Quaternary

quaternary (quaternaire) A quaternary is a structure which com-

prises four elements. Although Lacan's rejection of dualistic schemas in

favour of an emphasis on the triangular structure of the Symbolic involves a

predominance of triadic schemes in his work (see DUAL RELATION), Lacan also

insists on the importance of fourfold schemes: 'A quadripartite structure has,

since the introduction of the unconscious, always been required in the con-

struction of a subjective ordering' (Ec, 774).

     The emphasis on the quaternary first comes to the fore in Lacan's work in

the early 1950s, and is perhaps due to the influence of Claude LÈvi-Strauss,

whose work on the structure of the avunculate shows that the basic unit of

kinship always involves a minimum of four terms (LÈvi-Strauss, 1945). Thus,

in a 1953 paper which deals with the neurotic's 'individual myth' (another

reference to LÈvi-Strauss), Lacan remarks that 'there is within the neurotic a

quartet situation' (Lacan, 1953b: 231), and adds that this quartet can demon-

strate the particularities of each case of neurosis more rigorously than the

traditional triangular thematisation of the Oedipus complex (Lacan, 1953b:

232). He concludes that 'the whole oedipal schema needs to be re-examined'

(Lacan, 1953b: 235). Thus, in addition to the three elements of the Oedipus

complex (mother, child, father), Lacan often speaks of a fourth element;

sometimes he argues that this fourth element iS DEATH (Lacan, 1953b: 237;

S4, 431), and at other times he argues that it is the Phallus (S3, 319).

    In 1955, Lacan goes on to compare psychoanalytic treatment to bridge, 'a

game for four players' (E, 139; see E, 229-30). In the same year, he describes a

quaternary made up of a triadic structure plus a fourth element (the LETTER)

which circulates among these three elements (Lacan, 1955a).

    Other important quaternary structures which appear in Lacan's work are

SCHEMA L (which has four nodes), the four partial drives and their four

corresponding part-objects, and the four discourses (each of which has four

symbols assigned to four places). Lacan also enumerates four 'fundamental

concepts of psychoanalysis' (Lacan, 1964a), and speaks of the sinthome as a

fourth ring which prevents the other three rings in the BORROMEAN KNOT (the

three orders of the Real, the Symbolic and the Imaginary) from becoming

separated.