Mathemes

Lacan called his algebraic-looking notations mathemes (mathème, on the model of philosophème). They are not equations in any working mathematical sense — they are minimal letters meant to transmit theoretical structure without surrendering to the imaginary capture of natural language. This page is the symbol key. Refer to it whenever a formula appears in another schema.

Core symbols

Symbol	Reads as	Means
S	"subject" (uppercase)	The classical philosophical subject; the Cartesian "I." Used in the L Schema before the late move to $.
$ (S barred)	"barred subject" / "split subject"	Splitting of the Subject. The Subject of the unconscious — divided by language. The standard Lacanian subject from the late 1950s onward.
A	"Other" (capital A)	The The big Other</td> </tr> <tr> <td><strong>Ⱥ</strong> (A barred)</td> <td>"barred Other"</td> <td>The Other lacks too. Late-Lacan move: there is no "Other of the Other" guaranteeing the symbolic from outside.</td> </tr> <tr> <td><strong>a</strong></td> <td>"(little) other" / "object a"</td> <td>Two uses: (1) [[Little Other, the imaginary peer in early schemas; (2) Objet petit a, the object-cause of desire in middle and late Lacan. Context disambiguates.
a'	"ego" (a-prime)	The Ego in the L Schema — the imaginary other-of-self that appears in the Mirror Stage.
Φ (capital Phi)	"Phallus" / "phallic function"	The Phallus as signifier; the Phallic Function in the formulas of Sexuation.
φ (lowercase phi)	"phallus" / "imaginary phallus"	The phallus in its imaginary register, often as the object the subject identifies with or compensates for.
−φ	"minus-phi"	The phallus as castrated / lacking; the negation written into the visual / scopic field (see Castration).
S₁	"master signifier"	The Master Signifier — the empty signifier that quilts a discourse closed; the S₁ of the Four Discourses.
S₂	"knowledge"	The chain of signification, taken as a system; savoir; the S₂ of the Four Discourses.
S(Ⱥ)	"the signifier of the lack in the Other"	A formula on the upper level of the Graph of Desire — what marks the Other's incompleteness.

Punctuation in formulas

Notation	Means
A → B	A determines / produces B
A / B (or A over B)	A over B — usually A is the manifest position and B is the underlying truth or remainder. In the Four Discourses, the upper register is "what addresses" and the lower is "what is hidden / produced."
A ◇ B	The "lozenge" / "poinçon": a generic relational operator. Reads variously as desire of, covers, encircles, cuts, depending on context. The most common formula is `$ ◇ a` — the Subject in relation to Objet petit a — the formula of Fantasy.
A ∧ B / A ∨ B	Logical and / or. Used in the vel of Alienation: `(your money) ∨ (your life)` — the forced choice.
∀x · Φx	"for all x, x is subject to the Phallic Function" — the masculine side of the formulas of Sexuation.
¬∃x · ¬Φx	"there is no x not subject to the phallic function" — the feminine not-all side.
( · ) / **(	)**

The Fantasy formula in detail

   $ ◇ a

Reads: "the barred subject in relation to objet petit a." This is the formula of Fantasy — Lacan's claim that fantasy is the structure relating the divided subject to the lost object that drives it.

The lozenge ◇ stands in for the entire complex relation: the subject desires a, the subject is constituted by losing a, the subject covers over its own division by interposing a. All of these are condensed into one operator deliberately — fantasy is what holds these in unstable simultaneity.

The Discourse formula skeleton

Each of the Four Discourses is a formula in this fixed shape:

       agent ────→ other
       ─────       ─────
       truth       product

What changes between discourses is which letter sits in which position. See Four Discourses for the four substitutions.

The signifier-over-signified bar

   S
   ─
   s

From Saussure, repurposed by Lacan: the signifier (S) over the bar over the signified (s). The bar is resistant — Lacan's claim is that the signifier doesn't transparently produce the signified; the bar is a barrier that signification has to cross retroactively. The Point de capiton is the operator that briefly traverses the bar.

Notational inconsistency warning

Lacan's notation drifted across his career. S in Seminar II is the same as $ in Seminar XI. a as little other in L Schema is not the same as a as Objet petit a in Seminar XIJacques Lacan · 1964. Translators sometimes silently update older notation. Always check the seminar period.

Bruce Fink's editions of the seminars use a consistent late-period vocabulary ($ for the subject, objet a for object a) and footnote where Lacan's own notation differs.