Establishing a pre-logical setting in a quantum model of psycho-analytic theory
Giulia Battilotti, Rosapia Lauro Grotto
TL;DR
The paper addresses the origin of mental representations in cognitive and psychoanalytic theories by proposing a pre-logical setting that blends Freudian and Kleinian ideas with a quantum spin-state model. It formalizes this setting in first-order logic with modalities, introducing infinite singletons and a modal projector $\square$ to capture coherence, indefiniteness, and affect. By mapping Freudian, Matte Blanco, Klein, and Bion into a quantum-cognitive formalism, it develops a framework where unconscious dynamics transit to rational thinking via normalization, integration, and duality between modal operators $\square$ and $\Diamond$. The approach aims to provide a mathematical bridge for quantum cognition and AI decision-making, enabling models that handle indefinite, affect-laden representations in computational contexts.
Abstract
A crucial issue both in cognitive and psychoanalytical theories deals with the origin of mental representations. In order to explore this issue, the paper analyzes a pre-logical setting, by considering a formalized approach to the foundations of psychoanalysis in logic, interpreting and integrating the views by Freud, Matte Blanco, Klein and Bion. The formalized approach derives from a quantum model of spin states. A representation of the spin state of a particle in first order logic is abstracted to get a modality interpretable as an abstract projector. The last can be decomposed into a positive, negative and irreal component. The irreal component cannot emerge and, in logic, is absorbed by the two others, giving rise to logical duality. Due to its treatment of undefiniteness and coherence, the paper is meant to contribute to quantum cognition, in its particular sense of affective quantum cognition.