“Most tantumising state of affairs”: Mathematical and non-mathematical in quantum-like understanding of thinking - Plotnitsky, Arkady (Frontiers in Psychology, 2022)
This article recognizes the effectiveness of, to use the title of this special issue, the “predictive modeling of cognition and behavior based on quantum principles,” and will consider some of the reasons for this effectiveness. Its aim is, however, also to explore the limitations of mathematical modeling so based, also known as quantum-like (Q-L) modeling, and ultimately all mathematical modeling, including classical-like (C-L), based in mathematics of classical physics, in considering human cognition and behavior. It will discuss certain alternative approaches to both, essentially philosophical in nature, although sometimes found in literary works, approaches that, while not quantitative, may, nevertheless, help compensate for limitations of mathematical modeling in human and social sciences, and be used together with the latter there, in contrast to physics itself, where mathematics is sufficient. The article will consider quantum phenomena and quantum theory, before turning to human thinking and decision making. Most Q-L and C-L approaches beyond physics are realist, insofar as they offer representations of human thinking by the formalism of quantum or classical physical theories. Whether such a representation, as opposed to only predicting the outcomes of experiments, is possible in Q-L theories of human thinking or in quantum theory itself is one of the questions addressed in the article. The position adopted in it is that such a representation may not be possible, which is not the same as that it is impossible. I designate interpretations that do not make this assumption reality-without-realism, RWR, interpretations, and in considering mental processes as ideality-without-idealism, IWI, interpretations. One such interpretation, with certain additional assumptions, will be adopted by this article.