Infinite Singletons and the Logic of Freudian Theory

The aim of this paper is to advance a formal description of the implicit logic grounding of the psychoanalytic theory. We therefore propose a new interpretation of the logical features of the Freudian unconscious process, starting from the Bi-logic formulation put forward by the Chilean psychoanalyst Matte Blanco. We conceive the universal undifferentiated state of the deep psychoanalytic Unconscious in terms of particular sets named infinite singletons, and we show how they can represent the logical foundations for a formal description of the Primary process. We first disclose some implicit assumptions underlying the common logical language. In doing so, we discover an unexpected presence of symmetry even in the most basic of logical and verbal structures. In the approach derived, we show that infiniteness, not finiteness, is the primary mode of sets, and therefore, of thinking. The pivotal consequence of this model is that the unconscious elements cannot be characterised in the absence of external reality, which produces the collapse of infinite sets and allows for the emergence of linguistic representations. Finally, we discuss how the model could represent a platform to formalise further developments of psychoanalytic theory, in particular with respect to the shift from the First to the Second Topics in Freudian theory.