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The Seminar of Jacques Lacan, Book XIX bis: The Knowledge of the Psychoanalyst

Jacques Lacan

by Jacques Lacan

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Synopsis

The Knowledge of the Psychoanalyst (Seminar 19A, 1971–72) is a series of seven informal talks delivered by Lacan at Sainte-Anne hospital, running in parallel with the formal Seminar XIX ("…ou pire"). Rather than presenting systematic exposition, the talks work by returning again and again to a single core thesis — that there is no sexual relationship — and progressively grounding that thesis in increasingly rigorous formalisms: from the discourse theory of Seminar XVII, through topology (Klein bottle, Borromean knot, non-orientable surfaces), through a critique of Aristotelian logic, and finally through set theory and the formulas of sexuation. The argument arc moves from ignorance-as-passion (the psychoanalyst's constitutive relation to non-knowledge) through the structural claim that psychoanalytic knowledge is knowledge bound to jouissance and the body's descent toward death, to the conclusion that the sexuation formulas — not mythology, not biology — are the only proper formalisation of what the speaking being's relation to sex actually is. Along the way Lacan polemically distinguishes his project from Freud's self-misunderstanding (the Copernican/Darwinian framing of resistance), from University discourse's conversion of knowledge into semblance, and from any Eros-as-fusion mythology. The seminar culminates by mapping the four modal operators (necessary, contingent, possible, impossible) onto the sexuation quadrant and equating the Real with the impossible, feminine not-all with contingency, and the paternal exception with necessity — a reordering of Aristotle's modal square through the analytic experience.

Distinctive contribution

What this seminar contributes that no other text in the Lacanian corpus quite replicates is its documentation of a thinking-in-progress, spoken to a mixed audience that includes psychiatric interns, where Lacan explicitly performs the difficulty of the psychoanalyst's relation to knowledge — including his own. The recurring confession that he writes to the audience between sessions, that he only "hears what he is saying" in the days immediately before the seminar, and that he lives under what he calls his own "failure" (discussed in Scilicet), is not merely rhetorical self-deprecation but a demonstration of the thesis: the psychoanalyst occupies a structurally difficult position in the discourse of the analyst, where knowledge about truth is simultaneously perceived and repudiated. No other primary text places the practitioner's horror of his own knowledge so nakedly at the centre of the theoretical exposition.

The seminar also provides the most pedagogically worked-through bridge in Lacan's oeuvre between set theory and the formulas of sexuation. The extended treatment of Pascal's triangle, the substitution of "partition" for "parts of a set" (yielding 2^n − 1 rather than 2^n), and the derivation of the One from the empty set are nowhere developed at comparable length in the concurrent Seminar XIX or the Écrits. The argument that the One operative in analytic theory is not the One of Platonic similitude but the One of pure difference — the S1 as reiteration of lack, grounded in the empty set — provides a set-theoretic foundation for the concept of repetition (Nachträglichkeit) that is spelled out here more accessibly than anywhere else in the primary corpus.

Finally, the talks offer the most sustained meditation in Lacan's late period on the discourse of capitalism as a variant of the master discourse that specifically forecloses castration. The brief but pointed remark that the capitalist discourse is structurally identical to the master discourse "except that it works better — you are all the better screwed" and that it makes subjects not even notice their subjection, connects the four-discourse schema directly to a social critique that Seminar XVII initiates but does not carry through into the topology and sexuation territory that is the horizon of Seminar XIX.

Main themes

  • The psychoanalyst's constitutive relation to ignorance and the horror of knowledge
  • The structural impossibility of the sexual relationship in the speaking being
  • Topology (Klein bottle, Borromean knot, non-orientable surfaces) as formalisation of castration and discourse
  • Set theory and the derivation of the One from the empty set as foundation of repetition and sexuation
  • The formulas of sexuation: masculine universal-grounded-by-exception versus feminine not-all without exception
  • Four Discourses as structural necessity, and the discourse of capitalism as foreclosure of castration
  • Lalangue, the matheme, and jouissance as what escapes articulation but conditions knowledge
  • Modal logic reordered: necessity/contingency/possibility/impossibility mapped onto the sexuation quadrant
  • The paternal exception (the One who says no to castration) as logical precondition for all thought about human relations
  • Repetition, Nachträglichkeit, and the logic of the third (beyond the dyad)

Chapter outline

  • The Psychoanalyst's Knowledge — 4th November 1971 — p.5-16
  • The Psychoanalyst's Knowledge — 2nd December 1971 — p.17-35
  • The Psychoanalyst's Knowledge — 6th January 1972 — p.30-49
  • The Psychoanalyst's Knowledge — 3rd February 1972 — p.50-71
  • The Psychoanalyst's Knowledge — 3rd March 1972 ('I Ask You to Refuse What I Am Offering You') — p.72-95
  • The Psychoanalyst's Knowledge — 4th May 1972 — p.96-122
  • The Knowledge of the Psychoanalyst — 1st June 1972 — p.123-148

Chapter summaries

The Psychoanalyst's Knowledge — 4th November 1971 (p.5-16)

The opening talk begins with Lacan's return to Sainte-Anne and an invocation of ignorance as passion — not as deficit but as a structuring relation to knowledge, citing Nicholas of Cusa's docta ignorantia as the highest form. The central polemical move is a critique of Freud's 1917 essay 'A Difficulty in the Path of Psycho-Analysis', which explained resistance to psychoanalysis through the Copernican and Darwinian 'revolutions'. Lacan argues that Freud thereby masks the truly novel epistemological claim of psychoanalysis: not a new content of knowledge but a transformation in the very structure and function of knowledge — specifically, the discovery of an unconscious knowledge that is unknown to itself, structured like a language, and bound to jouissance.

The talk pivots to the fifth point of the current year's seminar — 'there is no sexual relationship' — introduced here in deliberately stark and apparently paradoxical form. Lacan distinguishes the 'relationship' as something that must be written to exist from the mere fact of sexual intercourse, and argues that the impossibility of writing the sexual relationship in the speaking being is what psychoanalysis actually reveals. The connection to Freud's death drive is made obliquely: the drive circles around jouissance's fundamental failure, and suicide is offered as the illustration of an act that fails even when 'completed' — because it accomplishes nothing from the standpoint of jouissance. The analyst's knowledge is thus constituted as a knowledge of impotence, irreducible to scientific or religious discourse.

Key concepts: Ignorance as passion, Knowledge, Discourse of the Analyst, Jouissance, Death Drive, No sexual relationship Notable examples: Nicholas of Cusa; Freud 1917 Imago article; Copernican revolution; Darwin; Buddhist self-immolation

The Psychoanalyst's Knowledge — 2nd December 1971 (p.17-35)

The second talk opens with a question posed to Lacan by a member of his School: 'Is the incomprehension of Lacan a symptom?' Lacan refuses the diagnosis. Incomprehension of his discourse is not a symptom because the symptom, in its proper Lacanian sense (introduced via the Marxist tradition and refined by psychoanalysis), has a specific truth-value — it is a one-directional equivalence between something said and something meant, not mere misunderstanding. He also distinguishes his 'word' from his 'discourse': the fact that listeners feel helped even when they do not feel they have understood is evidence not of pathological resistance but of the ordinary functioning of lalangue.

The talk then addresses 'mathematical incomprehension' — the discomfort of subjects who feel that mathematical truth lacks the weight of full truth — and uses it to establish the distinction between truth and semblance, against the bivalence (true/false) of propositional logic. Bertrand Russell is cited as having made explicit that mathematics concerns statements about which it is impossible to say whether they have a truth value. This sets up the argument that the matheme is the proper vehicle for psychoanalytic formalisation precisely because it approaches the real at the border where truth and semblance are indistinguishable. The Subject Supposed to Know is introduced as the structural ground of transference, independent of any certainty about the analyst's actual knowledge — a crucial clarification about what is and is not required for analysis to begin.

Key concepts: Symptom, Truth vs. semblance, Subject Supposed to Know, Mathematical incomprehension, Matheme, Transference Notable examples: Bertrand Russell on mathematical statements; Propositional logic / bivalence

The Psychoanalyst's Knowledge — 6th January 1972 (p.30-49)

The January talk opens with a reflection on repetition: there can only be a 'first time' retroactively, because repetition requires a third moment, not merely a second. Lacan ties this to the Christian Trinity (invoking Kojève's reading) and to Plato's dyad as insufficient for analytic Nachträglichkeit. The argument is that the structural logic of retroaction — the second constituting the first as first — is what distinguishes psychoanalytic temporality from any dyadic philosophical tradition.

The talk moves to the topology of the Klein bottle and the six-verse poem Lacan had introduced in the previous session: the relation between man and woman passes through love, then the world substitutes for the sexual partner, and terminates at a wall. The wall is not metaphorical — it is the topological structure of a non-orientable surface where, at every point, the 'circle of return' is homogeneous. This means that castration is not localised but ubiquitous: it is present at every point of the relational surface between man and woman. The Four Discourses are then mapped onto the wall-structure: the mathemes ($, S1, S2, a) constitute the logical positions behind which enjoyment, surplus-jouissance, truth, and semblance are located. The talk closes with a pointed aside: the discourse of capitalism is the master discourse with a small 'turning point' that makes it function better — a structure that forecloses castration and thereby subjects its participants more thoroughly, even invisibly.

Key concepts: Repetition, Nachträglichkeit, Topology, Castration, Four Discourses, Discourse of Capitalism, Klein bottle Notable examples: Christian Trinity / Kojève; Plato's dyad; May 1968 and University discourse

The Psychoanalyst's Knowledge — 3rd February 1972 (p.50-71)

Returning to the 'wall' and love, this talk uses the Borromean knot as its central topological figure. Three rings, each closed and flexible, hold together only so long as all three are present — remove one and the chain dissolves. Lacan uses this to pose the question of the conditions of the discourse of the unconscious and of what language is. Language must be tackled through its topology (grammar as topological structure) before its semantics: René Thom's catastrophe-theory approach to language from the semantic angle is presented sympathetically but ultimately found insufficient, because it is forced to group radically different types of action under a single grammatical category like 'verb'.

The central theoretical advance of this session is the claim that the tetrahedron (four discourses structured as four points in space) is not a heuristic device but a logical necessity derivable from the topology of four-point structures. Speech is identified as the unique form of action that posits itself as truth — this is the epistemological basis of the psychoanalyst's knowledge. The phallus is then argued to be the sole Bedeutung (meaning/denotation in Frege's sense) through which language signifies at all. The objet petit a is reframed not as a localised object but as the metonymic cause of desire that structures the divided subject within discourse; the two poles of the quadripode — semblance (analyst's position) and jouissance — are irreducible and do not resolve into any 'harmonious' sexual relation. The 'scrap of knowledge' that the analyst extracts from the analysand's jouissance — through slips, dreams, and the analysand's own work — is what distinguishes analytic knowledge from scientific or mathematical writing.

Key concepts: Borromean knot, Topology, Four Discourses, Phallus as Bedeutung, Objet petit a, Tetrahedron, Speech as truth-positing Notable examples: René Thom / catastrophe theory; Jakobson on the phallus as meaning; Daniel 5:25-28 (Mene Tekel)

The Psychoanalyst's Knowledge — 3rd March 1972 ('I Ask You to Refuse What I Am Offering You') (p.72-95)

Given while Lacan was ill, this talk advances the formulas of sexuation through a sustained critique of Aristotelian logic and a set-theoretic grounding of sexual difference. The fundamental move is the claim that there is no sexual Other in the sense of a heteros — the Other as such is structurally emptied by the entry of language into the speaking being. Sexual difference is therefore not a natural binary but a topological-linguistic problem: 'Man' and 'Woman' are universals required by language itself, not grounded in the fact of animal copulation. The absence of the Other is not gendered but structural, grounded in the logic of Zero and One.

Lacan develops the sexuation formulas in explicit opposition to standard propositional logic. The masculine side is structured by a universal ('All x undergoes castration') grounded in a constitutive exception ('there exists at least one x who says no to the phallic function'). The feminine side is 'not-all' within the phallic function — not because there is a feminine exception to ground a different universal, but because there is no exception on the feminine side, which means the feminine universal cannot consolidate. Far from symmetrically grounding a feminine universal, the absence of exception further undermines any universal claim about women, making the feminine position essentially dual rather than universal. The talk further argues that feminine jouissance is irreducible to phallic jouissance — it opens onto something that cannot be captured by the phallic function — and it is precisely this asymmetry that marks the non-existence of the sexual relationship. Eros as fusion toward the One is rejected as a mythological delusion without analytic warrant.

Key concepts: Sexuation formulas, Not-all, Universal and exception, Phallic jouissance, Feminine jouissance, Big Other as empty, Universality Notable examples: Aristotle's Prior Analytics (critique); Socrates as hysteric; Chinese tradition / Yang essence (critique); Van Gennep, Sexual Life in Ancient China

The Psychoanalyst's Knowledge — 4th May 1972 (p.96-122)

The May talk opens with Lacan reading from notes written over the preceding weekend — itself an enactment of the seminar's theme, that knowledge is constituted between sessions through an uncontrollable relay of writing and forgetting. The two 'horizons of the signifier' — the maternal/material and the mathematical — are proposed as the coordinates between which any psychoanalytic intervention must locate itself. The analytic discourse is identified as the discourse of fact: it implicates Lacan in its effects to the point that its consequences are 'designated by his name' rather than belonging to him as author.

The bulk of the session is devoted to set theory. Lacan disputes the standard didactic introduction of non-numerability via induction, arguing that substituting 'partition' for 'parts of a set' yields 2^n − 1 rather than 2^n, and that this small difference has major consequences for the question of how the One emerges. Working through Pascal's triangle, he shows that the empty set functions as an element at the level of the previous set's monads — it is only by this operation of adding the empty set to the monads of the preceding column that the cardinal number of the next set's elements can be obtained. The argument is that the One in analytic theory is not the One of similitude or Platonic universality but the One of pure difference — the S1 produced at the level of surplus-jouissance, grounded in a founding lack (the empty set). Sex as dual-real can never produce a relationship precisely because the One that emerges from the empty set is a One of difference, not of fusion. The analytic discourse is also identified as the only discourse in which blackguardism (corruption of desire, canaillerie) necessarily produces stupidity — because analysis maps out rather than veils the jouissance organised by the signifier's positional effects.

Key concepts: Set theory, Empty set, One of pure difference, Repetition, Surplus-jouissance, Lalangue, Discourse of the Analyst Notable examples: Pascal's triangle; Frege on zero and one; Cantor's set theory (implicit)

The Knowledge of the Psychoanalyst — 1st June 1972 (p.123-148)

The final talk opens with Lacan's acknowledgement that the psychoanalyst is placed by discourse itself in a structurally difficult position — Freud called it 'impossible' (unmöglich). The talk is explicitly devoted to the psychoanalyst's knowledge as knowledge about truth, mapped onto the four-discourse quadrant: semblance, enjoyment, truth, surplus-enjoyment (plus-de-jouir). Foreclosure (Verwerfung) is invoked not merely as the mechanism of psychosis but as a socially legitimated rational force that operates on the analyst's own knowledge — practitioners experience a horror of what they know and are given ample social support for repudiating it.

The major formal move of this session is the full deployment of the sexuation formulas with their logical relations named explicitly: existence (∃x·φx), contradiction (∀x·φx and ∃x·¬φx), undecidable (the feminine side's relation to the phallic universal), and lack/desire/objet a (the relation across the quadrant). The masculine side — universal castration grounded by the exceptional father who 'says no' — is formalised as the necessary (∃x·¬φx is 'the necessary'). The feminine side — not-all, grounded not by an exception but by the void of any denial — is identified with contingency. The Real occupies the place of the impossible. This is Lacan's explicit reordering of Aristotle's modal square (necessity, contingency, possibility, impossibility) through the lens of the analytic discourse. The talk closes with the remark that the function of the father is not primarily legislative or Oedipal but é-pater — to astonish — and that this function is strictly necessary as a logical precondition for any thought about human relations, independently of whether the biological father performs it.

Key concepts: Modal logic, Necessity, Contingency, Impossibility, Real, Sexuation formulas, Name of the Father, Foreclosure, Discourse of the Analyst Notable examples: Freud, Totem and Taboo (Abraham's sacrifice); Grotto of Lascaux; Schreber's father as legislator; Aristotle's modal square (reordered)

Main interlocutors

  • Jacques Lacan, Seminar XIX (…ou pire)
  • Jacques Lacan, Seminar XVII (The Other Side of Psychoanalysis)
  • Jacques Lacan, Écrits
  • Sigmund Freud, Beyond the Pleasure Principle
  • Sigmund Freud, Civilization and Its Discontents
  • Sigmund Freud, Totem and Taboo
  • Sigmund Freud, 'A Difficulty in the Path of Psycho-Analysis' (1917)
  • Aristotle, Prior Analytics
  • Gottlob Frege, Foundations of Arithmetic
  • Georg Cantor, Set Theory
  • Alexandre Kojève, Introduction to the Reading of Hegel
  • Hegel, Phenomenology of Spirit
  • Plato, Republic
  • René Thom (catastrophe theory / topology of language)
  • Bertrand Russell (mathematics and truth)
  • Roman Jakobson (phallus as meaning / Bedeutung)
  • Marcel Granet, Danses et légendes de la Chine ancienne
  • Jacques Lacan, Seminar XVIII
  • Jacques Lacan, Seminar XI

Position in the corpus

Seminar 19A occupies a liminal but indispensable position in the late Lacan corpus: it runs in parallel with the formal Seminar XIX ("…ou pire") and is best understood as its popular companion, translating the seminar's most technical moves into a spoken, improvisational register for a mixed audience that includes psychiatric interns as well as analysts. Readers who have encountered Seminar XVII (The Other Side of Psychoanalysis) and its four-discourse framework will find 19A extending that framework toward the topology and sexuation territory that will be consolidated in Seminar XX (Encore). The treatment of the formulas of sexuation here is less compact than in Encore but more pedagogically explicit — especially on the set-theoretic derivation of the One and the modal-logical reordering of Aristotle — making 19A invaluable reading before or alongside Seminar XX for anyone who wants to understand why the formulas have the structure they do rather than merely applying them.\n\nWithin the broader Lacanian corpus, 19A sits closest to Seminar XIX, Seminar XX, and the Écrits essay 'Science and Truth'. Its sustained engagement with the psychoanalyst's own horror of knowledge also makes it a useful companion to Seminar XI (The Four Fundamental Concepts), where the analyst's desire is theorised as the condition of analysis. Readers approaching this seminar should be familiar with the four discourses (Seminar XVII), the basic topology of the subject (objet a, $ , the mathemes), and the distinction between jouissance and phallic jouissance introduced in Seminar XVI (From an Other to the other). After 19A, the natural next step is Seminar XX, where the not-all and the formulas of sexuation receive their canonical elaboration, and 'L'étourdit' (1972) in the Autres écrits, which formalises much of what 19A presents discursively.

Canonical concepts deployed