Count-as-One, Forming-into-One, Unary Trait, S1

While a significant amount of research has recently been carried out that investigates the similarities and differences between Alain Badiou and Jacques Lacan's theories of the subject, less attention has been paid to the direct relationship between the latter and Badiou's set-theoretical ontology. This article applies some of the most important conceptual propositions advanced in the first two Parts of Being and Event to the key psychoanalytic issue of the identification of the conscious and unconscious subject as expounded by Lacan in his ninth Seminar, L'identification. More specifically, this article aims to show how Badiou's notions of the "count-as-one" and the "forming-into-one" can profitably be put to work in order better to understand Lacan's notions of the "unary trait" and the S1, the "master-signifier". What is at stake in both cases is the relationship between structure and metastructure, presentation and representation. Furthermore, this article provides an outline for a set-theoretical formalisation of the relation between consciousness and the unconscious as developed by Lacan in L'identification. Lacan's breaking of the solidarity between unity and totality allows him to work with parts: from the inexistence of totality as a one follows the possibility of thinking the part as "partial system". Lacan identifies this system with the unconscious. Applying a number of set-theoretical axioms, this article argues that the existence of the unconscious as partial system ultimately relies on the in-existence of the void, or, more specifically, the existence of the void as part that in-exists as element.