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Title
Abstract
Introduction
General Discussion
Bounded Rationality and Resource Limitations
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Philosophy
Epistemology

Descriptive and foundational aspects of quantum cognition

Profile image of Reinhard BlutnerReinhard Blutner

2014

https://doi.org/10.13140/2.1.2512.6407
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53 pages

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Abstract

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 dealing with concepts, conceptual composition, vagueness, and prototypicality. In both cases of the historical development, the underlying basic ideas are of geometric nature. 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. The main suggestion of the present approach is that geometric models of meaning can be improved by borrowing basic concepts from (von Neumann) quantum theory. In the first part of this article, we consider several puzzles of bounded rationality. These include the Allais-and Ellsberg paradox, the disjunction effect, the conjunction and disjunction fallacies, and question order effects. 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. One reason is that quantum approaches introduce additional parameters which possibly can be fitted to empirical data but which do not necessarily explain them. Hence, the phenomenological research has to be augmented by responding to deeper foundational issues. In the second part of this article, we aim to illustrate how recent progress in the foundation of quantum theory can help to answer the foundational questions of quantum cognition. This includes the opportunity of interpreting the free parameters, which are pure stipulations in the quantum probabilistic framework. Making a careful distinction between foundational and phenomenological research programs, 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. Another important aspect of the foundational issue is that it automatically leads to a distinction between probabilities that are defined by pure states and probabilities arising from the statistical mixture of such states. It is possible to relate this formal distinction to the deep conceptual distinction between risk and ignorance. A third outcome is the possibility to identify quantum aspects in dynamic macro-systems using the framework of symbolic dynamics, closely related to the operational perspective of Piron, Foulis, Randall, and others. This helps to understand the ideas of epistemic complementarity and entanglement, and to analyse quantum aspects in third generation neural networks.

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