This article focuses on the most important problem of scientific pragmatism and historical knowledge, an attempt to use the category of «the unrealized» for its solving on the basis of the advanced modeling and mathematical approaches. The urgency of the stated problems is associated with the crisis of the social function of history, partly caused by methodological problems of research, as well as high practical and theoretical importance of forecasting the future historical processes.

At the beginning of the 21st century globalization exerts a transformational impact on the socio-cultural dynamics of the Circassian ethnic group. The main manifestations of social and cultural globalization in the spiritual life of the author identifies are Circassian interethnic marriages, international tourism, interdiasporal contacts, foreign TV and radio channels broadcasting and spread of the Internet and multimedia technologies. The indicated manifestations of the mondialization ambivalently implemented in a regional context of Circassian society and, therefore, require scientific understanding

The article is devoted to the analysis of the triad of "personality's world", "vital world" and "culture world". Different approaches are considered to apprehension of the personality's world and specific character of its axiological fullness. According to the author the informational and axiological aspect of constructing the personality's world helps to highlight the hierarchy of cultural value orientations, their evident subordination as well as value system transformation in the informational society. Heterogeneity of scientific knowledge, its social and cultural significance is realized in the traditions of axiology. The scientific knowledge begins to lose its purely academic character and acquires the value of a person's vital resource.

Civilization development is closely connected with such a phenomenon as city which should be considered in various aspects: 1) morphological (spatial dimensions, architecture of buildings, their functional and physical parameters), 2) phenomenological (subjective experiences) and 3) value-semantic. Some other factors are also expedient: ascertaining of environmental parameters; formation of subjective opinions; estimating descriptions; cause and effect analysis. The dominating concept of city as "a form of territorial organization of life and activity of people" are complemented by other representations coming from various fields of knowledge.

The paper is devoted to the analysis of the socio-cultural space of the North Caucasian community which represents a complex open system. In the conditions of modernization of the North Caucasian society the ethnic factor continues to play an important role in the region. Ethno-cultural traditions, as a basis of cultural identity, are stable elements in this system. The interaction of traditions and innovations in the North Caucasus is shown by example of identity as a multilevel hierarchical formation uniting traditional and modern types of identities: ethnocultural, regional, national, civilizational. They are based on various values which do not exclude, but rather supplement and strengthen each other.

This article is concerned with the Russian philosophers' treatment of life meaning as a system of values and the highest blessing. In the center of the authors' attention is the attitude to the traditional understanding of life meaning and way of life in the rival schools of philosophical thought of the 19th -20th centuries headed by Chernyshevsky and Dostoyevsky and the assertion that Christian spiritual and moral meaning and lifestyle are of primary importance as an effective way of liberating and creating personality as a basis of national identity.

The article is devoted to the problems of understanding the human in works by V.I. Vernadsky. The main emphasis is put on the study of the nature of man, as well as the future of all mankind. In the works of the thinker the interrelationship of man and the universe, man and environment are considered. The author justifies the principles of mankind's new attitude towards nature and itself and its activities, which becomes more exacting. In V.I. Vernadsky's works man is treated as an intelligent and creative being, a unity of physiological, social and psychological aspects of his existence. V.I. Vernadsky managed to consider the future of mankind in close connection with the life of an individual, cosmos, nature and the universe.

The article systematizes and analyzes the most important category of moral perfection of man, formulated in the works of the thinkers of the Cappadocian school on the basis of rethinking the provisions of classical philosophical ideas and early Christian heritage. The relevance of the subject is confirmed by a continuous interest to the problem of improvement of the human in the Patristic Era and at present. The author claims that from the Cappadocian point of view of the utmost moral task of man is the attainment of virtue which is boundless by nature and the longing for which is limitless.

Understanding symbolism both in verbal and in ritual form is the most important question of theological as well as philosophical problems. Symbolism undertakes an attempt to show the eternal in temporary. Considering the problem of symbolism in Florensky's works, the author highlights the thinker's close relationship with the philosophy of cult. The article pays attention to the relative nature of a symbol that has a dual sense (external and internal) as well as the symbolism of Christian art. The article mentions that the origin of Florensky's symbolism is rooted in symbolic ontology the aim of which is cognition of God. The symbol as an ontological reality is synergy, i.e. divergence, interpenetration of energy that is not mechanically but organically thought. The philosopher believes that a symbol exists as a thing in real existence, but it appears to a person as a symbol; in case of being understood it becomes the way of assimilation of the transcendent.

While in Soviet Russia it was Marxism that established itself as the leading scientific methodology, Russian scientists abroad continued the traditions of cultural studies of the history of civilization. The civilization process was studied by such proponents of culturological approach as N.A. Berdyayev, P.M. Bicilli, R.Yu. Vipper, I.A. Ilyin, L.P. Karsavin, A.A. Kizevetter, G.P. Fedotov. The article presents an analytical review of conceptual and methodological heritage of the Russian scholars of the first wave of emigration.

The article is concerned with the priority of methodological standards, ideals and norms of contemporary historical knowledge. The specific character of the differentiation of the general tendency of historical epistemology and contemporary concepts of epistemology of history is investigated. The author studies the relationship of the organic-shaped idea of history and myth, which makes it possible to better understand some new forms in which the structuring of integral historical consciousness and knowledge takes place. The possibilities of organic thinking are explained capable of leading separate and even hostile elements of historical theories to an agreement.

Based on vast historical material the paper studies the preconditions of a productive dialogue established between mathematics and natural sciences. The mathematician studies the subject in a «pure» way by using abstract models, thus anticipating their subsequent research by corresponding sciences. Based on this assumption it is possible to claim that the role of mathematics in scientific cognition will be increasing with years.

The article discusses the rationale and development of a means of social and philosophical analysis of the discourse of physicality in the artistic culture of the Middle Ages and the art of modern times. Since the Renaissance, the problem of the meaning of existence in the art characteristic of the Middle Ages denied the transcendent dimension. The main problems associated with the current art of the moment, with modernity, the boundaries of this narrow scope of tasks of art in time and space, creating a situation of autonomy of the artist from the church and liturgical obligations, emancipation limit is expressed in upholding the right of artistic creation as an independent and self-sufficient quite work, does not subordinate to any religious or moral values.