In [5] it has been shown that for first-order definability over the reals there exists an effective procedure which by a finite formula with equality defining an open set produces a finite formula without equality that defines the same set. In this paper we prove that there exists no such procedure for Σ-definability over the reals. We also show that there exists even no uniform effective transformation of the definitions of Σ-definable sets into new definitions of Σ-definable sets in such (...) a way that the results will define open sets, and if a definition defines an open set, then the result of this transformation will define the same set. These results highlight the important differences between Σ-definability with equality and Σ-definability without equality. (shrink)

Mikhail Bulgakov's novel The Master and Margarita was written between 1929 and 1940. Although delayed for a quarter of a century, it quickly found a stable place in our life as soon as it was published [for the first publication of the novel see: Moskva, 1966, no. 11; 1967, no. 1]. It is usually classified as a satirical philosophical novel. The satirical element puts it in the same family as such well-known works of the end of the '20s as (...) the novels of I. Il'f and E. Petrov, Twelve Chairs [Dvenadtsat' stul'ev] and The Golden Calf [Zolotoi telenok], but its emphatically philosophical orientation makes it all but a unique phenomenon in the history of Soviet literature. The novel's philosophical aspects have already been examined in a number of essays. Thus, for example, N. P. Utekhin analyzes the reflection of certain general philosophical categories in the novel. G. Chernikova and I. L. Galinskaia have endeavored to determine the concrete literary sources of the novel's philosophy [Chernikova 1971, pp. 213-219; Galinskaia 1986]. (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)

During the German-Soviet War and in the decades that followed, the Volyn Orthodox clergy functioned under a cohesive social ghetto, which was to ensure the gradual assimilation of the social group in accordance with the needs of the totalitarian regime. In this situation, the national self-awareness of a part of the sacred priests did not fit into the coordinates of the Nazi religious and ethnic politics and, later, into the process of creation of the Soviet people. The question of national (...) identity remains relevant, and now, when it is the basis of the newest Ukrainian state-making, it has caused division in the Orthodox field. The national consciousness of the Volyn clergy in the years of war and in the era of Soviet totalitarianism never became a topic of separate study. To date, scientists have only partially addressed the problem. Although in 1960, the head of the ROC Council, V. Kuroedov, said that the remnants of religious remnants contributed to preserving the bourgeois nationalist sentiment. The compilers of the first volume of documents and materials “Martyrology of the Ukrainian Churches” Osip Zinkevich and Alexander Voronin, analyzing the national composition of the bishopric of the Russian Church in Ukraine as of 1986, hoped that in case of revival of Ukrainian Orthodoxy, the origin of some of them role. (shrink)

There is much to be learned philosophically from this volume, but philosophical instruction was not Kierkegaard's aim here, except in the broad sense of self-knowledge and deepened awareness. Indicating the intention of the discourses, the titles include "The Expectancy of Faith," "Love Will Hide a Multitude of Sins," "Strengthening in the Inner Being," "To Gain One's Soul in Patience," "Patience in Expectancy," and "Against Cowardliness."In tone and substance these works are in accord with the concluding words of encouragement in Either/Or, (...) which was paired with the first volume of discourses: "Ask yourself and keep on asking until you find the answer, for one may have known something many times, acknowledged it; one may have willed something many times, attempted it--and yet, only the deep inner motion, only the heart's indescribable emotion, only that will convince you that what you have acknowledged belongs to you, that no power can take it from you--for only the truth that builds up is truth for you.". (shrink)

The idea of the common good has been a signature feature of Catholic social teaching and so of modern Catholic engagement in public affairs. It has recently been suggested that the notion is now obsolete due to changes in the culture and politics of the West. In keeping with this suggestion, some argue that Catholics should abandon it in favor of an appeal based on lower intermediate goods in a manner more related to Augustine’s engagement with the largely pagan culture (...) of his time than to Aquinas’s categories tailored to an integrally Christian society. I argue that such a solution misreads aspects of the tradition and of the present political and cultural situation and I suggest some alternative grounds on which Catholic engagement with contemporary public life should proceed and that thinking again about the common good is a necessary part of such engagement. (shrink)

The development of the social sciences needs to rely on precise methods. The nomological model of explanation adopted in the natural sciences is ill-suited for the social sciences. An algorithmic model of society can be a promising solution to existing problems. In its most general form, an algorithm is a generally understood prescription for what actions to perform and in what order to achieve the desired result. Any algorithm can be represented as a set of rules of the form «If (...) A, do D to get P». People are the bearers of this kind of rules that apply in different areas of their activities. The rules are subject to change based on personal and collective experience. There is a special mathematical discipline that studies the laws of evolution of such rules. This discipline is called genetic programming. Contrary to the threatening name, the algorithmic model does not imply the deprivation of a person’s right to free choice, but it needs this right as a necessary condition for the evolution of social algorithms. These algorithms allow us to give a non-causal, but law-like explanation of many well-known social phenomena, as well as to effectively model the future, which is critically important today. A retrospective look at the evolution of social algorithms shows that the current global crisis of human society is associated with the approach to the point of singularity in their evolution. This is due to the fact that there is no need for direct human participation in the implementation of social algorithms, which is reflected in a fundamental change in the sphere of employment and less need for further development of the sciences. (shrink)

В сборнике представлены очерки, герои которых - художники, философы, священнослужители, ученые, император Индии, французская крестьянка, Учитель Гималайского Братства и другие - сыграли немаловажную роль в земном творчестве Космической эволюции. Для широкого круга читателей.