Formulas of Sexuation

The most-cited and most-misunderstood diagram in late Lacan. Two columns of quantifier-logic formulas describing two ways of being a Subject under the Phallic Function (Φx). Sexuation is not gender, not anatomy, not social role — it is a logical inscription.

The diagram

           Masculine side                     Feminine side
       ─────────────────────             ─────────────────────
                ∃x · ¬Φx                          ¬∃x · ¬Φx
                ∀x · Φx                           ¬∀x · Φx

       (there is one who                  (there is no one who
        escapes the phallic                escapes the phallic
        function)                          function)
       (all are subject to                 (not-all are subject
        the phallic function)              to the phallic function)

Two pairs of formulas, with negation flipped column-to-column. Read top-to-bottom in each column.

What each formula says

Masculine side

∃x · ¬Φx: "There exists an x such that x is not subject to the phallic function." The classical exception — the one (the primal father, in Freud's Totem and Taboo) who escapes castration.
∀x · Φx: "For all x, x is subject to the phallic function." The set of those-who-are-subject is closed — it is a whole, defined precisely by its exception.

The masculine side is the logic of the whole-with-an-exception. It is the structure of the set: a defined totality, made coherent by what it excludes.

Feminine side

¬∃x · ¬Φx: "There is no x that is not subject to the phallic function." There is no exception. Every speaking being is subject.
¬∀x · Φx: "Not all x are subject to the phallic function." This is the crucial formula and the most contested. Not-all is not equivalent to "some are not." It claims: there is no totalizing predicate that closes the set. The "all" doesn't apply.

The feminine side is the logic of the not-all (Not-all). It is not a different set with different members — it is the same set (every speaking being) inscribed without the totalizing closure.

What it claims

There are two sexed positions, but they are not biological or social. They are two logical inscriptions under the same function (Φ).
The masculine side is closed by an exception. It says: "everyone is subject to the rule, except one." This is the logic of phallic identity — defining itself by what it excludes.
The feminine side is open without exception. It says: "everyone is subject to the rule, but not as a totality." This is the logic of singularity — each speaking being inscribed under Φ without being captured by a "for-all."
There is no sexual relation (il n'y a pas de rapport sexuel) — the two sides do not write a relation in the Symbolic. They are not complementary. They are two ways of being inscribed separately under the same function.
Sexuation is choice, not assignment. Every speaking being makes an unconscious choice (alienation) which side to be inscribed on. This choice is not consciously controlled and does not determine social presentation.
The not-all has access to "Other jouissance." The feminine inscription, because it is not closed, has a second jouissance available beyond the Phallic Jouissance — jouissance Autre / Other Jouissance. This is what Encore is fundamentally about.

Where Lacan introduces / develops it

Seminar XX: Encore (Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and KnowledgeJacques Lacan · 1972 / Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and KnowledgeJacques Lacan · 1972) — the formulas are written on the blackboard across the seminar. Read sessions on jouissance and sexuation back-to-back.
Seminar XIX: …or worse — the immediate predecessor; the not-all logic is being worked out.
Seminar XVIII: On a discourse that might not be a semblance — the prelude.
Television (1973) — Lacan repeats the formulas in compressed form.

Concepts deployed

Sexuation · Not-all · Phallic Function · Phallus · Phallic Jouissance · Other Jouissance · Subject · Castration

Interpretive traps (this is the most-contested late Lacan diagram)

Treating "masculine" and "feminine" as biological or gender-identity categories. This is the worst error. Lacan is explicit and his commentators repeat: these are positions in a logical structure, not properties of bodies or identities. Anyone of any gender can be inscribed on either side. Trans-affirming readings of Lacan rely heavily on this point.
Reading "not-all" as "some-not." Logically, ¬∀x · Φx looks like "there exist x such that ¬Φx." But Lacan's claim is precisely that this is wrong: not-all is a different modality — it negates the totalizing operation, not the inclusion of any specific x. The formula doesn't carve out exceptions; it dissolves the totality. (Joan Copjec's and Alenka Zupančič's commentaries are clearest on this.)
Treating the formulas as describing actual sex. Il n'y a pas de rapport sexuel is not a claim about sex acts. It is a claim that the two sides do not write a symbolic relation — there is no signifier or formula in the symbolic that inscribes one side's inscription as the complement of the other's.
Reading Other Jouissance as mystical. Lacan deliberately invokes the mystical (Teresa of Ávila, Hadewijch of Antwerp) as figures for Other jouissance — but the point is not that Other jouissance is mystical experience. The point is that it is jouissance not captured by the phallic signifier, and the mystics are formal exemplars of this position.
Equating sexuation with Sexuality or Drive. Sexuation is the logical inscription under Φ. Sexuality is the broader phenomenology of erotic life. Drive is the partial-drive structure traversing both. The three are linked but distinct.

Cross-corpus readings

After synthesis runs, the Sexuation page's Tensions section will surface the major intra-corpus disagreements:

Žižek vs Copjec: on whether the not-all should be read primarily ontologically (Žižek: an antinomy of being) or epistemically (Copjec: a Kantian antinomy of reason)
Zupančič's intervention: in What is Sex?, Zupančič argues both sides have under-read the ontological status of the formulas. Sexuation is the structure of being-as-non-coincident-with-itself, not (only) a logic of sexed inscription.
Mari Ruti's caveat: the not-all should not be romanticized as freedom from the phallic. The feminine inscription is also subject to Φ, just inscribed differently.

The cross-framework tensions (against Object Oriented Ontology, psychoanalytic feminism in non-Lacanian veins, queer theory's relation to sexuation) will populate the Across frameworks section.