This paper analyzes a stage of Lacan's work as a researcher, concerning methodological issues in the move from the graph of desire to formalization of the mathema of four discourses. In the graph, the line-shaped hook cutting the two horizontal lines configured the effect of discourse in three stages, which proved to be equivalent to three clinical structures. With the four discourses, Lacan establishes a framework of four basic positions on which occurs a turn of four elements. The mathema of four discourses reminds us of the operations of the group structure of Klein. However, two rules restrict the interchangeability: the movement of one quarter of rotation of the elements only in a sense; secondly, in the four basic positions, there is disjunction between the positions of know (savoir) and truth. We can then conclude that the four discourses consist of a partial appropriation of the structure of the Klein group in order to demarcate the difference between psychoanalysis and scientific discourse.
Psychoanalysis; Logic; Graph of desire; Four discourses
