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Lacan Seminar 1965 object a

The Seminar of Jacques Lacan, Book XIII: The Object of Psychoanalysis (alt. translation)

Jacques Lacan

by Jacques Lacan

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Synopsis

Lacan's Seminar 13, "The Object of Psychoanalysis" (1965–1966), pursues a sustained and technically rigorous elaboration of the objet petit a as the structural cause of desire — the "rejected stone" that psychoanalytic practice encounters everywhere yet has never properly theorised. The seminar's central argument is that the o-object cannot be understood through the lens of object-relations theory (which collapses the Symbolic into a Real-Imaginary opposition), nor through any representational or perceptual register (since it is constitutively non-specularisable), but only through the combinatorial resources of topology and projective geometry, which alone can formalise the subject's constitutive split and the way the object both causes and eludes desire. Lacan moves through a series of theoretical stations — Frege's logic of zero and the suture, the Möbius strip, torus, cross-cap and Klein bottle, Pascal's Wager as a model of the subject's relation to lack and infinity, Jones's concept of aphanisis and feminine sexuality, Dante's Divine Comedy as an unwitting topology of the o-object, and Velázquez's Las Meninas as a structural diagram of the scopic drive and the gaze — each of which illuminates a different facet of the same central problematic. The seminar also develops the distinction between the four partial objects (breast, faeces, gaze, voice) and insists that the gaze and voice, as objects at the level of desire rather than merely demand, require a topology that goes beyond Freudian–Kleinian object-relations. Running through these analyses is a sustained critique of Hegelian dialectics (specifically the master/slave account of jouissance), a productive engagement with Foucault's archaeology of representation, and a preview of the tripartite RSI framework and the "logic of fantasy" that will dominate subsequent seminars. The seminar closes by positioning castration not as Oedipal prohibition alone but as the structural barrier that introduces a negative sign onto the phallus and makes possible — always asymmetrically — the encounter between masculine and feminine jouissance.

Distinctive contribution

Seminar 13 is the most sustained and technically dense treatment of topology as psychoanalytic method in the entire Lacanian corpus. While Seminar 11 (Four Fundamental Concepts) introduces the gaze and the scopic drive with remarkable conceptual force, it does so largely through clinical and phenomenological argument. Seminar 13 goes further by grounding these same structures in projective geometry: the seminar constructs an explicit account of how the two "subject poles" of a perspective picture — the vanishing point and the point at infinity — formalise the barred subject's double presence/absence within any representational field, and it uses this construction to argue that topology is not a metaphor for psychoanalytic structure but its very substance, the material into which the analyst cuts. The sustained engagement with Velázquez's Las Meninas across four consecutive sessions (with Foucault as interlocutor) is without parallel in Lacan's teaching: the painting is not treated as an illustration but as a structural proof — a "trap for the look" that demonstrates in a non-metaphorical way why the o-object cannot appear in the specular field and why the Other (figured by the monarchical gaze of the absent King and Queen) must be empty in order to function as the support of truth.

The seminar is also distinctive in its historical-materialist dimension. Lacan's travelogue of the United States and Mexico (Seminar 12) is deployed to articulate a structural distinction between two modes of the past: an inert, sedimented past without repetition (American suburbia) versus a past structured by repetition (the properly psychoanalytic dimension). More significantly, the seminar offers an original historical argument about the preconditions for modern science: it was the "reserved park of jouissance" delegated to slaves in the ancient world — not any theoretical lack — that prevented the emergence of the Cartesian subject of science and thus of psychoanalysis. This positions jouissance not merely as a clinical concept but as a historical-economic category, linking Socrates, Freud, and the birth of modern science through a single structural thread. No other seminar in this period develops this historical-structural argument in quite this way, and it anticipates the analysis of capitalism and discourse that will become central in Seminar 17.

Main themes

  • Objet petit a as cause of desire and non-specularisable remainder
  • Topology (Möbius strip, torus, cross-cap, Klein bottle, projective plane) as the non-metaphorical substance of psychoanalytic structure
  • The gaze as objet a and the scopic drive: from Las Meninas to perspectival geometry
  • Pascal's Wager as a structural model of the subject's relation to lack, infinity, and the divided Other
  • Jouissance as historical-structural category: the ancient reservation of jouissance and the birth of science
  • Critique of object-relations theory and the Hegelian master/slave dialectic
  • Castration as the barrier of desire that bars the subject from jouissance, and the phallus as signifier of loss
  • The Subject Supposed to Know and the analyst's position of epistemic scepticism
  • Feminine sexuality, aphanisis, and the woman's relation to the phallus as objet a
  • Knowledge and truth: the double-truth doctrine, modern science, and psychoanalysis as their structural heir

Chapter outline

  • Seminar 1 (1 December 1965): Science and Truth [reconstructed from cross-references] — p.1
  • Seminar 2 (8 December 1965): The Subject and Lack — p.2-6
  • Seminar 3 (15 December 1965): Topology and the Subject — p.7-27
  • Seminar 4 (22 December 1965): André Green on the O-Object — p.28-45
  • Seminar 5 (5 January 1966): The O-Object — p.59-71
  • Seminar 6 (12 January 1966): Subject of Science and of Psychoanalysis — p.72-83
  • Seminar 7 (19 January 1966): Mirror Stage and the Divine Comedy — p.84-101
  • Seminar 8 (26 January 1966): Discussion on Conrad Stein's Work — p.99-117
  • Seminar 9 (2 February 1966): Pascal's Wager I — p.118-133
  • Seminar 10 (9 February 1966): Pascal's Wager II — p.130-137
  • Seminar 12 (23 March 1966): Lacan on America — p.139-150
  • Seminar 14 (20 April 1966): Summary of Crucial Problems; Jouissance — p.152-163
  • Seminar 15 (27 April 1966): Jones' Female Sexuality — p.164-181
  • Seminar 16 (4 May 1966): Visual Structure of the Subject — p.182-201
  • Seminar 17 (11 May 1966): Perspective — Las Meninas I — p.194-214
  • Seminar 18 (18 May 1966): Michel Foucault — Las Meninas II — p.211-229
  • Seminar 19 (25 May 1966): Summary of Object of Psychoanalysis — Las Meninas III — p.230-245
  • Seminar 20 (1 June 1966): Re-thinking Freud — Las Meninas IV — p.242-251
  • Seminar 21 (8 June 1966): Jouissance and Castration — p.252-272
  • Seminar 22 (15 June 1966): O-Objects — Safouan's Case; Perversion and Methodology — p.273-288

Chapter summaries

Seminar 1 (1 December 1965): Science and Truth [reconstructed from cross-references] (p.1)

This opening session, referenced throughout the seminar as a 'written lecture' distributed in roneotyped form, establishes the year's governing thesis: psychoanalysis originates from science and stands in a unique and fractured relationship to truth. Lacan introduces the Cartesian cogito as the inaugural moment of the subject of science — 'I think, therefore I cease to be' — and distinguishes this modern scientific subject from all earlier philosophical articulations of the knowing subject. The session also introduces the distinction between knowledge and truth that will organise the entire seminar, positing the o-object as what occupies the field of intersection between these two registers, represented heuristically via Euler circles but warned against being read as literally extensional.

Key concepts: Subject of science, Cogito, Knowledge/truth distinction, Objet petit a, Signifier, Alienation Notable examples: Descartes' Cogito

Seminar 2 (8 December 1965): The Subject and Lack (p.2-6)

Lacan opens with a methodological reflection on the difference between his spoken and written teaching, using this to introduce the claim that his cogito might better be formulated as 'I think, therefore I cease to be.' He then elaborates the seminar's governing schema: a small graph in which the signifier is related to its phonematic, indicative, and imitative poles, with the logical resultant at the end of the horizontal axis providing the basis for science's relationship to truth. The session revisits the logic of the unary trait and the function of zero as 'one missing,' positioning the scientific object as essentially metonymic: the constancy of a number is always the constancy of a lack elsewhere. The cave-man who 'connotes one missing' is already a set-theorist, and the object of science is always the object as lacking.

Key concepts: Signifier, Unary trait, Subject of science, Lack, Object as lack, Metonymy Notable examples: Conservation of energy; Frege's logic of zero

Seminar 3 (15 December 1965): Topology and the Subject (p.7-27)

This session introduces the topological figures that will structure the entire year: the Möbius strip, its cuts, and the resulting non-specularisable residue. Lacan begins with Euler circles (used metaphorically to show the intersection of knowledge and truth) and transitions to a Buddhist monk's knotted diagrams as evidence that 'writing' and meditation share a structural logic. He then argues that the sphere is an inadequate model for the subject: spherical space, the homogeneous Cartesian extension, supports the mirror illusion of a central subject adequately reflecting a peripheral world. Against this, the Möbius strip provides a non-orientable surface in which the cut is itself the strip — the subject is the division, not a substance divided. The session argues that cutting the Möbius strip in its centre does not destroy it but produces a strip applicable to the torus, which Lacan identifies with the barred subject ($), while the discal residue models the o-object as non-specular and non-representable.

Key concepts: Möbius strip, Torus, Cross-cap, Topology, Splitting of the Subject, Objet petit a Notable examples: Jiu Oun's Buddhist diagrams; Möbius strip cuts

Seminar 4 (22 December 1965): André Green on the O-Object (p.28-45)

This session is devoted to a lecture by André Green, 'J. Lacan's o-object, its logic, and Freudian theory,' which provides a systematic overview of the o-object's trajectory through Lacan's earlier schemas: from the mirror-stage graph (o as mediation between subject and Other), through Schema R (o as mediation between subject and ego ideal), to the o-object as cause of desire. Green argues that Lacan, unlike object-relations theorists, valorises the negative dimension of the object: it is the witness and veil of lack (the fetish as paradigm), the non-representable cause of desire (the agalmata of Alcibiades in the Symposium), and the remainder produced by the operation of the signifier on lack. Green also raises the question of suture — whether the signifying chain sutures over the lack it opens — and introduces Frege's logic (via Miller) to show how the subject's exclusion from the signifying chain mirrors the zero-object's ambiguous status as both exclusion and first object.

Key concepts: Objet petit a, Mirror Stage, Schema R, Suture, Fetish, Cause of desire Notable examples: Alcibiades and the agalmata in Plato's Symposium; Frege's zero-object (via Miller); Hamlet (Polonius on cause and remainder)

Seminar 5 (5 January 1966): The O-Object (p.59-71)

Lacan returns to the problem of why the o-object, omnipresent in clinical practice, has never been properly theorised. The difficulty, he argues, is structural: the o-object is constitutively invisible in the world of vision because it is what organises that world — the eye cannot see what enables it to see. He attacks the 'pre-genital object' as a mythical substitute that garbles the structure. Moving to topology, he returns to the torus as the structure that allows us to exit the homogeneous spherical space of Cartesian extension. The torus models the relationship between demand and desire: any loop around the inner void of the torus requires at least two loops around the outer void, so that desire always presupposes at least two demands and a demand at least two desires. This structural description is deployed against the fantasy of auto-erotic fusion ('primary narcissism' as the remainder of the old theory of knowledge) and prepares the ground for the Möbius strip's role in modelling the subject.

Key concepts: Objet petit a, Torus, Demand, Desire, Topology, Mirror Stage Notable examples: Torus model of demand/desire relationship

Seminar 6 (12 January 1966): Subject of Science and of Psychoanalysis (p.72-83)

This session addresses the theoretical status of Lacan's topology, arguing that it claims to be scientific — demonstrably not myth — precisely because it is constructed by cuts and combinations rather than by meaning-effects. Lacan returns to the topology of the torus and its cuts: one circuit on the torus reveals the gap between the two holes; two circuits envelope the structure. He distinguishes the Möbius strip's lining — which requires two circuits to duplicate it — from the sphere's lining (one circuit), and shows that the surface produced by cutting the Möbius strip is applicable to the torus and structurally models the barred subject. The session also engages the Stoic logic of aletheia (truth as that which cannot be revealed without hiding itself) and Heidegger's account of Being, arguing that psychoanalysts have more to say about aletheia than Heidegger does about Sein, because the o-object provides a non-metaphorical account of the truth-structure that philosophy only approximates.

Key concepts: Topology, Möbius strip, Torus, Truth, Signifier, Alienation Notable examples: Stoic aletheia; Heidegger on Sein

Seminar 7 (19 January 1966): Mirror Stage and the Divine Comedy (p.84-101)

Lacan reads Roger Dragonetti's article 'Dante et Narcisse ou les faux monnayeurs de l'image' through the lens of his topology of the o-object. The Narcissus myth, structuring Dante's entire Divine Comedy, is deployed to show how the subject mistakes the image-of-nothing for the real — the 'counterfeit' structure that Lacan identifies with conscience itself (malice as the originary falsification of the image). In Hell, Master Adam's counterfeit florins (gold alloyed with base metal, the 'mirror of Narcissus' as hardened reflection) figure the fraudulent identification of the image with truth. In Paradise, the 'error contrary to Narcissus' — confusing real apparitions for reflected images — maps the o-object's apparition in the field of God: objects appear there as transparent against a background of transparency, non-specular, images of nothing. Lacan uses this to argue that when the o-object appears, if there is a mirror, nothing is reflected in it — precisely the non-specularisability that defines the o-object. The session links this to the structure of courtly love and the Beatrice figure, via the terms I (ego ideal), o (o-object), i(o) (specular image), and $.

Key concepts: Objet petit a, Mirror Stage, Narcissism, Gaze, Imaginary, Truth Notable examples: Dante's Divine Comedy; Narcissus myth; Master Adam the counterfeiter; Beatrice and courtly love

Seminar 8 (26 January 1966): Discussion on Conrad Stein's Work (p.99-117)

This closed session is devoted to a critical dialogue with Conrad Stein's theory of narcissistic regression in the analytic situation. Stein argues that in ideal analysis both patient and analyst enter a state of primary narcissistic fusion ('it speaks'), which is broken by the analyst's word acting as a cut that restores the subject-object duality. Lacan's interlocutors (Conté, Melman, Green) press Stein on whether this framework — organised essentially around a Real-Imaginary opposition — can accommodate the properly Symbolic dimension, and whether 'narcissistic myth' (conscious, the analyst as idol) can be distinguished from 'narcissistic phantasy' (unconscious). Lacan intervenes to establish a grammar of predication: the 'he speaks' (formal-symbolic), the 'it speaks' (imaginary, where predicating subject and subject of predicate collapse into one), and the analyst's word as that which operates from a place irreducible to the transference position — constituting desire through a Verneinung (denial) rather than Bejahung (affirmation). The session introduces the Subject Supposed to Know as the patient's structural trap for the analyst's epistemological drive.

Key concepts: Narcissism, Subject Supposed to Know, Imaginary, Big Other, Transference, Demand Notable examples: Conrad Stein's theory of narcissistic regression

Seminar 9 (2 February 1966): Pascal's Wager I (p.118-133)

Lacan introduces Pascal's Wager as a structural model for the subject's relationship to the o-object, lack, and the divided Other. The 'epistemophilic drive' — the desire to enjoy truth — is shown to be mythical (plutôtmythique), a pun combining 'rather mythical': the analyst is the Subject Supposed to Know, but this supposition is itself what obliges the analyst to be deceived, since truth cannot be enjoyed. Lacan reads Pascal's preliminary argument about infinity — we know the infinite exists without knowing its nature, just as numbers are neither all even nor all odd — as establishing the structure of the divided Other: the infinity that opens at the level of lack is the real infinity dissimulated behind the indefinite. The session also introduces the distinction between being and existence (Avicenna, Aristotelian-religious thought) as the philosophical antecedent of the subject's structural division, and gestures toward the God of Pascal ('not the God of the philosophers but the God of Abraham, Isaac, and Jacob') as a figure of the Other that cannot be assimilated to the supreme being.

Key concepts: Subject Supposed to Know, Pascal's Wager, Lack, Big Other, Jouissance, Truth Notable examples: Pascal's Wager; Pascal on infinity and God; The Parcae (Clotho, Lachesis, Atropos)

Seminar 10 (9 February 1966): Pascal's Wager II (p.130-137)

Lacan completes his reading of Pascal's Wager by showing that the stake is not happiness in the ordinary sense but the o-object itself: what is wagered is the existence of the partner (the divided Other), and what is placed on the other side is precisely the object as cause of desire — apparently nothing, but structurally everything. Feminine masochism is introduced as the 'profile of jouissance reserved for the one who enters the world of the Other insofar as this Other is feminine Other, namely Truth'; the woman is not narcissistic in the sense of seeking to be i(o), but the world puts her in the position of the o-object, which she 'energetically refuses.' Lacan develops the three distances (philosophical, religious, psychoanalytic) at which the search for truth can be situated, and reads Pascal's doctrine of predestination and grace as anticipating the psychoanalytic account of the subject's constitutive encounter with an Other that cannot guarantee its own truth. The session connects chance (Pascal's 'rule of parts,' the gambler's passion) to the real as what science touches at its limit — the point of absolute chance.

Key concepts: Pascal's Wager, Jouissance, Objet petit a, Feminine sexuality, Real, Truth Notable examples: Pascal's Wager; Acteon myth; Communion of saints; Life as a dream theme

Seminar 12 (23 March 1966): Lacan on America (p.139-150)

After an absence for a US visit, Lacan delivers an open seminar reflecting on his American experience as a structural lesson. The key theoretical distinction is between two modes of the past: a 'past without repetition' — the inert, fully settled American suburban milieu, where the past exists in a state of hyper-perfection (universities more perfectly preserved than they were in fact, Impressionist paintings frozen like flies in amber) — versus a past structured by repetition, which is the properly psychoanalytic dimension. America, he argues, offers a retroactive figure of everything that failed in the past, an adherence to something never actually lived. Mexico by contrast (through Diego Rivera's fresco on the Alameda) presents the caricature of this clinging to an idealized, unlivable past. The session also contains a vigorous critique of a philosophical misappropriation of his teaching and a methodological defence of his structuralist programme against the dilution of 'structuralism' as a fashionable rubric.

Key concepts: Real, Repetition, Subject, Knowledge, Signifier, Truth Notable examples: Pop Art and Op Art; University of Chicago; Diego Rivera's Alameda fresco

Seminar 14 (20 April 1966): Summary of Crucial Problems; Jouissance (p.152-163)

Returning from vacation, Lacan reads and comments on his published summary of the preceding year's seminar (Crucial Problems for Psychoanalysis), using it as a hinge between that seminar and the current one. The summary reaffirms that 'the being of the subject is split' — Freud's repeated discovery that the unconscious has the structure of language — and introduces the analytic experience as requiring a 'radical, structural, absolutely total recasting of the topology of the question.' The session is pivotal for the introduction of the voice as an o-object: Lacan argues that its status has not yet been established clinically, and uses the example of Schreber and Socrates's daimon to show that the voice is a structural rather than sensorial phenomenon. He then makes the historical-structural argument that jouissance was 'resolved' in the ancient world by being delegated to slaves, and that this reserved park of jouissance — not any theoretical lack — prevented the emergence of the subject of science and of psychoanalysis. The analyst's implication in the symptom (as a being of knowledge and truth simultaneously) is compared to Oedipus before the Sphinx.

Key concepts: Jouissance, Voice, Subject of science, Splitting of the Subject, Knowledge, Truth Notable examples: Schreber's voices; Socrates's daimon; Oedipus and the Sphinx

Seminar 15 (27 April 1966): Jones' Female Sexuality (p.164-181)

Mademoiselle Grazien presents Jones's 1927 article 'The early development of female sexuality,' which Lacan uses to develop the concepts of aphanisis and feminine jouissance. Jones's concept of aphanisis — the total, irrevocable disappearance of all capacity for sexual pleasure — is read by Lacan as a precursor of the subject's fading ($) but also as a failed articulation, since Jones stops at the phenomenological level without grasping the structural dimension. The session argues that orgasm should be understood not as the essence of jouissance but as a privileged surface-point where jouissance 'surfaces' on the Klein bottle of the subject. Feminine sexuality is approached through the torus: jouissance of femininity in the fullest sense arises from a homosexual structure in which the woman, rather than retaining the father-object (becoming rivalrous with men, claiming the phallus), takes the place of the phallus as objet a — 'giving what she does not have.' This is the structural high point of love.

Key concepts: Aphanisis, Jouissance, Feminine sexuality, Phallus, Objet petit a, Torus Notable examples: Jones's aphanisis; Jones's father-daughter couple; Klein bottle topology; Proust

Seminar 16 (4 May 1966): Visual Structure of the Subject (p.182-201)

Lacan initiates the seminar's sustained engagement with the scopic drive and projective geometry. Against the spherical, homogeneous Cartesian space and the optical model of representation as a point-by-point doubling of the object, he proposes that topology — specifically the structure of the screen — is what psychoanalytic experience reveals as the foundation of the visual world. The session introduces projective geometry's principle of duality (Pascal's and Brianchon's theorems are dual: substitute 'point' for 'line' and vice versa) as the model for understanding how a combinatorial system can generate representations without requiring a unifying subject at its centre. The screen, not the eye or light, is the founding structure of analytic experience: what is seen does not reveal but hides something. The session also introduces the two 'subject poles' of perspective — the vanishing point (the eye inscribed inside the picture) and a second, hidden point at infinity — as the formal articulation of the barred subject's double presence/absence.

Key concepts: Scopic Drive, Gaze, Topology, Projective geometry, Screen, Splitting of the Subject Notable examples: Pascal's theorem / Brianchon's theorem; Desargues's geometry; Alberti and Dürer on perspective

Seminar 17 (11 May 1966): Perspective — Las Meninas I (p.194-214)

Lacan turns to Velázquez's Las Meninas as the exemplary structural demonstration of the scopic drive and the gaze as objet a. He begins with an account of the 'knower' (savant) and how the preservation of the status of knowledge distorts the content of knowledge — a critique that prepares the ground for the analyst's need to occupy a different position. He then develops the perspectival analysis of Las Meninas: the painting is not a representation but a 'trap for the look' in which the painter shows himself unable to reach the canvas (the distance between Velázquez and the picture being a 'capital point'), while the mirror at the back — reflecting the King and Queen — is shown to be structurally incompatible with the hypothesis that the painter is painting himself from a mirror. The session argues against the thesis that the large canvas in the picture is a portrait of the royals, and identifies the central figure — the Infanta — as the hidden object (the 'slit,' a structural term) around whose presence the whole economy of vision is organised.

Key concepts: Gaze, Objet petit a, Scopic Drive, Mirror Stage, Fantasy, Splitting of the Subject Notable examples: Velázquez, Las Meninas; Perspective theory (Alberti, Vignola, Dürer, Panofsky)

Seminar 18 (18 May 1966): Michel Foucault — Las Meninas II (p.211-229)

Foucault attends as a guest, and the session consists of a dialogue between Lacan's structural-topological reading of Las Meninas and Foucault's archaeological reading in the first chapter of Les mots et les choses. Lacan credits Foucault's conclusion — that the picture is a 'representation of the world of representations,' the infinite system of reciprocal application characteristic of classical thought — and accepts it as a historically accurate account of what the painting maps in the epistemic order of the seventeenth century. But Lacan insists that a structural supplement is required: projective geometry shows that the subject is not external to the picture but inscribed within it at two points (the vanishing point and the hidden point at infinity). The 'representative of the representation' (Vorstellungsrepräsentanz) is thus not simply an epistemological category but a topological one, and the interval between picture-plane and fantasy-plane is the only genuine Dasein of the divided subject. The session closes with Velázquez's formula — 'you do not see me from where I am looking at you' — as the fundamental formula of the scopic drive.

Key concepts: Gaze, Objet petit a, Scopic Drive, Fantasy, Imaginary, Subject Notable examples: Foucault, Les mots et les choses (The Order of Things); Velázquez, Las Meninas; Balthus painting

Seminar 19 (25 May 1966): Summary of Object of Psychoanalysis — Las Meninas III (p.230-245)

Lacan delivers a published summary of the year's seminar and then returns to Las Meninas to clarify the distinction between the picture and the mirror. Good painting, he argues, is not the painter's self-portrait (the mirror-image of the microcosm) but a 'trap for the look' that frees the scene from representation; it is the presence of a picture-within-the-picture (the large canvas Velázquez is painting) that accomplishes this liberation. The Las Meninas scene is analysed as a tableau vivant — a life rendered into a still-life — in which the Infanta at the centre figures the hidden slit-object, while the empty monarchical gaze (the King and Queen visible only in the mirror at the back) figures the empty Other, the void of an abstract theological God who must be there to support what does not need him. The session connects this to the Cross-cap topology: the fall of the o-object (the painter's falling look) simultaneously produces the barred subject and installs the empty Other as the support of truth.

Key concepts: Gaze, Objet petit a, Big Other, Imaginary, Fantasy, Cross-cap Notable examples: Velázquez, Las Meninas; Cross-cap topology; Fénelon's theology

Seminar 20 (1 June 1966): Re-thinking Freud — Las Meninas IV (p.242-251)

Lacan completes the Las Meninas sequence and turns to a comparative account of the four partial objects and their relationship to the topology of the year's seminar. He argues that the o-object is literally 'in the hole' of topological structures like the torus: it is representable precisely by not being represented. The session distinguishes neurotic structure (in which demand is aimed at the desire of the Other, and desire at the demand of the Other — an interlacing linked to the torus) from the dimension opened by the gaze and voice as objects at the level of desire rather than demand. The voice, in particular, is the instrument in which the desire of the Other is manifested: it is not only the causal object but the instrument through which the Other's desire speaks. Lacan closes with a preview of the year's final topological demonstration: the o-object as the 'look' inscribed in the gap between two parallel lines that are represented in the picture-plane as a single, untraceable point.

Key concepts: Objet petit a, Torus, Gaze, Voice, Desire, Demand Notable examples: Torus topology; Las Meninas (final reading); Amphisbaena serpent

Seminar 21 (8 June 1966): Jouissance and Castration (p.252-272)

In the final open session Lacan addresses jouissance and castration directly, using as his point of departure a mathematician's confession that mathematical discourse 'does not say what it is speaking about' — it conceals its own referent — to illuminate the structural parallel with the psychoanalyst's position: the Urverdrangung (primal repression) prevents any direct saying of the subject of analysis, and only topology can begin to approach jouissance. The body's recovery from the Other (the breast as biological appendage that has strayed into the Other's field) grounds the o-objects of demand; but castration reframes the penis as a signifier of the loss that jouissance undergoes through language and law, not merely as an organ of copulation. Lacan then inverts the Hegelian master/slave dialectic: jouissance remains with the slave, not the master; the master's desire is constituted precisely by the renunciation of jouissance; and the 'cement' of the society of masters is Freud's homosexual bond, not Hegel's recognition. Feminine jouissance and masculine jouissance are shown to be asymmetric and non-polar — 'masculine-feminine' is not a polarity — with the sole intermediary being that feminine jouissance can include the desire of the man as object, which means fantasy and desire are for the woman at once barriers to jouissance and the only route toward it.

Key concepts: Jouissance, Castration, Phallus, Objet petit a, Real, Fantasy Notable examples: Mathematician's confession about mathematical discourse; Hegelian master/slave dialectic; Ovid's myth of Tiresias; Oedipus Complex

Seminar 22 (15 June 1966): O-Objects — Safouan's Case; Perversion and Methodology (p.273-288)

The final session opens with Lacan's methodological critique of psychoanalytic 'scientific papers' as a genre that systematically falsifies its object by conspiring against the patient. He then argues that perversion must be theorised from Freud's foundational claim that 'perversion is normal,' so that the clinical problem becomes explaining why abnormal perverts exist — a historical-structural question he aligns with Foucault's archaeological method and illustrates with the Abbé de Choisy's memoirs (a clergyman who lived in female dress with full social acceptance, demonstrating that under different historical configurations perversion does not stand out as pathology). Jean Genet's observation that the pervert always wants to stamp the act with the 'mark of falsity' is linked to the counterfeiter structure from Seminar 7. Safouan then presents a case of obsessional neurosis featuring the 'duplication of the feminine object' — a narcissistic beloved and an anaclitic partner — and a dream in which a stocking-clad male friend figures the jewel-case/castration structure, with Lacan's codicil connecting the jewel-case to the anal object (Talleyrand's stocking full of shit) and the o-object's polyvalence.

Key concepts: Objet petit a, Perversion, Castration, Phallus, Narcissism, Jouissance Notable examples: Abbé de Choisy's Mémoires; Jean Genet on the mark of falsity; Foucault on archaeology; Safouan's case of obsessional duplication

Main interlocutors

  • Sigmund Freud, Beyond the Pleasure Principle
  • Sigmund Freud, The Interpretation of Dreams
  • Sigmund Freud, Screen Memories
  • Sigmund Freud, The Ego and the Id
  • Blaise Pascal, Pensées (The Wager)
  • Gottlob Frege, Foundations of Arithmetic
  • Jacques-Alain Miller (suture and logic of the signifier)
  • Michel Foucault, The Order of Things (Les mots et les choses)
  • Ernest Jones (aphanisis and female sexuality)
  • André Green (o-object and Freudian theory)
  • Conrad Stein (narcissism and the analytic situation)
  • Velázquez (Las Meninas)
  • Dante Alighieri, Divine Comedy (via Roger Dragonetti)
  • René Descartes, Meditations
  • Hegel, Phenomenology of Spirit
  • Heidegger, Being and Time
  • Erwin Panofsky, Perspective as Symbolic Form
  • Robert Musil, Young Törless
  • Lévi-Strauss (on the mask and structuralism)
  • Lacan, Seminar XI (Four Fundamental Concepts)
  • Lacan, Seminar XII (Crucial Problems for Psychoanalysis)
  • Lacan, Seminar X (Anxiety)
  • Lacan, Écrits

Position in the corpus

Seminar 13 sits at the intersection of two major trajectories in Lacan's teaching. It is the immediate successor to Seminar 12 (Crucial Problems for Psychoanalysis, 1964–65), which introduced the being of the subject in terms of the suture, Frege's arithmetic, and the Cartesian cogito's torsion. Seminar 13 takes all of this for granted and pushes toward the formalisation of the o-object's topology, the elaboration of the scopic and invocatory drives, and the beginnings of a theory of jouissance that will reach its mature formulation in Seminars 16–20. It is best read alongside Seminar 11 (Four Fundamental Concepts, 1964), which introduces the gaze and voice in a more clinical-phenomenological register; Seminar 13 provides the geometric and topological grounding that Seminar 11 presupposes but does not fully supply. The Las Meninas analysis is indispensable background for understanding the account of fantasy and the screen in the later seminars, particularly Seminar 14 (The Logic of Fantasy, 1966–67) to which Seminar 13 explicitly gestures in its closing sessions.

For readers working in the Lacanian-cinema or Lacanian-visual-theory tradition (Metz, Copjec, Žižek on the gaze), Seminar 13 is the primary source for Lacan's own sustained engagement with a specific artwork's structure. Foucault scholars will find the dialogue in Seminar 18 invaluable — it is one of the very few moments in which Lacan and Foucault are in direct, documented conversation, and the exchange illuminates both the convergences (representation, the episteme, the subject's structural inscription) and the divergences (Lacan's insistence on topology over archaeology, on the o-object over the epistemic formation) between their projects. Readers approaching Lacan's topology should read this seminar before Seminars 22–24 (on the Borromean knot and RSI), as it establishes the logical necessity of topology for psychoanalytic formation before those later seminars take it as given.

Canonical concepts deployed