempts to symbolise it, what returns regardless of how we try to integrate it into meaning.
Yet the Real is not chaos or pure negativity. Rather, it has structure, though this structure is not linguistic or symbolic. The Real operates according to its own principles, follows its own logic. Understanding psychic life requires attending to this Real dimension, to what operates beyond or beneath the symbolic order.
This conception of the Real has clinical implications. It means that analysis cannot simply be about symbolisation, about bringing the unsymbolised into language. There remains a Real that will never be symbolised, that must be managed or navigated rather than eliminated or integrated.
Lalangue
Late Lacan introduces the neologism lalangue, written as a single word, to distinguish from la langue, the language. Lalangue refers to language in its material dimension, to the sounds and rhythms and nonsensical elements that precede meaning, to language as it is first encountered by the infant.
Lalangue is not yet organised into grammar and syntax, not yet structured according to the rules of language. Rather, it is the pre-linguistic babble, the phonetic material, the pure play of sounds that the infant experiences before acquiring language proper.
Yet lalangue is not simply left behind when the subject acquires language. Rather, it persists, continues to operate beneath structured speech, emerges in slips of the tongue, in puns, in the material play of signifiers. Lalangue is where the Real of language appears, where language touches the body, where signifiers produce effects that exceed their semantic content.
Clinical attention to lalangue means attending to how patients speak, to their particular rhythms and intonations, to the material dimension of their speech rather than merely its content. Lalangue is where the subject’s singular mode of jouissance appears in language, where their particular relationship to the Real manifests.
Clinical Implications of Late Lacan
Working with Psychosis
Late Lacan’s thinking about knots and sinthome has particular importance for work with psychosis. If psychosis involves a failure of the Borromean structure, then clinical work cannot simply apply techniques developed for neurosis.
Rather than interpretation aimed at revealing unconscious meaning, work with psychosis might involve helping to establish stabilising structures, helping the subject develop a sinthome that can hold together what the failed Borromean knot cannot. This might involve supporting creative work, artistic production, intellectual systematisation: activities that can serve structural functions.
The analyst working with psychosis must be cautious about interpretation. If the symbolic order is not functioning properly, if the knot has failed, then interpretations that work for neurotic patients might be destabilising for psychotic patients. The work requires different techniques, different aims, different understanding of what analysis can accomplish.
This does not mean psychotic patients cannot be helped through psychoanalytic work. Rather, it means recognising that psychosis requires different approaches, that the goal is not necessarily resolving unconscious conflicts but rather helping to establish or maintain psychic functioning despite structural failure.
The End of Analysis Reconsidered
Late Lacan’s thinking about the sinthome leads to reconsideration of what the end of analysis might involve. Earlier Lacan had spoken of traversing the fundamental fantasy, of subjective destitution, of the subject coming to recognise the impossibility of complete satisfaction.
Yet late Lacan suggests that analysis might also involve the subject developing their own sinthome, their own particular way of knotting the three registers, their own solution to the structural impossibilities of psychic life. The end of analysis would not be elimination of symptoms but rather transformation of the subject’s relationship to their sinthome.
The subject would come to identify with their sinthome, to recognise it as their particular mode of managing impossibility, to take responsibility for it rather than experiencing it as alien or pathological. This represents a different understanding of cure, one that accepts that certain structural features cannot be eliminated but can be lived differently.
This has ethical implications. It means accepting the subject’s singularity, their particular way of being, their unique solution to psychic impossibility. Rather than trying to normalise or standardise, analysis would aim at helping the subject recognise and assume their own singular mode of existence.
Jouissance and the Drives
Late Lacan’s differentiation of forms of jouissance has implications for understanding the drives. Rather than being simply instinctual or biological, drives are understood as ways in which jouissance is organised around particular bodily zones or activities.
The oral drive, anal drive, scopic drive, invocatory drive: these are not simply biological urges but rather ways in which the body becomes organised as a site of jouissance. Each drive has its own circuit, its own particular way of producing satisfaction and dissatisfaction.
Understanding drives through jouissance means recognising that drives are fundamentally about excessive enjoyment rather than about need or instinct. The subject does not simply satisfy needs through the drives; rather, they pursue forms of jouissance that go beyond need, that involve the body in ways that exceed biological function.
Clinical work with drives therefore cannot simply be about sublimation or redirection. Rather, it involves understanding the subject’s particular relationship to jouissance, how their drives are organised, what forms of excessive enjoyment they pursue. The goal is not to eliminate drive satisfaction but to help the subject recognise and take responsibility for their own jouissance.
The Body in Late Lacan
Late Lacan’s thinking about the body becomes increasingly sophisticated. The body is not simply biological organism or imaginary gestalt or symbolic inscription. Rather, the body is where the three registers knot together, where Real, Symbolic, and Imaginary meet.
The body has its own consistency, its own Real dimension that resists symbolisation. Yet the body is also organised through the Symbolic, carved up by language, given meaning through culture. And the body is imagined, perceived through identifications, structured through body image.
Understanding the body requires attending to how these three dimensions knot together, how they hold each other in place, how disturbances in one register affect the others. Psychosomatic symptoms, for example, might involve failures in how the registers are knotted at particular bodily sites.
Clinical work with the body therefore requires attention to all three registers, requires understanding how imaginary, symbolic, and Real dimensions are functioning and how they might be reorganised. This cannot be reduced to either pure symbolisation or pure attention to biological processes.
Topology and Formalisation
The Torus and the Structure of Desire
Before the Borromean knot, Lacan had used other topological figures to model psychic structures. The torus, a doughnut-shaped surface, was particularly important for thinking about desire.
The torus has two fundamental circles: one going around the central hole, one going through it. These two circuits are irreducible to each other, cannot be transformed into each other through continuous deformation. Yet they are both essential to the torus’s structure.
Lacan uses the torus to model the relationship between demand and desire. Demand circulates on the surface, moving around the outside. Yet desire follows a different circuit, one that goes through the central void. Desire and demand are irreducible to each other, yet both are necessary for the subject’s psychic functioning.
This topological model helps think about why desire cannot be satisfied through meeting demands, why giving the subject what they ask for does not address what they actually desire. Desire and demand follow different circuits; satisfying demand does not touch the circuit of desire.
The Möbius Strip and Unconscious Continuity
The Möbius strip, a surface with only one side, provides another crucial topological figure. If you travel around a Möbius strip, you return to your starting point having traversed both “sides” of the surface, revealing that there is actually only one continuous side.
Lacan uses the Möbius strip to think about the relationship between conscious and unconscious. These are not separate domains but rather continuous, different aspects of the same psychic surface. What appears as inside and outside, conscious and unconscious, are revealed to be continuous when properly understood topologically.
This helps explain how unconscious formations appear in conscious life, how slips and symptoms manifest. The unconscious is not hidden in some separate domain but rather is continuous with consciousness, appearing on what seems to be a different side but is actually the same surface.
The Cross-Cap and Psychotic Structure
The cross-cap or projective plane provides a model for thinking about psychotic structure. This surface cannot be embedded in ordinary three-dimensional space without self-intersection, without passing through itself.
This topological impossibility mirrors something about psychotic structure: an inability to maintain the distinctions that neurotic structure requires, a collapse of boundaries that should remain separate, a confusion of registers that should be differentiated.
Understanding psychosis topologically suggests that it is not merely a deficit or impairment but rather a different structure, one that operates according to different spatial logic. Clinical work must respect this difference, must recognise that psychotic structure cannot simply be converted into neurotic structure.
Mathematical Formalisation and Its Limits
Late Lacan increasingly uses mathematical notation, algebraic formulas, logical formalisation. This might seem obscure or unnecessarily complex. Yet Lacan argues that ordinary language is inadequate for psychoanalytic theory, that linguistic formulations inevitably import assumptions and associations that distort psychoanalytic insights.
Mathematical formalisation, whilst difficult, offers precision and rigour that ordinary language cannot achieve. The formulas are not merely illustrative; rather, they attempt to capture psychic structures in ways that resist the ambiguities and multiple meanings of ordinary speech.
Yet Lacan also recognises limits to formalisation. Not everything can be written, not everything can be captured in formulas. The Real resists complete formalisation, persists beyond what mathematics can represent. The turn to mathematics is not an attempt to eliminate the Real but rather to approach it more rigorously, to mark its limits more precisely.
Late Lacan and Contemporary Theory
Influence on Psychoanalytic Practice
Late Lacan’s concepts have influenced contemporary psychoanalytic practice in several ways. The concept of sinthome has encouraged analysts to be more cautious about symptom removal, more attentive to the structural functions that symptoms might serve.
The differentiation of jouissance has helped analysts recognise that there are multiple forms of satisfaction, that phallic jouissance does not exhaust the possibilities, that clinical work must attend to the subject’s particular relationship to different forms of enjoyment.
The topology of knots has provided new ways of thinking about psychic structure, about the relationship between registers, about how analysis works to restructure the psyche. This has been particularly important for work with psychosis and borderline conditions.
Feminist Engagements
Late Lacan’s thinking about feminine jouissance has generated extensive feminist engagement. Some feminist theorists have found in late Lacan resources for thinking beyond phallic organisation, for conceptualising forms of experience and enjoyment that escape patriarchal structures.
The idea that feminine jouissance is supplementary, that it exceeds phallic logic, suggests possibilities for pleasure and satisfaction that are not organised through castration or lack. This has been used to theorise feminine sexuality, pleasure, and subjectivity in ways that resist phallocentric frameworks.
Yet other feminists remain critical, arguing that even late Lacan’s formulations remain too invested in the phallus, that feminine jouissance remains defined in relation to phallic jouissance rather than on its own terms. These debates continue to generate productive theoretical work.
Queer Theory and Non-Binary Subjects
Late Lacan’s work has also been important for queer theory. The recognition that sexual difference is not reducible to biological sex, that there are multiple relationships to the phallic function, that jouissance exceeds binary categorisation: these insights resonate with queer theoretical projects.
The concept of sinthome has been particularly productive, suggesting that subjects might develop singular solutions to sexual positioning, might create their own modes of identification and desire that do not conform to heteronormative structures.
Late Lacan’s emphasis on the Real and on what escapes symbolisation has also been important for thinking about bodies and identities that resist categorisation, that cannot be fully captured by existing symbolic frameworks.
Philosophy and Continental Theory
Late Lacan’s turn to mathematics and topology has influenced continental philosophy beyond psychoanalysis. Thinkers like Alain Badiou and Slavoj Žižek have drawn extensively on late Lacan, particularly on concepts like the Real, the sinthome, and the formalisation of psychic structures.
The relationship between late Lacan and contemporary philosophy remains productive and contested. Some philosophers find in late Lacan essential resources for thinking about subjectivity, truth, and the limits of knowledge. Others argue that late Lacan becomes too abstract, too removed from clinical practice and lived experience.
These philosophical engagements demonstrate late Lacan’s continuing relevance beyond psychoanalysis proper, his contribution to broader theoretical conversations about subjectivity, language, and the Real.
Related Episodes in The William Gomes Podcast Series
Episode 1: Why Lacan Still Matters Today Episode 6: The Real: Lacan, Trauma and What Lies Beyond Words Episode 14: The Phallus: A Symbol of Desire, Value and Meaning in the Psyche Episode 16: Jouissance: The Paradox of Painful Enjoyment Episode 17: The Real: What Lies Beyond Language and Symbolic Meaning Episode 20: The Lacanian Body: Imaginary, Symbolic and Real Dimensions of Experience Episode 21: Symptoms and Repetition: Why We Repeat Patterns and What They Reveal Episode 25: [Next episode in series]
Listen to the Full Episode: Available on Spotify, Apple Podcasts, YouTube, and at williamgomespodcast.com
This article is part of The William Gomes Podcast’s ongoing exploration of Lacanian psychoanalysis and neurodevelopmental psychology. For more information, visit williamgomespodcast.com or connect with William Gomes on LinkedIn.
