Battilotti Giulia, Borozan Miloš, Grotto Rosapia Lauro
Department of Mathematics, University of Padua, Via Trieste, 63, 35122 Padova, Italy.
Department of Neurosciences, Imaging and Clinical Sciences, G. d'Annunzio University of Chieti-Pescara, Via dei Vestini, 31, 66100 Chieti, Italy.
Entropy (Basel). 2022 Oct 4;24(10):1419. doi: 10.3390/e24101419.
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
在本文中，我们旨在发展一种关于人类思维中意识与无意识过程相互作用的形式量子逻辑理论，这一目标在量子认知领域中已经有所设想；在此过程中，我们将展示形式语言与元语言之间的相互作用如何使得将纯量子态表征为无限单元素集成为可能：在自旋可观测量的情况下，我们得到一个定义模态的方程，然后将其重新解释为一个抽象投影算子。通过在方程中纳入时间参数并定义一个模态否定算子，我们推导出一种类似直觉主义的否定，对于这种否定，非矛盾律被视为等同于量子不确定性。基于马特·布兰科的双逻辑精神分析理论，我们使用模态来解释从无意识表象中产生有意识表象的过程，并且我们证明这种描述与弗洛伊德关于否定在心理过程中作用的观点非常契合。因此，精神分析——其中情感不仅在塑造有意识表象，而且在塑造无意识表象方面都起着重要作用——被视为一个合适的模型，可将量子认知的领域扩展到更广泛的领域。
