Ideas and Ideals

The world’s oldest 3x3 magic square, discovered/invented in Ancient China and now known as Luoshu 洛書/ ‘Document [from the River] Luo’, was endowed by Chinese tradition with unprecedented dignity and placed at the very heart of Chinese thought. The bewitching geometric-numerical imagery of Luoshu, open to a great many different visions, when reading-interpretation becomes the final moment of the very act of perception, turns this Chinese mandala into a real eye trap. With its disturbing persistence, it resembles the magically attractive ‘Zahir’ from Borges’ short story of the same name.

   Among the most diverse ritual and ideological instrumentalizations of the Luoshu magic square (from the sacred emblem of cosmic harmony to the requisite of a geomancer), the mobilization of this esoteric figure for the arithmetization of the cornerstone of all Chinese philosophy, the fundamentally non-verbalizable Tao, is dominant. The coding of the dao by the number 15 is reinforced by its spatialization, so that the entire “Document [from the river] Lo” appears as a map of the various trajectories of the Tao within this nine-field square. Moreover, the coincidence (in number 15) of differently composed sums appears as an inscrutable variety of paths leading to the same goal - the final implementation of Tao.

     By virtue of the validity of the equality 15 =mod10 5 the magic sum of the Luoshu square (Const₁₅) immutably, although covertly (in the form of a number 5), centers the entire Luoshu configuration. This secrecy of the magical constant (the latter is absent in the entire observable space of the “Document [from the river] Lo”) refers to the hidden “back-side” of Luoshu numbers, represented by the number 10 (in its role as a modulus of comparison in the arithmetic of residues modulo 10).

      Judging by the directly visible, so to speak, ‘front’ part of the magic square of order 3, it is allowed to count only up to nine in it. But the already absent-present magic sum (number 15), breaking the seemingly inescapable circle of arithmetic of residues, brings to light the comparison module (number 10) as Luosh’s hidden ‘truth’, which alone gives meaning to the entire nine-cell construction. Awareness of this truth is the first step in the transition to the ‘register of truth’ of this extraordinary gestalt. The subsequent connection to it of problems focused by the Pythagorean theorem radically expands Luoshu’s ‘register of truth’.

      The geometrized arithmetic of the Luoshu magic square, which is a unique spatial-numerical fixation of the seemingly fundamentally non-objectivable Tao (i.e., combining the apparently incompatible) marks the possibility of a paradoxical union of Heraclitus with Pythagoras, successfully realized by the Chinese tradition.

The article discusses the current situation in mathematics, which is interpreted as a crisis. The problems that allow making such a conclusion are considered: the question of the scientific status of mathematics, the possibility of its substantiation, the mental or experimental nature of mathematics, the time of its formation. The author presents the results of the genesis of geometry, the generalization of which makes it possible to assert that mathematics, on the one hand, can be considered a kind of empirical science, on the other, a constructive scientific discipline, in which more complex ideal objects are created on the basis of initial ideal objects and knowledge. Two different understandings of the foundations of mathematics are considered - general scientific and David Hilbert’s, as well as what paradoxes are in science and how they are removed. The author is inclined to believe that antinomies in mathematics cannot be eliminated once and for all, their source is attributing inconsistent characteristics to objects of mathematics, which is due to the very structure of mathematics. The fact is that the construction of ideal objects of mathematics proceeds under the influence of at least four areas: the empirical area, describing which mathematicians create initial ideal objects and knowledge; areas of design based on the original more complex ideal objects; areas of geometric theorem proofs; area of ​​construction of the theory of geometry. In addition, here it is necessary to add the concept of the foundation of mathematics by D. Hilbert, and also take into account that there are different concepts of the foundation of mathematics. At the end of the article, the features of the current crisis in mathematics and the possible direction of its resolution are discussed.

Philosophy of love as a subfield of moral philosophy and history of philosophy questions the very foundations of how people love each other. Within the philosophical debate, not only the sources of love but forms and types are questioned. Does the source of love correspond to a concrete form of love? What is the difference between parental love and friendship love? What is the main difference between romantic love and the abovementioned? A philosopher from Chicago, Raja Halwani made a methodological and pithy impact in the debate. On the one hand, his main achievement in the recent debates is the distinction between two kinds of love: romantic love 1 and romantic love 2. Halwani notes that the main disagreement among philosophers stems from the fact that philosophers usually don’t see this difference. And if philosophers would keep this difference in mind, it would clarify our debates. On the other hand, professor Halwani doesn’t propose a conceptual novelty but interestingly refines the current debates on love’s aspects. These debates are debates concerning the main characteristics of love and how we can defend these characteristics. Halwani clarifies the central concepts of romantic love such as “constancy”, “exclusivity”, “uniqueness”, “irreplaceability”. The philosopher devoted special attention to reflections upon how exactly we can apply existing moral theories to love. At the end of the article, an attempt is made to compound many of Halwani’s statements about RL1 and RL2 in a unified table.

In the system of classical arts, music has always been perceived as a human actional breakthrough to understanding the Universe. The musical language, considered as a cultural universal, is the basis of intuitive cognition, a felt view of the axiological unity of Truth, Goodness and Beauty. The article offers an analysis of the formation of the main philosophical theories of the ontological nature of musical creativity in their historical continuity.

In the history of ideas, the phenomenon of musical creativity has been perceived as a special kind of revelation. This reveals the obvious importance of the aesthetic approach in understanding the transcendental world; the objectified connection of man with ontological processes. Modern theories of universal evolutionism represent the development of the Universe as a single system based on the unity of its laws. It is in our time that comprehension of the essence of musical creativity opens a fundamentally new page in the philosophical understanding of the centuries-old history of music. The key point is the idea of the Μελῳδός aspiration to the Λόγος, the tendency to move from particular theoretical constructions and critical assessments to considering the phenomenological foundations of music, fundamentally presented, in particular, in the works of A. Losev and T. Adorno.

In the XX century, there was an obvious surge in the formulation of generalizing musicological concepts, and it was in the XX century that the philosophy of music received qualitatively new worldview foundations for its comprehensive interpretation. In this respect, the study of the epistemological nature of musical creativity has reached, it would seem, its peak.

However, comprehension of the investigated theories allows us to draw conclusions only about the possible approximation of a true understanding of the essence of musical creativity as a special cognitive practice. This turns out to be possible on the methodological basis of cumulative generalization, taking into account the religious, aesthetic, cultural, psychological, educational and other approaches in comprehending the value of the “world of sound”.

The subject of the article is the problem of the ontological boundary of religious extremism as a socio-cultural phenomenon. The methodological basis of the research is the non-classical linguistic semantics of Frege – Russell. Within its framework, meaning, concept and sign are distinguished for the subject of thought. This methodology complements the predominance of the activity approach in the research of religious extremism. Such methodological unilateralism creates the illusion of the scholastic nature of the investigated problem, when the scientific result is expected to comment, clarify and systematize the known knowledge about religious extremism. As a result, religious extremism is considered metaphysically as an unchanging phenomenon that has no spatial and temporal boundaries. This research was conducted in two stages. The first one highlights the essential signs of religious extremism. The traditional triad of signs “subjects, sphere of activity, implementation methods” is supplemented by the fourth: “the purpose of activity”. Based on the analysis, religious extremism is defined as extreme actions of religious elements in the political life of society, aimed against the structural elements and ideology of secular society. The article rejects the provisions on uncritical identification with religious extremism of the following social phenomena: violation of national legislation on freedom of conscience and religious associations; religious fanaticism; religious sectarianism; nationalism. At the second stage of the research, the spatial and temporal boundaries of religious extremism are comprehended. Spatially religious extremism is typical for both post-industrial and traditional societies of the second half of the twentieth and early twenty-first centuries. The article puts forward historical-religious arguments and an argument against the thesis of the timeless nature of the existence of religious extremism. Based on the formation of a secular society on the economic basis of an industrial society since the second half of the XIX century, four factors of the emergence of religious extremism have been identified: secularization of public consciousness; desacralization of power; inversion of violence; limited support. As a result of the conducted research, the metaphysical consideration of religious extremism as an unchangeable phenomenon has been overcome and its conceptual understanding has been deepened.

The article presents a detailed response to the new book of the philosopher Oleg Bazaluk “Discursive Thinking through Education”. The problem of understanding Plato’s terms is discussed, in connection with which the author of the article expresses the idea that the correct reconstruction of the statements of ancient philosophers allows not only to choose the necessary values from the existing ones, but also to set new ones; at the same time, he believes, understanding the narratives of a foreign culture (or one’s own, but cultivating a different type of thinking) is quite possible, however, the condition for this is a change in one’s own consciousness, which, figuratively speaking, must be re-educated through the methodology and practice of historical and cultural thinking. The author reconstructs the picture of the world that Plato built and the ontological foundations taken by Bazaluk as the basis of his research and constructions. The author of the article raises the questions why the author of the book took the project of Plato as a basis, who began to doubt it even in antiquity, and also whether knowledge of the cosmos and its evolution can help in building a good society and sociality, as well as make a person happy. Special attention is paid to the issue of Bazaluk’s reconstruction of the evolution of the cosmos and the support of the discursive thinking of education on the knowledge and results obtained in this reconstruction. A number of questions and problems are discussed here: what the author of the book understands by education, what are the features of his reconstruction of the evolution of the cosmos, if it is possible to deepen his understanding of the basic reality (matter) in the direction of taking into account not only the first nature, but also the second. Evaluating the book, the author of the article proceeds from the understanding of Bazaluk’s work as a tradition and discourse that implements at least three principles: Plato himself, Russian cosmism, and the cognitive approach, which is popular nowadays. The author of the article understands his response as a benevolent discussion of the book, calling on other readers to do the same.

The article shows the causes and consequences of the deplorable state of the Russian economic science and higher economic education. They are rooted, first of all, in the persecution to which economics was subjected in Soviet times, especially during the Stalinist period. As a result, it lost the most talented scientists. There was no need for good economists in the command economy, so higher economic education had low prestige. In the post-Soviet period, due to the transition to a market economy, the need for economists to work in government institutions and commercial structures increased. However, it turned out that the current system of higher economic education is unable to satisfy it. The author shows negative consequences of a low level of economic education for solving national economic problems and managing companies. The low level of economic science did not allow economists to justify an effective transition to a market economy, taking into account the peculiarities of the Soviet economy and Russian history. In the post-Soviet period, the political leadership focused only on economists loyal to the government, without taking into account their professionalism.

The author proposes the ways of improving the quality of economic science and higher economic education. The emphasis is on a sharp reduction in the number of researchers and teaching staff (and a reduction in the number of students), with a simultaneous significant increase in the remuneration of researchers and teachers basing on objective criteria for evaluating their activities. This will allow democratizing the management of universities and scientific institutions, abolishing bureaucratic control over their activities.

This paper is a critical response to the article by professors P.A. Orekhovsky and V.I. Razumov “The Onset of Narcissistic Culture: Consequences for Education, Science and Politics”. The idea of treating Western post-war culture as narcissistic has been expressed in the United States since the 1970s of the XX century, but it will also be relevant in relation to the post-Soviet culture of Russia. Considering the ambiguity of the cognitive metaphor of Narcissus in relation to the described socio-cultural transformations caused by the possibility of an almost arbitrary interpretation of something as narcissism, the article presents its own interpretation of the foundations of narcissistic culture. Following the idea of opposing a narcissistic culture to a culture of service, modern narcissism is viewed not so much as an individual’s selfishness, but as a loss of an object and opportunity for service. Secularism, understood in the spirit of Charles Taylor as the loss of any higher, transcendent, hierarchical ontological concepts, deprives a person of a higher authority that legitimizes any service to something. This means a horizontal ontology of equivalent objects that do not have the highest value in relation to the individual. Post-traditionalism means impermanence, “fluidity” of any institutionalized forms of sociality and their perception, the dynamics of the emergence and decline of which does not allow the individual to find an object of service. A person remains in conditions of “minimal humanism”, which means that this person, having neither a higher reality that determines it, nor the constancy of social institutions, remains for himself the only possible value, a kind of “narcissist against his will”. We also believe that narcissism is not an external, but an internal factor of social processes that constitutes the motives and interests of the participants in these processes. While agreeing with the thesis about the connection between narcissistic culture and postmodernity, we believe that it is not a “young culture” opposite to mass society. On the contrary, narcissistic culture is the culture of a mass society that has gone further along the path of secularism, post-traditionalism and humanism, just as postmodernity is called late, far-reaching modernity by such sociologists as E. Giddens, U. Beck, Ju. Habermas.

This article continues the discussion of the phenomenon of modern culture published in the paper by P.A. Orekhovsky and V.I. Razumov “The Onset of Narcissistic Culture: Implications for Education, Science and Politics”. Arguments are presented for those consequences that lead culture to new states and guide thinking to explain the efforts needed to strengthen it in the role of developing us.

The judgments are based on a sense-genetic conception of culture that eliminates the naïve identity between the concepts of ‘cultural’, ‘civilized’, ‘cultivated’, ‘ethical’, ‘aesthetic’, ‘high’ and other assessments of specific properties of human behavior. The method of deriving consequences from judgments is based on the dialectical regularities of the development of living wholes and the products of their activity.

For the sake of continuing the semantic line of the original article, an attempt is made to rely on the phenomena of narcissism disclosed therein to see in them the signs of the future, the approach of which one could rejoice in without demonstrating its quite understandable experiences as an ugly form of the value landscape of modernity. In this sense, the idea, not developed but sown by the authors, that “narcissistic culture” brings to the world high diversity that can serve as a stimulus for the beginning of a new round of human development is supported here. There is a reason for this thought. They point to the approaching of gracious time when anarchic individualism will develop into another form of long-term sustainable coexistence of people under conditions of heterogeneity of values and interests. These conclusions make it possible to outline the contours of the tasks that need to be solved now in order to multiply this grace.

The article deals with the theme of mysticism in the works of Plato. The study begins with the concept of magic and comes to the conclusion that modern scientists do not know what the word μαγεία/magic really meant for the ancient Greeks.

However, Plato is considered to be the philosopher who laid down all the basic concepts of mysticism. The original ancient Greek definition of the word ‘mysticism’, derived from the Greek μυστικός, differs from the modern understanding of this concept and is directly related to the ancient Greek mysteries and the cult of the goddesses of fertility Demeter and Persephone. Very little is known about the mysteries, but it is obvious that for the ancient Greeks it was a way to gain immortality, a kind of action during which the soul descended to the underground world of the dead and returned from there. Many researchers note that such journeys of the soul among the Greeks are extremely similar to shamanic ones. But we are talking here about archaic views, and not about the shamanism that modern ethnography describes.

The most important part of the mysteries was contemplation. What exactly the participants of the mysteries contemplated, what the high priest showed them, remains a mystery. However, Plato in the dialogue “Republic” gives a lesson on how to reveal the ability to such contemplation with the help of mimesis, or imitation. This is not just an external theatrical imitation, namely, it is getting used to what is being contemplated.

Plato believed that actors and temples are not needed for a real mystery, it should unfold in contemplation, and therefore only you are needed for it. The author of the article finds confirmation of this idea in the dialogue between Socrates and Cephalus, which ends with the myth of Er’s travels to the world of the dead. Plato describes these journeys in such a way that his disciples, if desired, can enter the state of Er and, with the help of contemplative imitation, live everything that happened to him. These journeys are similar to the shamanic journeys of the soul to the underground world.

The author concludes the article with the assumption that Plato tried to create a kind of mysteries within his school for a philosopher who wants to master contemplation.