In Greek, mathêma means "that which is taught." Following the same path that led Freud to the discovery of slips and jokes, Lacan forged connections between the fields of spoken discourse and logical inscription. In 1955, he introduced what could be called his first matheme, schema L.
The main Lacanian mathemes in order of their appearance are:
- Schema L (1955), which identifies four points in the signifying chain: first, the unconscious, or the discourse of the Other (A), and then the subject (S), which in turn results from the relation between the ego (a ) to the other (a ) to the other (d ).
- The formula of the signifier (1957), S/s, links the laws of the unconscious discovered by Freud to the laws of language (metaphor and metonymy).
- The "big graph" (1957) represented two different stages of the signifying chain. Lacan situated jouissance, castration, the signifier, and the voice at the various points of intersection on this graph.
- The four discourses (1969) were used to link the discourses of the master, the university, the hysteric, and the analyst. Four terms—S1, the master signifier; S2, knowledge; /S, the subject; and a, surplus enjoyment—turn in a circular motion to take up four successive positions defined by the discourse of the master: the agent, the other, the production of the discourse, and truth.
- The formulas of sexuation (1972) present sexual difference as a logical inscription. Using the signs ∃x, Φx, and ∀x outside of the field of mathematics where they originated, Lacan inscribed a masculine psychical structure on one side and a feminine psychical structure on the other.
The Lacanian matheme is characterized by being both open and asymmetrical. It does not tend towards closing discourse, and in spite of its character as a statement, it is primarily an enunciation. And there lies the paradoxical aspect of the enterprise—to found a science of the subject. Even though Lacan finally concluded (at the 1978 Congress of theÉcole freudienne de Paris) that there can be no transmission of psychoanalysis, he always situated psychoanalysis within knowledge: access to the unconscious is legible and transmissible. Mathemes advance and illustrate the theses that in relation to speech and writing, another structure besides that of grammar or syntax organizes speech, namely the structure of the signifier.
The Lacanian matheme proceeds neither by faith nor by pure mathematics. Lacan situates religion on the side of making real, or "realizing," the symbolic of the imaginary, or RSI (Seminar 21, session of November 13, 1973). On the other hand, Lacan defined mathematics as imagining the real of the symbolic, or IRS. If such were the case with the matheme, then it could become a model of the real. In fact, it is no such thing. Lacan never used mathematics as a demonstration, but as an exercise necessary for a better reading of the unconscious. Thus the mathemes should be read with a shift that allows for them to be situated as a symbolizing of the imaginary of the real, or SIR .
Henri Cesbron Lavau
See also: Four discourses; Graph of Desire; L and R schemas; Sexuation, formulas of; Signifier/signified.
Darmon, Marc. (1990). Essais sur la Topologie Lacanienne. Paris:Éditions de l'A.F.I.
Lacan, Jacques. (2002).Écrits: A selection (Bruce Fink, Trans.). New York: W. W. Norton.
——. Le Séminaire-Livre XXI, Les non-dupes errent [Those Who Aren't Duped Err/The Names of the Father] (1973-1974). Unpublished seminar.