In recent decades, some epistemological issues have become especially acute in mathematics. These issues are associated with long proofs of various important mathematical results, as well as with a large and constantly increasing number of publications in mathematics. It is assumed that (at least partially) these difficulties can be resolved by referring to computer proofs. However, computer proofs also turn out to be problematic from an epistemological point of view. With regard to both proofs in ordinary (informal) mathematics and computer proofs, the problem of their surveyability appears to be fundamental. Based on the traditional concept of proof, it must be surveyable, otherwise it will not achieve its main goal — the formation of conviction in the correctness of the mathematical result being proved. About 15 years ago, a new approach to the foundations of mathematics began to develop, combining constructivist, structuralist features and a number of advantages of the classical approach to mathematics. This approach is built on the basis of homotopy type theory and is called the univalent foundations of mathematics. Due to its powerful notion of equality, this approach can significantly reduce the length of formalized proofs, which outlines a way to resolve the epistemological difficulties that have arisen.

The article explores the arguments in favor of feminist epistemology used in the works of L. Code, S. Harding, D. Haraway, J. Lloyd and other gender (radical) feminists. The sources of feminist epistemology are the naturalized epistemology and the thesis of underdetermination by W. Quine, the views of W. Sellars, Marxism, the strong program of sociology of knowledge, logical positivism. The features of feminist epistemology include many signature schemes, the tendency to use different schemes from suitable disciplines, rethinking of the concepts «knowledge» and «knower» for previously excluded or non-included groups of women, people with disabilities, representatives of different races, sexual minorities. Another feature is that «Feminine» experience and voice, viewed from an essentialist or non-essentialist approach, are considered the grounds for the position of «knower». The article examines the critical remarks made by feminists against the assumptions of traditional epistemology: universal human nature, «a view from nowhere», pure impersonal reason, the assumption of «Robinsonade». Attention to subjectivity, values and selfish interests in the production of knowledge should be considered a merit of feminist epistemology. However, L. Laudan has already shown that no one, including representatives of feminist epistemology, have demonstrated the plausibility, let alone the veracity of judgements that justify any number of possible interpretations of the knowledge gained. The paper shows that feminist epistemology cannot avoid the well-known vicissitudes of epistemological relativism. However, feminist epistemology deserves the attention of philosophers because it is part of a broader relativist turn in social sciences and the humanities that seeks to extend its criticism to scientific knowledge.

It is already the case that philosophical foundations of mathematics and physics, need a serious critical analysis and revision of a number of generally accepted assumptions. In the future, this work may lead to a shift in the paradigm related to mathematics and physics. The article deals with the problem of the ideas of actual and potential infinity being not distinguished in the «fragmented thinking» of many mathematicians. We consider it necessary to differentiate between the concept of «representation of a number by an infinite decimal fraction» and the concept of «writing a numeral». A real number can be written in different ways, but every number must be uniquely represented using an infinite decimal fraction. First of all, we overcome the ambiguity of the representation of number 1 by assuming a potentially infinite set of signs of a periodic fraction and an actually infinite set of signs of a non-periodic fraction. This leads to the following harmonious scientific and philosophical system required by broad-minded scientists. 1. Every real number, including 0, (9) is represented by a single point of a continuous number line. 2. Every irrational number in decimal representation, unlike a rational number, does not have the last digit. 3. Real space, as well as past and future time are not mathematically equal and are referents of potentially and actually infinite, countable and uncountable sets. 4. The motion of a quantum micro-object, as a fundamental particle, is mathematically imaginary because a quantum particle has a countable set of points in time that is insufficient to move temporally and an uncountable set of points in space that is excessive for moving along the trajectory. Therefore, the motion of a quantum particle can be described as the path of a point in the plane of a complex variable.

Тhe article explores the question of being. Its relevance is revealed through ontological obligations. This question belongs to the domain of the transcendent, the subject of metaphysics. Being is considered through the concepts «order of being», «predicates of being» and «dignity of being». The paper introduces the concepts of inreality and connected being and gives the argument of the «third being». The concepts of real and ideal, some types of proofs of existence are discussed. The dilemma of being is formulated, which is formed by the recognition that being exists upon condition that being is an action and acts directly, on the one hand, and, on the other, by the recognition that being acts through some phenomenon, therefore it is identified with some object and is considered objective, mediated being. In other words, it is a statement about the existence of being in itself and being distributed in a certain order, the order of being, namely: the existence of things, being, essence, man, etc. The aspects of the dilemma of being are created by the differentiation between being and becoming, being and living, being and thinking. These ontological distinctions lead to such resolution of the dilemma of being when being is recognized as: 1) the measure of things that they «matter (are the essence)» and that they «are not the essence», i.e, become; 2) the measure of things that make sense and those that do not, and 3) the measure of things imaginable and unimaginable. As a result, the paper offers the following definition of being: being is immediacy as such (non-objective being) which combines the immediacy of things, actions, phenomena, processes, sensations, etc. (objective being).

The purpose of this article is a philosophical and anthropological analysis of the ideal of androgyne in V.V. Rozanov’s metaphysics of sex. The main focus is on the comparison of the destructive and constructive forms of the androgyne in his philosophy. According to the philosopher, destructive forms include people of «moonlight» or «third sex», who are considered the founders of New Testament Christianity, denying the life of the flesh. Constructive forms are the natural androgyny of a child and the androgyny of a married couple, which reveals itself in love, dynamics, mutual complementarity of a man and a woman. The paper draws parallels between N.A. Berdyaev’s and V.V. Rozanov’s concepts of androgyne, which are antipodal in terms of direction of thought but have common meanings. It is concluded that the similarity between the concepts lies in the understanding of gender as a dynamic and metaphysical principle that penetrates through not only the bodily but also the spiritual life of a person, and therefore cannot be rejected. The concepts are also similar in that they draw a boundary between the androgyne and the hermaphrodite, of which the former is the ideal of the human wholeness, while the latter is an unsuccessful attempt to achieve it. The differences between these philosophers consist in the priority of spiritual love in Berdyaev’s system and worldly, bodily love in Rozanov’s, as well as in a different understanding of the process of an androgyne being generated in a person, which, in Berdyaev’s conception, is individual and arises in each of the persons who are in love with each other, while, according to Rozanov, it is exclusively achievable in couples. The paper also pays attention to Rozanov’s own theology, which renews the Old Testament family ideals, offering the concept of God as a «sexual» being and proposing to consider the act of love within marriage as a sacred mystery that unites a person with God in co-creation. The study allows us to rethink the modern problems of gender self-determination of a person, returning to the metaphysical foundations of the Russian philosophy of gender, the main task of which was the synthesis of the spiritual and bodily principles in a person.

The article analyzes the attempt to develop a synthesized concept of man, or the «unified science of man», undertaken in the 1980s by a group of Soviet philosophers led by academician I.T. Frolov. The complex interdisciplinary study of the human phenomenon, first presented to the academic community in this period, included not only the traditional synthesis of philosophical data with the data of natural and social sciences but also the experience of co-optation of certain religious philosophy provisions into philosophy. Some scientists put forward a hypothesis about the convergence of science and religion in the future. However, the idea of abandoning a strict materialistic worldview was not accepted by the academic community. The article reconstructs and analyzes the basic provisions of the «unified science of man»: ideas about the anthropological ideal, the origin of man and the correlation of biological and social principles in his nature, the interrelation of freedom and necessity, external and internal freedom, the meaning and purpose of life, the relationship of personality and society. The paper concludes that in the 1980s there was developed a strategy in the USSR for the holistic solution of the philosophical problems of man based on the creative development of classical Marxism, which could subsequently lead to the transition of Russian philosophical anthropology and philosophy in general to a whole new level. Due to external circumstances, this work was actually stopped at the very beginning, and the task declared paramount in terms of scientific and social significance was never solved.

The study focuses on the phenomenon of alterity found in experience, in general, as the «other» or Others (other subjects as such). The research is based on phenomenological and dialectical approaches and orientation on the problem field of philosophy of education proceeding from an anthropological perspective. The article outlines the context of the problem of the other in philosophy and social sciences, based on which there was set an objective of developing an understanding of the meaning of the other, especially in relation to education. In considering the experience of «being a human» as the foundation of education, there are identified ‘layers’, starting with the ‘simplest’ — the level of «order», at which «self» and the «other» are revealed. This is a perspective determined by self-identity, which explains such areas of education as «embedding», training in relations with different environments; «systems thinking»; «learning» to «cope». A special relationship between «self» and the «other» is revealed in the layer of the experience of the «living». This layer is found to be nonstatic and should be designated as the phenomenon of «agency». The dialectics of the relations between the self and the «other» within this layer also explains the processes of «reflection» inherent in living things and accompanying human experience in its development at all further levels. The paper conceptualizes the significance of the «other» in the experience of this level for the modern articulation of the principles of education and for the interpretation of «human education». In the layers of experience of a «living being» and a «person-in-particular», the article reveals the significance of the «other» and Others for the gradual development of the properties and characteristic phenomena of agency according to the levels of experience in the course of a lifetime up to «maturity». These properties and phenomena include «open agency»; «subjective experience»; «light of consciousness»; «understanding»; interactions and «relationships» with the Others; «discernment»; «thing»; «sign». The paper provides conclusions regarding the significance of the «other» and Others for human experience, in general, and for the essential characteristics of individual agency («self-expression»; «self-overcoming»; «inclusive nature» of agency), as well as for understanding the education required in the modern world.

The article discusses the feasibility and vistas of re-defining the concept «society» in an effort to make it fit for studying the current situation. The constant mobility of actors and the new virtual reality transcend the boundaries between social groups, which calls methodological capacity of any static and especially essentialistic understanding of the phenomenon called «society» into question. The author starts from defining society through communication acts, but at the same time distinguishes between them by the level of mutual understanding attained through communication, which makes it possible to scrutinize the internal structure of the term in question. Understanding of communication acts as a medium of memetic influence that shapes a person’s agency and ensures synchronicity between persons, adequate for a certain level of mutual understanding, enables the author to view society as a dynamic process, as a memetic field amid constantly changing and diverse challenges. The landscape contour of the challenges adds constant disturbing differentiations that guarantee continual social changes. By contrasting practical and discursive minds, the author discriminates non-reflexive mimetic processes of practical knowledge transfer from their reflexive comprehension. Thus, the author distinguishes two levels in social processes, incompatibility between which adds complexity to social dynamics. Using this understanding of the social, the author shows how in certain conditions a person may identify with a certain social group. In conclusion, the paper formulates three main practical questions the answers to which will let us assess the possibilities for further development of society.

Combined study of emotional intelligence and emotional regulation allows us to obtain information not only about individual differences in the understanding and management of emotions but also about the cognitive processes by which regulation is carried out. Emotion management becomes especially relevant in adolescence, as this age is characterized by emotional vulnerability and risk of deviant behavior. This study deals with the abilities being part of emotional intelligence in their relation to the cognitive components of emotional regulation, namely, the ways and strategies of response that prevail in the behavior of adolescents. The study involved 72 respondents aged 14–16 years. The results showed the specificity of cognitive regulation of emotions and emotional intelligence in older adolescents. The group of respondents with high emotional intelligence more often employ effective strategies for regulating emotions, while the rates of using destructive strategies decrease. Participants with low emotional intelligence use effective and destructive strategies almost equally. Those participants who effectively manage their emotions most often use strategies such as creating a positive meaning for the event or switching to more pleasant thoughts. Destructive strategies for regulating emotions have a negative relationship with emotional intelligence: the greatest number of correlations was revealed for the strategies «Catastrophizing» and «Rumination», also associated with depression. The results obtained clarify the specific features of the relationship between cognitive regulation of emotions and emotional intelligence in older adolescents, and also allow us to describe the contribution of these abilities to the formation of the psychological well-being.

The paper argues for the importance of sociological analysis of the factors that determine the level of mental health such as public awareness of mental health, access to qualified help in case of mental deterioration and attitudes towards people with mental disorders. The expediency of using the term «competence in the field of mental health» in assessing the social conditionality of a mental state is shown. A three-component structure of mental health competence, being contradictory in its orientation and content, is defined. Based on the analysis of sociological research results, the study reveals the features of cognitive, affective and behavioral components of the competence as being manifested in individuals with different health status. There are identified and described stereotypes of public consciousness that significantly increase the level of social distance between mentally healthy people and people with mental disorders (for example, «depression is a manifestation of character», «a mentally ill person is unpredictable and dangerous», «consulting psychiatrists is a last resort»). The author notes the interrelation and interdependence of stigmatization and self-stigmatization, as well as the impossibility of solving the problem of communication solely by forming an adequate attitude towards people with mental disabilities in the social environment. The author suggests using a generalized characteristic of certain social groups whose educational training and activity can increase the level of the population’s competence in the field of mental health. These social groups, in particular, include medical workers, students of secondary specialized and higher educational institutions. The paper provides practical recommendations for solving problems of mental health competence intended for specialists in medicine, education, psychology and sociology.

The article examines the key characteristics of young scientists’ integration into scientific communities in the context of the new prospects offered by the VUCA world. We see the VUCA world as a time of opportunities and a favorable period for young scientists to take initiatives, and also a world of total uncertainty, where impetuosity and uncertainty, as well as the constant search for and change of various strategies, become a key to successful career building and advancement. The empirical base of the analysis consists of 30 biographical interviews with young scientists from a city of regional significance, a young science city, a large city and a city of federal significance. The article puts forward a hypothesis about the importance of horizontal integration of young scientists into scientific communities in young cities and innovative cities, as well as in a large city and in a city of federal significance. The paper also discusses the role of the city as an actor that forms scientific communities and strategies for interaction and integration of young scientists with scientific communities. Special attention is paid to the meanings of scientific careers and the individual role of scientific communities in the careers of young scientists and also to the strategies for integrating young scientists into scientific careers. The authors consider changes in the configurations of strategies for both building a scientific career and integration into scientific communities at the local, national and global levels as new opportunities that arise for scientists in the VUCA world. The main conclusion of the article is that the integration and career building strategies in science are influenced by both the city and the orientation of the city, the local scientific community, which may differ depending on particular scientific disciplines. A successful strategy that allows one to use the potential and resources of the VUCA world to the maximum extent possible is the horizontal integration of young scientists.

The paper describes the main results of the intense discussion of current challenges related to using new digital technologies and emerging online risks in various spheres of human life within a framework of the International Online Conference «The Topical Issues of Applied Psychology in the Current Social and Cultural Context» (November 30 – December 3, 2020) organized by the Udmurt State University (the city of Izhevsk, Russian Federation). The conference has been held primarily due to the necessity of drawing the authorities’ attention to the critical concerns regarding psychological prevention of suicidal behavior in the region. The conference included a variety of the events: three symposia, sections for university and secondary school students; workshops and a documentary film discussion. According to the results of the conference debates and discussions, it has been pointed out that incorporation of digital technologies in psychological practice (counselling, therapy, etc.) provides psychology professionals with new opportunities through expanding their self-boundaries and enriching the field of professional reflection with additional meanings and senses. It is recognized that using artificial intelligence tools for initial appointments, basic diagnosis, and psychological prevention will facilitate professional activities of a psychology practitioner. The problem of psychological effects of everyday life application of digital technologies to maintain individual well-being, notably, the regulation of one’s own inner space and coping with difficult situations is specified. It has been stated that transdisciplinary studies of the effectiveness of diverse organizational forms of teaching and learning (onsite, distance, online, etc.) in connection with the subjective well-being of students are believed to be forward-looking and promising.