Function of the Written

The "function of the written" names a formal principle Lacan elevates in Seminar XX as the genuine site of theoretical subversion — in contrast to merely displacing a centre (as the Copernican revolution does by swapping Earth for Sun). Lacan's argument is that what Newton actually achieved was not a new cosmological image but the inscription of a law: "things fall," formalised as a mathematical expression, written down. Writing here is not the transcription of speech but the materialization of a relation that cannot be captured by imaginary, sphere-centred, holistic thinking. The written, in this sense, functions as a break with the specular — it operates at the level of the letter, of the mark that persists independently of any speaking subject who might animate it. It is precisely because the written can carry a formal relation (a law, a formula, an algebraic matheme) that it resists absorption into the imaginary register of unified images and self-evident totalities.

In the frame of Seminar XX, this function is announced as one of the year's organising "poles," coordinate with the phallus, the Other, love, and the sign. The written is thus positioned not as a marginal technical point but as a structural pivot around which the year's teaching turns. Insofar as Lacan's four discourses are themselves written mathemes — formal inscriptions that prescribe structural relations among S1, S2, $, and a regardless of who is speaking — the function of the written is already implicit in that apparatus. What Seminar XX adds is the explicit thematisation: that the formalization itself, the act of writing down the law, constitutes the subversive move, not any change in the imaginary content of what is centred or privileged.

Within jacques-lacan-seminar-20-cormac-gallagher, the function of the written appears at a methodological hinge-point: Lacan uses it to distinguish genuine theoretical revolution (formalisation, inscription, the letter) from imaginary renovation (simply re-centring a sphere). This places the concept in productive tension with the cross-referenced canonical of the Imaginary: where imaginary thinking operates through specular identification, holistic images, and the narcissistic dyad, the function of the written operates through the letter — a mark that holds its relation independently of any reflecting subject. The written is, in this sense, a counter-move to imaginary captivation, aligned with what the Imaginary synthesis describes as the project of "dissociation" operative in the Seminar XX period.

The concept also resonates with the Four Discourses and their component elements. The discourses are themselves written mathemes — formal inscriptions of positions and relations — and the Letter, listed among the cross-referenced concepts, is the materiality of the signifier as it touches the Real. The function of the written can accordingly be read as the meta-level condition of possibility for the discourse-formulas themselves: it is because something can be written — fixed, transmitted, read independently of the speaker's intention — that the structural bonds named by the Four Discourses (Master, Hysteric, Analyst, University) can be identified and distinguished at all. In this sense, the concept functions as an epistemological anchor for Lacan's entire mathemic project in this period, without reducing to any single one of the discourses it enables.

Seminar XX · Encore: On Feminine Sexuality, the Limits of Love and KnowledgeJacques Lacan · 1972 (p.95)

There is something that was formulated last time: the function of the written. It is one of our points this year. One of our poles.

The terms "points" and "poles" are theoretically loaded: a pole is not merely a topic but a structural axis — an organising principle around which other elements are oriented — so by designating the function of the written as "one of our poles," Lacan signals that it carries co-equal structural weight with the phallus, the Other, and love as a fundamental compass-bearing for the year's entire inquiry, not a subordinate illustration.