Infinite Singletons and the Logic of Freudian Theory

Abstract

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.

The Modal Components of Judgements in a Quantum Model of Psychoanalytic Theory

“…We would like to add that non-extensional views of sets are exploited in our normal reasoning. For example, as in [12], let us consider the sentence "every day of last week was sunny in my town". In order to find out if it is true, someone who was out of town last week may observe that the ground in their garden is wet and conclude that the sentence is false, without knowing which day it rained, considering the week as a whole.…”

“…In terms of the Freudian theory, infinite singletons allow us to form thing-presentations, namely the open representations of objects, prior to word-presentations (see the above section). As seen in [12], infinite singletons can be processed by the primary process, in the form of assertions given by the quantification by ∀ or ∃, which is equivalent for them indeed. We would like to observe that this creates, ipso facto, a prelogical environment for the world of infinite singletons.…”

“…The latter constituted a domain that had accommodated linear science, whose proper object, Bion felt, was inanimate objects but which was blind to human experience and to the existence of an ultra-sensual world beyond the third dimension-until the arrival of the theories of relativity and uncertainty (pp. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Animate objects (humans) defied the confines of linear science, he believed (1963, p. 11).…”

“…In order to model Bi-logic, introduced by the Chilean psychoanalyst I. Matte Blanco [11], we found a way to tackle the issue of first-order language via the notion of infinite singleton, namely a particular kind of domain for logical quantifiers (see [12]). In turn, this setting has been derived from a model of quantum states in first-order language ( [13]).…”

“…On the other side, the secondary process takes into account the external reality and then it can form rational thinking. In the following section, we introduce infinite singletons, namely those formal elements adopted to discuss how displacement and condensation, namely the peculiar mechanisms of the Unconscious, could be formally represented (see [12] for a discussion). In the present paper, we show that they correspond to thing-presentations, and see how this fact enables us to explore the border between the primary and the secondary process, namely to represent and discuss, from the point of view of a formal logical approach, the role of external reality and its advent in the mental life.…”