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arXiv:2511.04708

Establishing a pre-logical setting in a quantum model of psycho-analytic theory

Giulia Battilotti, Rosapia Lauro Grotto

physics.soc-phmath.LOquant-phSubmitted Nov 5, 2025• Announced Nov 6, 2025• 0 citations
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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.

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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.
In the present paper, we develop a theory of thinking based on an attempt to formalize the construction of mental representations as described in psychoanalytic theory. In previous work, we described Freud's and Matte Blanco's structural Unconscious in a formal model in which the properties of unconscious representations are captured by particular sets-infinite singletons-that can be derived in first-order logic language. Here, we afford the issue of the finitization of unconscious representations by assuming that the mind can form an all-purpose modality, originating from abstraction from infinite singletons; in this way, a symmetric prelogical setting for mental representations is formally created, and this is interpreted in a quantum spin model by a modal (necessity) projector. Then, by introducing time, one can describe the links that mental representations can establish with reality, and hence finitize the representations. The modality is so split into finite components, here termed positive, negative and irreal; the splitting of the modality is traced back to the decomposition of the spin observables by means of the Pauli matrices, which can offer a quantum semantics to the method applied. Here, we suggest that the development of the modal approach and its quantum logic implementation can be considered as a proper formalization of some aspect of the psychoanalytic theory of thinking proposed by Bion; namely, we will show that the process of abstraction leading from raw data to preconceptions, and therefore to the definition of the content-container relationship, is adequately captured by our model, and further correspondences can be detected with Bion's theory about links and transformations, implying different ways in which the mind can get in touch with both internal and external reality.
In the present paper, we aim to develop a formal quantum logic theory of the interplay between conscious and unconscious processes of the human mind, a goal that has already been envisaged in quantum cognition; in doing so, we will show how the interplay between formal language and metalanguage allows for characterizing pure quantum states as infinite singletons: in the case of the spin observable, we obtain an equation defining a modality that is then re-interpreted as an abstract projection operator. By including a temporal parameter in the equations and by defining a modal negative operator, we derive an intuitionistic-like negation, for which the non-contradiction law is seen as an equivalent of the quantum uncertainty. Building on the psychoanalytic theory of Bi-Logic by Matte Blanco, we use modalities in interpreting the emergence of conscious representations from an unconscious one, and we demonstrate that this description fits well with Freud's view of the role of negation in mental processes. Psychoanalysis, where affect plays a prominent role in shaping not only conscious, but also unconscious representations, is therefore seen as a suitable model to expand the domain of quantum cognition to the broader field of
In this paper, we are dealing with the fundamental concepts of Bi-logic proposed by Chilean psychoanalyst Ignacio Matte Blanco in the context of quantum logic, founded by Gareth Birkhoff and John Von Neumann. The main purpose of this paper is to present how a quantum-logical model, represented by the lattice of a closed subspace of Hilbert space, can be used as a computational framework for concepts that are originally described by Sigmund Freud as the fundamental properties of the unconscious psyche.
Abstract Quantum logics are non-classical logics defined from the mathematical formalism of quantum mechanics. While they are conventionally used to model inferential processes in physics, their scope of application is potentially much broader. We argue that quantum logics can serve as a framework to model human cognition, as their semantics seem able to capture not only how people make inferences about quantum mechanics, but also how they reason in general. We begin by defining quantum logics from an algebraic perspective in a classical first-order setting. Next, we present findings from cognitive science that suggest these logics are apt to characterize human reasoning. We then consider how such a connection between quantum logics and cognition contributes to longstanding philosophical debates about the epistemological status of logic and the problem of adoption. Finally, we discuss how cognitive applications of quantum logics could advance our understanding of human psychology and even quantum foundations.
The aim of such paper is to explain in detail the foundations of quantum cognition and to evidence the manner in which our pioneering experiments on quantum interference in humans should be correctly interpreted in the framework of a correct quantum mechanical elaboration. Often, studies on quantum cognition are elaborated from some authors evidencing that presently we have empirical evidence that the application of quantum rules gives better results respect to classical ones. Consequently, such studies are delineated as empirical tentative. It is not true. Quantum cognition is a scientific realization structured about robust quantum foundations and this is the reason because it gives such important results. Consequently, we discuss the evidence to correctly explain the foundations of this emerging discipline. In order to reach this objective we analyze the fundamental role of the abstract entity that is called quantum mechanical wave function. Soon after we describe the manner in which quantum operators must be entered in cognition studies by using the projectors that represent logic statements and thus relate directly our cognitive functions. We also discuss in detail the logical origins of quantum mechanics outlining that it does not represent a physical theory looking at the matter at microscopic level but a God Giano two faces looking simultaneously to material and to mental reality. We also discuss results establishing the nature of our consciousness and the unquestionable result that it obeys to the basic rules of quantum mechanics. We also give a further and pressing indication: in quantum cognition studies the quantum wave function must be intended as reconstructed experimentally a posteriori in our cognitive studies and cannot be confused with the standard examining elaboration that is used in usual textbooks of quantum mechanics. Also the question of the order effect is analyzed in detail using the important notion of reaction time of psychology. In substance, we give a total reformulation of the current quantum cognition studies evidencing that previous elaborations finalized to present the current status of this discipline as empirical tentative to characterize a quantum cognitive modelling result to be only approximate, incorrect and confusing prospects that damage the information about the robust structure of quantum cognition and therefore need to be rejected.
Quantum mechanics emerged as the result of a successful resolution of stringent empirical and profound conceptual conflicts within the development of atomic physics at the beginning of the last century. At first glance, it seems to be bizarre and even ridiculous to apply ideas of quantum physics in order to improve current psychological and linguistic or semantic ideas. However, a closer look shows that there are some parallels in the development of quantum physics and advanced theories of cognitive science. In psychology, geometric models of meaning have a long tradition. However, they suffer from many shortcomings which are illustrated by discussing several puzzles of bounded rationality. In the first part of this article, we argue that the present account of quantum cognition - taking quantum probabilities rather than classical probabilities - can give a more systematic description of these puzzles than the alternate and rather eclectic treatments in the traditional framework of bounded rationality. Unfortunately, the quantum probabilistic treatment does not always and does not automatically provide a deeper understanding and a true explanation of these puzzles. In the second part of this article, we explain the foundational issue from the perspective of Piron, Foulis, Randall, and others, and we apply it to the foundation of quantum cognition. In this connection, we show that quantum probabilities are of (virtual) conceptual necessity if grounded in an abstract algebraic framework of orthomodular lattices. This framework is motivated by assuming partial Boolean algebras (describing particular perspectives) that are combined into a uniform system while considering certain capacity restrictions. It is at this point that one important aspect of the whole idea of bounded rationality directly enters the theoretical scenery of quantum cognition: resource limitation.