The article is devoted to the memory of Vyacheslav Semenovich Stepin and Nikita Nikolaevich Moiseev, whose multifaceted work was integrally focused on philosophical, interdisciplinary and transdisciplinary research of the key ideas and principles of universal human-dimensional evolutionism. Other remarkable Russian scientists V.I. Vernadsky, S.P. Kurdyumov, S.P. Kapitsa, D.S. Chernavsky worked in the same tradition of universal evolutionism. While V.I. Vernadsky and N.N. Moiseev had been the originators of that scientific approach, V.S. Stepin provided philosophical foundations for the ideas of those (...) remarkable scientists and thinkers. The scientific legacy of V.S. Stepin and N.N. Moiseev maintained the formation of a new quality of research into the philosophy of science and technology as well as into the philosophy of culture. This new quality is multidimensional and it is difficult to define unambiguously, but we presume the formation of those areas of philosophical knowledge as constructively oriented languages of interdisciplinary and transdisciplinary co-participation of philosophy in the convergent-evolutionary development of scientific knowledge in general. In this regard, attention is paid to V.S. Stepin’s affirmations about non-classical nature of modern social and humanitarian knowledge. Quantum mechanics teaches us that the reality revealed through it is a hybrid construct, or symbiosis, of both mean and object of cognition. Therefore, the very act of cognitive observation constructs quantum reality. Thus, it is very close to the process of cognition in modern sociology and psychology. V.S. Stepin insisted that these principles are applicable to all complex selfdeveloping systems, and such are all “human-dimensional” objects of modern humanities. In all the phases of homeostasis changes, or crises, there is necessarily a share of chaos, instability, uncertainty in the selection process of future development scenarios, which is ineliminably affected by our observation. Therefore, a cognitive observer in the humanities should be considered as a concept of post-non-classical rationality, that is as an observer of complexity. (shrink)

We present a novel variant of decision making based on the mathematical theory of separable Hilbert spaces. This mathematical structure captures the effect of superposition of composite prospects, including many incorporated intentions, which allows us to describe a variety of interesting fallacies and anomalies that have been reported to particularize the decision making of real human beings. The theory characterizes entangled decision making, non-commutativity of subsequent decisions, and intention interference. We demonstrate how the violation of the Savage’s sure-thing principle, known (...) as the disjunction effect, can be explained quantitatively as a result of the interference of intentions, when making decisions under uncertainty. The disjunction effects, observed in experiments, are accurately predicted using a theorem on interference alternation that we derive, which connects aversion-to-uncertainty to the appearance of negative interference terms suppressing the probability of actions. The conjunction fallacy is also explained by the presence of the interference terms. A series of experiments are analyzed and shown to be in excellent agreement with a priori evaluation of interference effects. The conjunction fallacy is also shown to be a sufficient condition for the disjunction effect, and novel experiments testing the combined interplay between the two effects are suggested. (shrink)

In this article, Savage’s theory of decision-making under uncertainty is extended from a classical environment into a non-classical one. The Boolean lattice of events is replaced by an arbitrary ortho-complemented poset. We formulate the corresponding axioms and provide representation theorems for qualitative measures and expected utility. Then, we discuss the issue of beliefs updating and investigate a transition probability model. An application to a simple game context is proposed.

Nadezhnostʹ matematicheskogo dokazatelʹstva -- Nadezhnostʹ logicheskikh norm -- Ontologicheskoe obosnovanie matematiki -- Sistemnoe obosnovanie matematiki.

t. 1. Igry rynka -- t. 2. Torgovet︠s︡ v Khrame.

In his critique of empiriocriticism, V. I. Lenin also considered it necessary to characterize its relationship to religion in order to show more fully the social significance of this school, which was fashionable in its time. In contrast to those who took at face value the pretensions of Machism to present the scientific thought of the nineteenth century and who hastened to put it in place of "obsolete" materialist dialectics, V. I. Lenin unmasked the "completely reactionary character" of this essentially (...) subjective-idealistic current, which played into the hands of fideism despite the fact that E. Mach considered himself an atheist. (shrink)

Quantum cognition in decision making is a recent and rapidly growing field. In this paper, we develop an expected utility theory in a context of non-classical uncertainty. We replace the classical state space with a Hilbert space which allows introducing the concept of quantum lottery. Within that framework, we formulate axioms on preferences over quantum lotteries to establish a representation theorem. We show that demanding the consistency of choice behavior conditional on new information is equivalent to the von Neumann–Lüders postulate (...) applied to beliefs. A dynamically consistent quantum-like agent may violate dynamic recursive consistency, however. This feature suggests interesting applications in behavioral economics as we illustrate in an example of persuasion. (shrink)