It is shown that the uncertainty connected with a `random in a broad sense' (not necessarily stochastic) event always has some `statistical regularity' (SR) in the form of a family of finite-additive probability distributions. The specific principle of guaranteed result in decision making is introduced. It is shown that observing this principle of guaranteed result leads to determine the one optimality criterion corresponding to a decision system with a given `statistical regularity'.
We consider an experiment that conducts observations on an uncertain parameter. Experiments observing a parameter with a stochastic uncertainty have been studied exhaustively and their characteristics have been described by many authors [see, e.g., De Groot, M. (1974), Optimal Statistical Decisions (Russian translation)]. In this article, we assume that uncertainty is generated by a mechanism which is “random in the broad sense” [a term introduced by Kolmogorov, A.N. (1986), in Probability Theory and Mathematical Statistics (in Russia), pp. 467–471]. Ivanenko, (...) V.I. and Labkovskii, V.A. [(1986), Dokladi Na Bolgarskata Akademiya Na Naukite SSSR 287(3), 564–567; (1990), Dokladi Na Bolgarskata Akademiya Na Naukite SSSR 310(5), 1059–1062] have proposed the apparatus of “statistical regularities” for the description of such randomness. Statistical regularity (SR) is a family of finitely additive probability distributions such that particular SRs correspond to total uncertainty, stochastic uncertainty, and other forms of uncertainty. The problem in which uncertainty is specified by SR is accordingly called General Decision Problem (GDP). We investigate informativeness and optimality of experiments in GDP. (shrink)
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.
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)
The ´, or world's con flagration, followed by the restoration of an identical world seems to go against the rationality of the Stoic god. The aim of this paper is to show that Cleanthes, the second head of the School, can avoid this paradox. According to Cleanthes, the con flagration is an inevitable side-effect of the necessary means used by god to sustain the world. Given that this side-effect is contrary to god's sustaining activity, but unavoidable, god's rationality requires the (...) restoration of an identical world once the con flagration subsides. The paper also deals with the relation between Cleanthes and other early Stoics on the topic of con flagration. In particular, Cleanthes' position seems to diff er from Chrysippus'. For in contrast with the Cleanthean god, who causes the con flagration as a side-effect only, the Chrysippean god, according to an in fluential interpretation put forward by Jaap Mansfeld, causes the con flagration as his ultimate cosmological goal. (shrink)
Grigorii Savvich Skovoroda was a distinguished philosopher of the eighteenth century Ukraine who made a significant contribution to the development of philosophical thought and enlightenment ideas. A contemporary of N. I. Novikov, Ia. P. Kozel'skii, and A. I. Radishchev, he reflected in his work the protest of the laboring peasant masses against serfdom. This protest was the starting point for his philosophical interpretation of the world, man, problems of social justice, and the paths along which they could be resolved. Representing (...) the antifeudal movement for enlightenment in the Ukraine, he linked the freedom of his people to unification of the Ukraine with Russia and to the general struggle for implementation of anti-serfdom ideals. (shrink)
The name A. S. Khomiakov crops up in practically everything written on Slavophilism, especially when the discussion touches on sociophilosophical problems. But one thing here is odd. Most authors, in dealing with Khomiakov's analysis of universal history, touch barely in passing on his capital work Notes on Universal History [Zapiski o vsemirnoi istorii], although in volume it makes up almost half of his collected works. Although this text has been little studied, it is sometimes characterized very harshly. In the words (...) of one scholar, Khomiakov attempted in it to "marshal the data of religion and linguistics on behalf of fanciful conceptions that, pathetically, amounted to only a few pet notions about the triumph of Slavic orthodoxy." After such an unequivocal assessment, is it worthwhile digging about in the old rubbish and wasting time? On first glance the volume of Khomiakov's Notes is indeed a peculiar work. The notes were made by the author for himself, and this has left its mark. Nonetheless the Semiramis [Semiramida] is an extremely interesting and remarkable work in its own way. Since it has remained practically unstudied, it is necessary to give at least a general description of it and to examine its basic premises and ideas before going on to analyze it. (shrink)
The purpose of the present report is to draw the philosophical community’s attention to the universal principle of cognition, the principle of extrapolation, capable of integrating the present and possibly, the future methods of man’s cognitive attitude to the world. Extrapolation is interpreted as a key logical-and-gnosiological procedure and, depending on subject/object relationships, is subdivided into “actual” and “real”. According to the actual extrapolation principle in any kind of cognition, it is important to take account of the fact of the (...) ontological presence of the individual in the world. The real extrapolation method is based on the available gnosiological content of a cognizing subject and on the use of a totality of the logical, gnosiological, epistemological, methodological, content-related and even psychological wealth of accumulated knowledge with the aim of its augmentation. The all-important aim of new gnosiology (theory of knowledge) should consist in studying permissible bounds of extrapolation, and in identifying basic laws of extrapolation of knowledge in two forms of its being as a necessary condition of their possible synthesis. (shrink)