Seminar XII

Jacques Lacan's Seminars : I · II · III · IV · V · VI · VII · VIII · IX · X · XI · XII · XIII · XIV · XV · XVI · XVII · XVIII · XIX · XX · XXI · XXII · XXIII · XXIV · XXV · XXVI · XXVII I. Freud's technical writings II. The Ego in Freud's Theory and in the Technique of Psychoanalysis III. The Psychoses IV. The Object Relations V. The Formations of the Unconscious VI. Desire and its Interpretation VII. The Ethics of Psychoanalysis VIII. Transference IX. Identification The Names of the Father X. Anxiety XI. The Four Fundamental Concepts of Psychoanalysis XII. Crucial Problems for Psychoanalysis XIII. The Object of Psychoanalysis XIV. The Logic of Fantasy XV. The Psychoanalytic Act XVI. From One Other to the Other XVII. The Reverse of Psychoanalysis XVIII. On a Discourse That Would Not Be Semblance XIX. Or Worse XX. Encore XXV. The Moment of Concluding XXVII. Dissolution ← Seminar XI Seminar XIII →

Crucial Problems for Psychoanalysis
Seminar XII
Image often associated with Seminar XII.
French Title	Le Séminaire, Livre XII : Problèmes cruciaux pour la psychanalyse
English Title	The Seminar of Jacques Lacan, Book XII: Crucial Problems for Psychoanalysis
Seminar Information
Seminar Date(s)	1964–1965 (academic year)
Session Count	Weekly sessions
Location	École Normale Supérieure, Paris
Psychoanalytic Content
Key Concepts	Unconscious • Real • Symbolic order • Imaginary • Objet petit a • Extimacy • Topology • Moebius strip • Torus • Klein bottle • Fantasy
Notable Themes	Subject and language; Real and topology; extimacy and decentering; structure and surface; status of analytic knowledge; fantasy and reality; psychoanalytic training
Freud Texts	The Interpretation of Dreams • Beyond the Pleasure Principle • Instincts and Their Vicissitudes • Inhibitions, Symptoms and Anxiety
Theoretical Context
Period	Middle/structural period
Register	Symbolic/Real with topological formalization
Chronology
Preceded by	Seminar XI
Followed by	Seminar XIII

Crucial Problems for Psychoanalysis (French: Problèmes cruciaux pour la psychanalyse) is the twelfth annual seminar delivered by Jacques Lacan during the 1964–1965 academic year at the École Normale Supérieure (ENS) in Paris. Commonly referred to as Seminar XII, it follows immediately upon The Four Fundamental Concepts of Psychoanalysis and continues Lacan’s re-elaboration of Freud’s metapsychology by focusing on what he calls the “crucial problems” raised by the unconscious, repetition, transference and drive.

For Lacan, the fundamental issue remains the subject’s relation to language. In Seminar XII this problem is reconfigured by the systematic inclusion of the Real alongside the Symbolic and the Imaginary. The “crucial problems” now concern the way the Real limits and distorts the subject’s insertion in language, and how psychoanalysis can formalize this relation without reducing it to a psychology of consciousness. To this end Lacan introduces and develops a set of topological figures—among them the Moebius strip, the torus, the cross-cap and the Klein bottle—which are used to model the structure of the subject, the logic of demand, and the paradoxical continuity of inside and outside, love and hate, truth and appearance.

Seminar XII is widely regarded in Lacanian circles as marking the beginning of the fully “topological” phase of Lacan’s teaching. It consolidates notions such as extimacy (extimité), the idea that “the unconscious is outside,” and prepares later elaborations of fantasy and objet petit a in Seminar XIII: The Object of Psychoanalysis and Seminar XIV: La logique du fantasme.

Historical and institutional context

From Sainte-Anne to the École Normale Supérieure

Seminar XII belongs to the period immediately following Lacan’s exclusion from the list of training analysts of the International Psychoanalytical Association (IPA) in 1963 and his consequent departure from Hôpital Sainte-Anne, where his early seminars were delivered in a psychiatric hospital setting. From Seminar XI onward, Lacan’s teaching is hosted by the École Normale Supérieure on rue d’Ulm, a leading institution of French higher education with a strong tradition in philosophy, mathematics and the human sciences.

This new institutional context reinforces Lacan’s dialogue with structuralism, logic and topology, and further distances his teaching from the clinical and institutional routines of classical psychoanalytic societies. The audience at ENS included not only practising analysts but also philosophers, historians and mathematicians, which encouraged Lacan to articulate psychoanalytic concepts in more formal, and increasingly topological, terms.

The Act of Foundation and the École Freudienne de Paris

In 1964, between Seminar XI and Seminar XII, Lacan issued his “Act of foundation” (Acte de fondation) of the École Freudienne de Paris (EFP), a new psychoanalytic school whose stated aim was to ensure the transmission of Freudian psychoanalysis “in its purity.” Seminar XII unfolds in the first full academic year of the EFP and continually returns to questions of institutional structure, analytic training and the status of analytic knowledge.

The “crucial problems for psychoanalysis” are thus not only theoretical but institutional: how to organize a School so that knowledge (savoir) is not monopolized by a hierarchy of “masters,” how to formalize the pass as a procedure for testifying to analytic experience, and how to distinguish psychoanalysis from both religion and university discourse.

Place in the series of seminars

Seminar XII occupies a pivotal position between Seminar XI and Seminar XIII. Seminar XI presents the four fundamental concepts of psychoanalysis (unconscious, repetition, transference, drive) and introduces the Real as a distinct register. Seminar XII revisits these concepts from the standpoint of the difficulties they pose—for theory, for clinical technique, and for institutional organization—while Seminar XIII will focus more directly on objet petit a as the “object of psychoanalysis.”

Within Lacan’s teaching, the twelfth seminar is therefore often read as the place where the conceptual framework of the four fundamental concepts is subjected to a second-order reflection and is re-inscribed in a topological register.

Composition, transmission and textual status

Like many of Lacan’s seminars from the 1960s, Problèmes cruciaux pour la psychanalyse remains officially unpublished in a standardized, edited book form. The seminar is known from:

• stenographic notes taken by attendees,
• partial and complete French transcripts circulated within Lacanian Schools,
• and surviving audio recordings of certain sessions.

The lack of an official edition has made Seminar XII less accessible than some earlier and later seminars. Citations in the secondary literature typically refer to circulating French transcripts or to internal publications within Lacanian institutions. This textual situation is itself symptomatic of one of the “crucial problems” Lacan thematizes: the difficulty of stabilizing, without dogmatizing, a teaching that insists on the primacy of the unconscious and the contingency of transference.

Conceptual framework and methodology

Subject and language under the sign of the Real

For Lacan, “the fundamental problem is that of the subject’s relation to language.” Already in his earlier “Rome Discourse” (The Function and Field of Speech and Language in Psychoanalysis) he had argued that the unconscious is structured like a language. In Seminar XII he maintains this orientation, but insists that any adequate account of the subject’s relation to language must include the dimension of the Real.

Previously, Lacan notes, the crucial issues centred on the relations between identification, transference and demand. In Seminar XII, “taking into account the Real modifies the situation”: the question “will entail the holding out of a form, of an essential topology for analytic praxis.” The Real names what in the analytic experience resists symbolization and eludes the Imaginary; topology is invoked as a way of formalizing these limits within a rigorous conceptual schema.

The three registers and their “crucial problems”

Seminar XII presupposes the triad of Symbolic, Imaginary and Real, but the balance between them shifts. The Symbolic remains the register of signifiers, law and structure. The Imaginary remains linked to image, identification and narcissism. But the Real now appears not only as trauma or impossibility but as the point where the Symbolic and Imaginary meet their limit, a limit that can be approached but never fully captured.

The “crucial problems” of psychoanalysis arise at these points of tension:

• the limits of interpretation as a symbolic operation,
• the relation between analytic truth effects and knowledge (savoir),
• the place of jouissance and drive beyond the pleasure principle,
• and the question of how analytic praxis can be formalized without closing off the Real it confronts.

From language to topology

Lacan’s methodology in Seminar XII extends his earlier use of linguistics and structuralism by adopting topology as a privileged formal resource. Topological surfaces (Moebius strip, torus, cross-cap, Klein bottle) are introduced not as simple analogies but as non-intuitive constructions that can articulate structural properties of the subject’s relation to the Other, to demand and to the Real.

Lacan emphasizes that these figures, though constructed in a simple and combinatory way, are “nevertheless complicated to comment.” Their very resistance to intuitive visualization is taken as a guarantee that they “forbid imaginary capture”: unlike easily grasped images that may seduce the imagination, topological models must be reasoned through step by step, thereby preserving their status as formal structures.

Topological models and the structure of the subject

Moebius strip and the continuity of opposites

One of the most evocative figures discussed in Seminar XII is the Moebius strip, produced by giving a strip of paper a half-twist and joining its ends. The resulting surface has only one side and one edge, even though it appears to have two. For Lacan, the Moebius strip “subverts our normal (Euclidean) way of representing space,” because what seem to be opposed sides are in fact continuous.

The Moebius strip thus offers a model for the way psychoanalysis problematizes familiar binary oppositions: inside/outside, love/hate, truth/appearance, signifier/signified. The opposed terms are not radically distinct but “continuous with each other”: following the surface around, one passes from “inside” to “outside” without any identifiable point of crossing. The distinction between sides is temporal; it depends on the time it takes to traverse the strip.

Lacan connects this to the fantasy and its later “traversing.” Because the “two sides” of the fantasy—imaginary scene and Real kernel—are continuous, the subject can in principle cross from one to the other. Yet, phenomenologically, it is impossible to pinpoint when this passage is accomplished: the subject discovers after the fact that the framework which sustained their sense of reality has been transformed.

Torus, decentering and extimacy

Seminar XII also emphasizes the torus, a ring-shaped three-dimensional object formed by joining the ends of a cylinder. Lacan uses the torus to model certain features of the structure of the subject. The center of gravity of a torus lies outside its volume: in an analogous way, the “center” of the subject is “outside” itself, determined by signifiers and objects located in the Other. The subject is thus decentered or ex-centric.

Moreover, on a torus the central “hole” and the exterior region form a single continuous area. This serves to illustrate Lacan’s notion of extimacy (extimité), according to which the unconscious is both intimate and external: not an interior “thing” but an intersubjective structure inscribed in the field of the Other. As Lacan famously puts it, “the unconscious is outside.” The topological continuity of interior “void” and exterior space on the torus provides a formal model of this paradox.

From this perspective, the usual distinction between container and contained is called into question. A common understanding of structure opposes directly observable contingencies to “deep” phenomena that lie behind experience. Lacan challenges this opposition: observation is always already theorically mediated, and structure is present in the field of experience itself. The unconscious lies “on the surface,” and searching for it in imaginary “depths” is to miss it—just as focusing on the “inside” of the Moebius strip or the torus misses the continuity of the surface.

Cross-cap, projective plane and “holes”

Lacan also employs the cross-cap, a model of the projective plane, to introduce the idea of a surface with only one side, on which every line ultimately intersects itself. The cross-cap and associated Euler circles allow him to formalize how zones of the subject’s experience (for example, desire, demand, jouissance) can overlap and interpenetrate without reducing to one another.

Within these topological discussions, the notion of the “hole” becomes central. Holes in a surface model structural lacks: the lack in the Other, the absence of a signifier, the constitutive gap (béance) that defines the subject. Seminar XII insists that these holes cannot simply be “filled in” with additional meaning; they are structural features of the field and must be reckoned with as such.

Klein bottle, demand and the spiral

The Klein bottle—a non-orientable, closed surface that, like the Moebius strip, has only one side—appears in Seminar XII in connection with the “spiral of demand” and the maze of the torus. Demand enters the field of the Other and returns to the subject in a transformed guise; its trajectory can be modelled as a spiral on the surface of a torus or Klein bottle, where inside and outside intertwine.

These models underscore the way the subject’s relation to demand cannot be understood within a simple inside/outside or self/other opposition. Demand is always already inscribed in the Other’s discourse, and the subject encounters its own position as an effect of a trajectory that loops through the Other.

Topology as “structure itself”

Lacan’s interest in topology stems from his conviction that it provides a non-intuitive, purely intellectual means of expressing structure. Unlike intuitive images, in which perception risks eclipsing structure, topological models “forbid imaginary capture”: there is, he suggests, “no hidden of the Symbolic” in them. Everything is given in the construction and cutting of the surface.

For this reason Lacan insists that topology is not a mere metaphor for structure; it is structure itself. In Seminar XII, topology progressively displaces language as the primary paradigm of structure, even as it remains deeply connected to linguistic notions such as the signifier, metaphor and metonymy.

Subjectivity, fantasy and decentering

Fundamental fantasy and the frame of reality

Seminar XII contributes to Lacan’s redefinition of fantasy (fantasme) as more than a mere imaginary fiction opposed to reality. Fantasy is conceived as the “frame” that allows the subject to experience reality as such: it is “that little piece of imagination by which the subject gains access to reality,” the scenario through which the subject organizes the field of jouissance and of the Other’s desire.

Against the basic opposition between reality and imagination, fantasy is not simply on the side of the latter; it conditions the subject’s sense of what “really exists out there.” When the fundamental fantasy is shattered—whether in psychotic breakdown or in certain analytic experiences—the subject suffers a loss of reality itself. Reality is revealed as dependent on the fantasmatic frame that had previously gone unnoticed.

Traversing the fantasy

The later notion of the “traversing of fantasy” (la traversée du fantasme), more explicitly thematized in Seminar XIV: La logique du fantasme, is often read as foreshadowed in Seminar XII. The topological figures of the Moebius strip and Klein bottle provide models for such a traversal: because “inside” and “outside” belong to a single surface, it is possible in principle to follow a path that leads from one side of the fantasy to the other.

Later commentators, especially Slavoj Žižek, develop these hints into a broader theory. For Žižek, traversing the fantasy does not mean a sober stripping away of illusions so as to see reality “as it really is” but an act that disturbs the subject’s fundamental fantasy and “unhinges the level that is even more fundamental than basic symbolic identifications.” In this reading, traversing the fantasy involves a kind of over-identification with the field of imagination, through which the subject breaks the constraints of fantasy and confronts a terrifying, pre-synthetic field of fragmented bodily and signifying elements (disjecta membra) not yet unified by a fantasmatic frame.

While Lacan himself does not yet use the full formula $ \lozenge a$ in Seminar XII, the seminar’s emphasis on topology, extimacy and the Real prepares the ground for this later formalization of fantasy as the relation between the barred subject ($) and object a.

Gap (béance), empty subject and object a

In Seminar XII Lacan intensifies his emphasis on the structural “gap” (béance) that defines the subject. Subjective experience is not simply regulated by unconscious mechanisms “behind” self-experience; it is regulated by the very inaccessibility of the fundamental fantasy that sustains self-experience. When this fantasy is withdrawn, what remains is an “empty” subject, marked only by the effects of signifiers and by its relation to object a.

Later Lacanian notation will write the structure of fantasy as $ \lozenge a$, where the subject ($) is linked to object a through a relation of framing and masking. Seminar XII anticipates this by emphasizing that what characterizes human subjectivity is the gap between phenomenal self-experience and the non-phenomenal subject of the unconscious. There is an “impossible rapport” between the empty subject and the inaccessible phenomena of jouissance: a rapport that can only be registered in the articulation of fantasy and in its transformations in analysis.

Key themes and “crucial” problems

Analytic knowledge and the subject supposed to know

Seminar XII continues Lacan’s reflection on the subject supposed to know (sujet supposé savoir), a central notion in his theory of transference. In analysis, the analysand supposes that the analyst “knows” the meaning of their symptoms and dreams; this supposition grounds the transference. However, this knowledge is structurally linked to the unconscious, which “knows more than the subject” but only appears in gaps, slips and formations of the unconscious.

The “crucial problem” is the status of this knowledge: is it scientific, doctrinal, experiential? Seminar XII explores the idea that analytic knowledge is a knowledge of the structure of discourse and of the subject’s position in it, a knowledge that emerges in and through the analytic experience rather than pre-existing it as a set of doctrines.

Desire of the analyst and object a

Linked to the problem of knowledge is the question of the desire of the analyst. The analyst is not simply an interpreter who “applies” knowledge; their position must be formalized structurally. Seminar XII underlines that the analyst’s desire should not aim at normalization or adaptation but at sustaining the lack in the Other and allowing object a to function as cause of desire in the analysand.

This position is often described as the analyst occupying the place of object a: a position of radical decentering, from which the analyst refrains from filling in the subject’s lack with imaginary identifications or master-signifiers. The topological models of Seminar XII help formalize this decentered position as a point on the “surface” of discourse that is neither inside nor outside but “extimate.”

Science, religion and the Real

Continuing a line of thought in Seminar XI, Lacan in Seminar XII interrogates the relation between psychoanalysis, science and religion. Psychoanalysis emerges historically from Freud’s scientific ambitions, yet its institutionalization risks reproducing religious forms (orthodoxy, heresy, canonical texts). Lacan’s insistence on the Real introduces another complication: science too encounters a Real (for example, in quantum physics or Gödelian incompleteness) that resists complete formalization.

Seminar XII frames the “crucial problem” as how psychoanalysis can articulate its relation to the Real in a way that avoids both positivist scientism and religious dogmatism. Topology plays a mediating role here as a rigorous formalism that can register impossibilities and holes without positing a transcendent guarantee.

Training, School and the pass

Because Seminar XII coincides with the early years of the École Freudienne de Paris, questions of training and institutional structure are never far from view. Lacan reflects on the role of control analysis, on the difficulty of assessing the “end of analysis,” and on the institutional mechanisms that might allow the School to recognize analysts while respecting the singularity of each analytic experience.

These discussions foreshadow Lacan’s later introduction of the pass (1967) as a procedure by which an analysand, at the presumed end of their analysis, gives testimony about their experience to a small jury, who then report to the School. The pass is conceived as a structural device to address one of the “crucial problems for psychoanalysis”: how to transmit analytic knowledge without reifying it into dogma.

Theoretical significance and clinical implications

Topology and clinical structures

Seminar XII does not propose new categories of clinical structure (the tripartition neurosis, psychosis and perversion is already in place), but it rethinks these structures topologically. Rather than conceiving them simply as types or as defensive styles, Lacan invites analysts to consider how different “cuts” and “holes” in the subject’s surface correspond to different relations to the Other, to lack and to object a.

This topological re-articulation has implications for clinical diagnosis and for the reading of symptoms. In later Lacanian work, for example, the use of Borromean knots and other linkages will elaborate this approach, but Seminar XII is often seen as the crucial moment when topology becomes integral to the conceptualization of structure.

Interpretation, surface and the Real

For analytic technique, Seminar XII underscores that interpretation is less a matter of supplying hidden meanings than of making cuts in the subject’s discursive surface, producing new connections and disconnections. The topological figures suggest that an interpretation can be compared to a cut that, when re-stitched, transforms the global shape of the subject’s “surface” without adding new material.

The Real, in this context, is what appears at the edges and holes that interpretation cannot close. The analyst must be attentive not to “patch” these holes with imaginary solutions but to let them function as structuring points in the subject’s discourse, around which new positions vis-à-vis desire and jouissance can be articulated.

End of analysis and traversing the fantasy

Although Seminar XII does not offer a full-fledged doctrine of the end of analysis, it consolidates an orientation that will later be expressed in terms of the traversing of the fantasy: the end of analysis involves a decisive shift in the subject’s relation to the fundamental fantasy and to object a.

In contrast to ego psychology’s emphasis on “ego-strengthening,” Lacan suggests that the end of analysis is marked by the subject’s assumption of their division and their relation to lack, by a transformation in their relation to the Other’s desire, and by a different positioning vis-à-vis the Real of jouissance. Seminar XII’s topological models provide one of the first extensive frameworks for thinking this transformation in terms of surfaces, cuts and holes rather than in terms of psychological “integration.”

Reception and legacy

Within Lacanian psychoanalysis

Within Lacanian schools, Seminar XII is regarded as a key text in the development of Lacan’s topological formalization. Its elaborations of the Moebius strip, torus, cross-cap and Klein bottle have been widely used in training programmes, internal publications and commentaries as exemplary of Lacan’s attempt to “forbid imaginary capture” and to articulate the Real in a structural way.

At the same time, the seminar’s unpublished status and technical difficulty have limited its circulation relative to more accessible texts such as Écrits and Seminar XI. Many references to Seminar XII in the literature are indirect, filtered through later seminars (especially Seminar XIII and Seminar XIV) or through secondary works that summarize its central themes.

In philosophy, literary theory and cultural studies

In the broader humanities, the influence of Seminar XII is often mediated by later thinkers who draw on its concepts. Philosophers and cultural theorists such as Slavoj Žižek, Jean-Michel Rabaté and others have emphasized the importance of Lacan’s topology and of notions like extimacy for rethinking the status of the subject, the Real and ideological fantasy.

Žižek in particular makes extensive use of topological figures like the Moebius strip and the Klein bottle as models for paradoxical subject positions and for the way “inside” and “outside” are intertwined in ideology and enjoyment. While not always citing Seminar XII explicitly, his readings often echo its central motifs: the continuity of opposites, the decentering of the subject and the function of fantasy as the frame of reality.

Critiques and debates

Seminar XII has also been a point of reference in debates about the role of formalism in Lacanian psychoanalysis. Some critics argue that the increasing reliance on topology risks drifting away from clinical material and becoming an abstract game; others counter that topology provides a necessary antidote to imaginary and phenomenological reductions of analytic concepts.

Questions have also been raised about the mathematical rigour of Lacan’s topological constructions and about the legitimacy of applying these models to clinical phenomena. Nonetheless, even critics often concede that Seminar XII represents a significant and ambitious attempt to articulate psychoanalytic concepts in a way that takes seriously the Real as a structural impossibility rather than as a merely empirical unknown.

See also

• Jacques Lacan
• Seminar XI
• Seminar XIII
• Real
• Symbolic order
• Imaginary order
• Objet petit a
• Extimacy
• Moebius strip
• Torus
• Klein bottle
• Topology
• Fantasy (psychoanalysis)
• Traversing the fantasy
• Subject supposed to know
• Desire of the analyst
• École Freudienne de Paris

Further reading

• Lacan, Jacques. Le Séminaire, Livre XII : Problèmes cruciaux pour la psychanalyse (1964–1965). Unpublished seminar; French transcripts and recordings circulated in Lacanian institutions.
• Lacan, Jacques. The Four Fundamental Concepts of Psychoanalysis. Trans. Alan Sheridan. New York: W. W. Norton, 1977.
• Lacan, Jacques. Écrits. Paris: Seuil, 1966; Écrits: The First Complete Edition in English, trans. Bruce Fink. New York: W. W. Norton, 2006.
• Freud, Sigmund. The Interpretation of Dreams. In The Standard Edition of the Complete Psychological Works of Sigmund Freud, vols. IV–V.
• Freud, Sigmund. Beyond the Pleasure Principle. In Standard Edition, vol. XVIII.
• Freud, Sigmund. “Instincts and Their Vicissitudes.” In Standard Edition, vol. XIV.

• Evans, Dylan. An Introductory Dictionary of Lacanian Psychoanalysis. London/New York: Routledge, 1996.
• Fink, Bruce. The Lacanian Subject: Between Language and Jouissance. Princeton, NJ: Princeton University Press, 1995.
• Fink, Bruce. A Clinical Introduction to Lacanian Psychoanalysis: Theory and Technique. Cambridge, MA: Harvard University Press, 1997.
• Roudinesco, Élisabeth. Jacques Lacan. Trans. Barbara Bray. New York: Columbia University Press, 1997.
• Rabaté, Jean-Michel (ed.). The Cambridge Companion to Lacan. Cambridge: Cambridge University Press, 2003.
• Žižek, Slavoj. The Sublime Object of Ideology. London/New York: Verso, 1989.