lacan

French psychoanalyst (1901–1981). His "return to Freud" runs Freud through two imports: Kojève's Hegel (desire as the desire of the Other; recognition) and structural linguistics (Saussure/Jakobson — see signifier). The polemical motive: against ego psychology's adaptation therapy (strengthen the ego, adjust the patient), restore the unconscious as ein anderer Schauplatz — another scene — with a transmissible, non-biological formalization.

Three registers

Imaginary — the mirror stage: the ego is a (mis)identification with a specular whole (the fragmented infant sees a unified image). Resemblance, rivalry. The ego is an image — not the subject.
Symbolic — the order of signifiers: language, law, the big Other. The unconscious is "structured like a language" and is "the discourse of the Other".
Real — what resists symbolization absolutely. Not "reality" (an imaginary-symbolic construction) but the impossible kernel that "always returns to the same place".

The desire ladder

Need (biological) → Demand (need said in language, addressed to the Other — and always also a demand for love) → Desire = demand minus need: the irreducible remainder. Desire has no satisfying object; it is constituted by lack.

objet petit a — the object-cause of desire: not what is wanted but what makes one want. Every obtained object reveals ce n'est pas ça ("that's not it") and desire slides to the next link (metonymy).
"Desire is the desire of the Other" — one desires what the Other desires, as the Other desires it, and to be desired by the Other. Genetically: the infant's wanting forms inside the mother's wanting; deciphering Che vuoi? ("what do you want of me?") precedes wanting anything.

Small other, big Other

petit autre (a) — the counterpart: mirror image, rival, semblable. Symmetric; imaginary.
grand Autre (A) — the third position every exchange presupposes: language, law, the registry of truth (lying, promising and money all require it). A seat, not a person — mother, teacher, God, the market, the feed can occupy it; none is it. Where the "big" shows: asymmetric (protocol, not node — every protest is filed in its forms), prior and unchosen (one is spoken about before one can speak), extimate (the unconscious runs on its rails — nearer than the heart, yet foreign), and the seat of the enigma Che vuoi?.
The big Other does not exist (Ⱥ, barred): no actual referee — an inconsistent, hole-ridden presupposition sustained by everyone believing that the others believe. It works anyway (money, law, language). fomo-is-faith-in-the-other: FOMO as the felt proof of this faith.

The subject

$ — the barred subject: not a substance but a lack in the signifying chain; "a signifier represents the subject for another signifier". The ego (imaginary) is precisely not it.

Jouissance and the superego's "Enjoy!"

Jouissance: enjoyment beyond the pleasure principle — excessive, painful, unrenounceable (the pleasure principle keeps excitation low; jouissance overshoots). The derivation of the superego command:

Freud's clinical anomalies (Civilization and its Discontents): the superego grows more savage with obedience (each renounced satisfaction feeds it), and its cruelty is libidinal — the law enjoys punishing.
Lacan formalizes: the superego is the law stripped to a senseless pure imperative — "at once the law and its destruction", the obscene supplement of the symbolic Law (which pacifies by giving reasons and exchange).
"Kant avec Sade" (1963): an unconditional imperative indifferent to the subject's good, emptied of all content — its hidden content is jouissance. The categorical form, fully purified, speaks Sade's sentence. (A structural-isomorphism claim, not a deduction — the chain's most contested link.)
Prohibition produces the surplus enjoyment it forbids; the superego administers both sides of that economy. Said openly (Seminar XX): "Rien ne force personne à jouir, sinon le surmoi. Le surmoi, c'est l'impératif de la jouissance — Jouis !"
The command cannot be obeyed — commanded enjoyment cancels itself; the subject can only answer j'ouïs ("I hear", the homophone). Guilt re-attaches to not-enjoying-enough.
As symbolic authority declines, the imperative goes public: obligatory enjoyment as consumer society's background hum; plus-de-jouir (surplus-jouissance) coined on Marx's Mehrwert. (Continuation: labor-decoupled-from-recognition, terminal figure.)

What the apparatus is for (the prescriptions)

Clinical coordinates — locating which layer one is actually fighting (the rival small other vs one's stance toward the big Other):

Traversing the fantasy (la traversée du fantasme) — the end of analysis: seeing Ⱥ. The Other is inconsistent and has no answer to Che vuoi? — the verdict window is empty. Freedom lodges in the Other's gaps (Seminar XI: alienation into the Other's signifiers, then separation through the Other's lack).
Ne pas céder sur son désir (Seminar VII) — the only thing one is ever truly guilty of is having given ground on one's desire. Desire vs the "service of goods" (le service des biens): the Other issues the materials and forever offers to buy the product back with approval and comfort. Yielding does not buy peace — renunciation feeds the superego (the creditor strengthens with each payment), and the betrayed desire returns as symptom. Antigone as the limit case: the ethics of desire lies beyond the pleasure principle, with no happiness warranty.
Savoir y faire avec son symptôme (late Lacan) — don't dissolve the symptom, learn to use it: the sinthome as signature (Joyce).

Caveats

Deliberately obscure style (he held that clear statements get digested by the ego); the late mathemes/topology are suggestive analogy, not mathematics (Sokal's target); clinical efficacy contested. Read as a mine of structural intuitions, not a theorem set. Entry text: Bruce Fink, The Lacanian Subject.

kin: signifier · desire-is-labor · fomo-is-faith-in-the-other · labor-decoupled-from-recognition