The Seminar of Jacques Lacan, Book XX: Encore, On Feminine Sexuality, the Limits of Love and Knowledge, 1972-1973

Lacan's central claim is that there is no sexual relation—no signifying formula or logical cipher capable of writing the relation between the two sexes. The seminar rejects any conception of sexual difference grounded in anatomy, chromosomes, or choice of sexual partner, replacing it with the formulae of sexuation: a logical writing of masculine and feminine positions in terms of their relation to the phallic function and to the Other . From this follows the seminar's second major claim: feminine jouissance is supplementary, not complementary. It is 'beyond the phallus' in the sense that it is not wholly accountable to the phallic function, yet it remains within the symbolic order rather than outside it. The seminar is thus a formalization, not a celebration, of sexual difference.

The formulae of sexuation are introduced in chapter seven of Encore, in the session of March 1973 . They consist of four logical propositions written in mathemes: on the masculine side, the existence of a subject who says no to the phallic function (the exception, the primal father) and the universal affirmation of the phallic function by all speaking beings; on the feminine side, the negation of the universal (there is no woman who is not wholly subject to the phallic function is false) and the affirmation of a non-all, indicating that woman is not wholly determined by the phallic function . Patrick Monribot has emphasized that the formulae should be read in conjunction with two earlier Écrits essays: 'The Signification of the Phallus' (1958) and 'Guiding Remarks for a Convention on Female Sexuality' (1960) .

The phrase 'la femme n'existe pas'—the woman does not exist—is often misread as a denial of women's reality or a misogynist provocation. In the formulae of sexuation, the barred 'La' on the feminine side indicates that there is no universal Woman, no singular essence or class that could subsume all women under a single predicate . The masculine side operates under a universal quantifier (all subjects are subject to the phallic function, with one exception), while the feminine side is structured by the non-all—there is no set of all women defined by a common phallic predicate. The claim is logical and structural, not empirical. It also has clinical consequences: a woman is not wholly determined by the phallic function, which opens the possibility of a jouissance beyond the phallic.

Jouissance and desire are distinct in Lacan's later teaching. Jouissance is fundamentally of the One—autistic, concerning the One alone, without the Other; at most it relies on a detached piece of the other's body, what Lacan calls the 'plus-de-jouir' . Desire, by contrast, is a movement between the One and its object, structured by the fantasy ($ ◊ a), and aimed at a surplus of life. Love is a third term: it pertains to the Other as surely as jouissance pertains to the One . The formula 'only love allows jouissance to condescend to desire' links the three: love is what makes it possible for a subject to consent to another's jouissance, to accept that the other enjoys a detached piece of one's body . Encore's contribution is to situate feminine jouissance beyond this triangulation.

The Other with a capital O is the symbolic order—language, law, and the field of radical alterity in which the subject is constituted. In Encore, Lacan emphasizes that the Other is barred (S of A with a bar), meaning it is structurally lacking, incapable of providing the final signifier that would complete meaning or ground the sexual relation . This bar is not a contingent failure but a structural feature: the Other cannot say all the truth, and there is no metalanguage. The consequence for love is that the demand for love continues endlessly—'encore'—because the Other's lack cannot be filled by any object or declaration . Feminine jouissance, on the side of the non-all, has a distinctive relation to this barred Other: Lacan associates it with the mystics, who experience a jouissance that 'goes beyond' the phallic without being outside the symbolic.

Encore extends and transforms the discourse theory of Seminar XVII (1969-1970). Where Seminar XVII analyzed the four discourses—master, university, hysteric, and analyst—as structures of social bond, Encore shifts focus to the logical and clinical consequences of the barred Other for sexual difference and jouissance. The key development is the introduction of the formulae of sexuation, which formalize positions that Seminar XVII had treated under the rubric of discourse. One scholarly trajectory traces the passage from the divided subject and speaking subject of the earlier seminars to the 'speaking body' (corps parlant) of Encore, where Lacan identifies the speaking body with the unconscious itself in the session of 15 May 1973 . This shift marks a turn toward the real and the body in Lacan's late teaching.