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The process of comprehending the world is given by Wittgenstein in his “Logical Philosophical Treatise” (1920) as a visual image of a ladder. The world of science developed in the Treatise is a world of logic and mathematics, while the worlds given through language games are presented in later works. The former is based on the concept of complex, while the latter – on the concept of paradigm or a local sample which stipulates the rules of the game. The paradigm is formed historically, while the complex is formed geometrically and logically. The paradigm is a local rule, whereas logic is a universal rule. All the sentences of the Treatise are structured into seven theses and the whole work is visualized as seven rungs of a ladder. The path of exploring the Treatise by reading its sentences is a path of climbing the ladder and surmounting it. The aim of the explorer is the eighth rung. Making the next step and finding the next rung (or vice versa, finding the next rung and making the next step) is up to the reader of the Treatise. The aim of the work is to reveal the strategies of searching for the eighth rung. The process of searching for the eighth rung goes through individualization and interiorisation of the text of the Treatise. The research method includes classification, visualization and geometrisation of the concepts and texts reflecting the strategies of searching for the eighth rung of the Treatise’s ladder. The research conducted over a century of Wittgenstein’s works clearly shows three strategies of searching for the eighth rung. These strategies are defined as paths of the reader, of the disciple and the author. [ABSTRACT FROM AUTHOR]

The aim is to show the disintegration of a personality by analyzing the fragment of “Confession” by St Augustine. It allows us to come from the phenomenological description of personality transformation process to means of psychological defense. By solving the questions of love St Augustine uses hidden rhetorical constructions, which reflect his emotional processes in the most adequate way. They should be analyzed and clarified. The rhetorical aspect of this transformation can be reconstructed from that part of “Confession” where Augustine describes his Carthage impressions. He suffers psychological chaos: he “ran into love”, “loving love”. Augustine finally summarizes these impressions by saying “I loved not yet, yet I loved to love”. Thesis becomes antithesis and that is the circle. Wittgenstein wrote in “Tractatus Logico-philosophicus” (in German 1921, in English 1922; revised 1933, 1961): “3.333. A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself” – F (f). In “Remarks on the Foundations of Mathematics” (1942) Wittgenstein returns to this topic. For the description of this contradiction Wittgenstein proposes a kind of function: ”F (F), where F (ξ) = – ξ (ξ)”. It is “a shimmering concept”. Contradiction is part of logical symbolism, but topologically, the figures of contradictions, which use Augustine and Wittgenstein, are different. They describe a variety of psychological processes. The figure of contradictions by St Augustine is the paradox in time. The figure of contradictions by L. Wittgenstein is the antinomy in space. [ABSTRACT FROM AUTHOR]

In this work, the phenomenon of 'visions' and mysticism of Fr. John (born 25.09.1946) is considered within the framework of religious studies, philosophy and psychology of religion. The aim of the work is to establish the structure of the phenomenon of 'Visions of the Theotokos', its deployment and movement. The method of investigation is suggested by the description of the experience given by Fr. John is in his works. The key concept of his diaries and books is the notion of an 'archetype', which is interpreted in the spirit of C. Jung's deep psychology. The possible and the real are considered as real, and the attribution to the objective or subjective level of reality is taken out 'beyond the brackets' of the study. Such description includes a contradiction and is subordinated to the function that Ludwig Wittgenstein proposed: F(F), where F(ξ) = - ξ(ξ). This function remains unchanged in the modulus of the argument: F(F) = F(ξ) = |±ξ(ξ)| and corresponds to the description, whether it refers to a subjective or objective reality, but taken in its algebraic form it turns out to be 'flickering', including the break and the transition of the boundary: F(F), where F(ξ) = ±ξ(ξ). [ABSTRACT FROM AUTHOR]

The interest of the Renaissance to the antique culture and to the hermeticism consequential led to the study of the Old Egypt and to the research of the Egypt writing. But at the moment of appearance of this interest the understanding of it was lose. 1419 priest from Florence Christoforo de' Buoldemonti found on the island Andros in the Aegean See the manuscript "The Hieroglyphics of Horapollo Nilous". He bought it and got to Italy. 1505 the manuscript was published in Ancient Greek in Venice. According to the historian of writing systems, I. Gelb, the picture writing carries a magical load as such. Ideogrammatic writing was used by painters of the Renaissance. Telling a legend about the Egyptian god Thoth, he was an inventor of hieroglyphics. Born of Isis and Osiris, god Horus enters the battle with Set. In one of the episodes of the "litigation" of Horus and Set, the latter managed to wrest the eye of Horus and break it into 64 parts, which, however, god Thoth collected, "repaired" the eye, but left 1/64 part to him. Egyptologists and writing historian A. Gardiner note that the episode has an encoded mathematical interpretation - the creation of signs for fractions. In this moment a new conjugation of scientific and mythological ideas is taking place. Ideogram "The Eye of Horus" is not only a rendition of the myth, but a hidden approximation of the calculation of the numbers π (3.149). [ABSTRACT FROM AUTHOR]

Alchemy in modern consciousness ceased to be perceived as a scientific fallacy. This perception is due to the diversity of approaches to studying alchemy. The purpose of the article is to present the diversity of historically developed approaches to studying alchemy. The article lists and describes the main approaches; if necessary, illustrative examples are given showing their applications in the study. First approach is denoted by the word 'traditional'. The traditionalist approach is represented by the works of R. Guénon and J. Evola. The scientific-historical approach represents the development of the scientific-educational approach, supplementing it with other researches. The classical approach to alchemy is formed on the basis of educational, scientific and historical approaches. The educational-hypothetical approach is a complex synthetic inversion of the scientific-historical and educational approaches. The natural-scientific approach develops in the context of scientific revolutions. The psychological interpretation of C.G. Jung occupies a special chapter in the historiography of alchemy. The magical-erotic and sensual aspects of the imaginative approach are presented by I. Regardie. The diversity of approaches reflects the special topology of the phenomenon of alchemy, which makes it possible to obtain its various sections and consider them separately, yet none of them embraces the phenomenon of alchemy as a whole. [ABSTRACT FROM AUTHOR]

In the modern world, various projective images of alchemy, of the alchemist, of the 'great work' and of the philosopher's stone were formed. The aim of the work is to search for the prototype of an alchemic operation and to prove that it is an operation to create a measure for measuring an unknown quantity that can be chemical, geometric, psychological or of some other nature. The method of investigation is a representative measurement theory based on assigning numbers to things; in this case, things are the letters that make up the word 'alchim'. The assignment of figures to things in alchemy happened so that they began to present facts. This representation is due to the fact that the sequence of letters formed a word having historical origins, and the numerical sequence formed a digit having a mathematical meaning. The article distinguishes between the word and the term 'alchim'. As the term 'alchemy' is not the genesis of a word from some language but an artificial construction, one of the representation of the number 'p' (Ludolph's number). The side result was the search for approximations to the value of the number 'p'. The alchemists achieved a numerical approximation of the number 'p' and considered 'p' to be 3.1415 or 3.1418. [ABSTRACT FROM AUTHOR]

The questions of research and application of the creative heritage of L.Wittgenstein remain insufficiently studied. The report formulates the conditions for communication between the autonomous figures of the dream, including its subject. These conditions are necessary in the process of understanding and integrating the unconscious contents in the "my world". The aim of this research is to create an analytic model for the functional structures of dream images, the logic of events and transformations. The hypothesis of the research: the relation "of the autonomous figures of dreams" to "Ego" equals one of the relations in psychotherapeutic practices. For describing the contradiction Wittgenstein suggests a peculiar "shimmering concept" and function of symmetrical structure: F(F), where F(ξ) = - ξ(ξ). This report attempts to apply Wittgenstein's meta-function F(F) to the analysis of communication of autonomous dream figures. The study applies the method of geometrization (image) for logical structures and functional-typological and logical analysis to the clarification of the clinical case of "Visions" by C.Jung. The results are the development of methods for the philosophical analysis to the practices of psychotherapy. [ABSTRACT FROM AUTHOR]

In modern philosophical and psychological works alchemy is present as a phenomenon the essence of which is mysterious and incomprehensible. Alchemy and the philosopher's stone today in society is perceived as Magnum ignōtum (the Great Unknown). The subject of the work. Depending on the approach, the subject is determined and interpreted. The subject of this work is the legend of the 13th century alchemist Raymond Lully and his lover Ambrosia de Castello. The aim is to establish the transformational structure of the legend, to carry out the geometrization of the history and psychology of the characters, to create a psychological model of the protagonist's experiences, and to offer a psychological interpretation of the legend. The method is the topological correlation of the historical events stated in the legend, the events of the psychological transformation of its characters, and the establishment of correlation between psychology and history in the legend. Conclusion. The essence of the legend in the correlation and synthesis of historical and psychological events, their consideration as a whole, for which symmetrical historical and psychological structures and configurations are used. [ABSTRACT FROM AUTHOR]

The scientific-educational approach, combining the educational point of view with the scientific criticism of the educational approach, was formed, oddly enough, in the study of alchemy, and views the latter as a stage in the development of chemistry. It is this approach which combined the ideas of the Enlightenment with natural science and its history and became the basis for the formation of a classical view of the Hermetic tradition. This approach is based on the reality of the object of alchemy, proving that it is indeed real, and that behind the curtain of illusions and allegories lies the 'solid body' of chemical transformations and very unusual experiments of physics. This approach is focused on desacralizing the content of ancient and medieval 'dark' texts, to identify in them a scientific component and reformulate in modern scientific language the problems they solve. In this text the rational components of alchemy are considered from the point of view of the history of thermodynamics. One can give a 'thermodynamic' interpretation of the alchemical fragments of 'Atalanta fugiens' (EMBLEMS III, IV, V). Describing the stages of the Great Work, alchemists widely use metaphors, legends and various forms of allegory. The alchemists knew that thermal effects almost always accompany chemical changes. It is shown that the basis for a number of alchemic experiments is the correct scientific idea of the thermodynamic effect of a chemical reaction. [ABSTRACT FROM AUTHOR]

Alchemy is oriented towards 'tradition', and the latter can be understood very widely, including myths, superstitions, legends, parables. Any tradition at a certain level of development, in order to take the next step, turns to the study of itself, realizing the reflection of its sources, bases, concepts and methods. This approach is denoted by the word 'traditional'. For the present study this group of materials, on the one hand, acts as sources, on the other hand, as research, that is, the study of esoteric teachings is undertaken in them with the aim of continuing the tradition, often through interpretation and reinterpretation of their concepts and principles. The research side, of course, is not present in all works, yet it already occurs with ancient and medieval thinkers. The scientific and educational approach cut alchemy, separating the chemical component from it, discarding the rest. Quite unexpectedly, Jung conducted a different section of alchemy, singling out the deep-psychological content of the phenomenon, discarding the chemical content. From the point of view of topology, the phenomenon of alchemy has a very strange configuration, which involves two closed curves to obtain a section of its surface. The most important symbol of the elixir of immortality - Uroboros (a snake biting its tail) - is a graphic illustration of the geometric figure of the torus. [ABSTRACT FROM AUTHOR]

'War of the Knights' (Ritter Krieg) is a medieval alchemical narrative, written in the form of judicial combat between the allegorical figures of the Sun (gold) and Mars (iron). The purpose of the study is to show that if one considers the verbal duel of the 'knights' not as alchemic dispute, but as a clash of interests of various medieval social classes, the contents of the book is clear, and the alchemist is engaged in the analysis of the historical and socio-political situation in the late Middle Ages. The method of research is historical-philosophical and socio-cultural analysis. In the fifteenth century, the growth of trade exposed the aspect of gold circulation, namely, the deficit of gold. In the dispute a third party appears, the interests of which (the interests of society) are represented at the trial by the judge - Mercury. Mercury proposes to withdraw gold from the jewelry business and increase the mass of currency. These processes are relevant for the XV century but not for the end of XVII. The philosopher's stone in the Treatise is money, gold coins created from the wealth of the aristocrat by the work of the blacksmith. Wealth - the consequence of trade - is the last stage of alchemy, 'multiplication'. [ABSTRACT FROM AUTHOR]

Wittgenstein's views have been considered from different perspectives: from the standpoint of logic, philosophy, methodology of science, theory of mind and, finally, from the standpoint of religion, mysticism and myth. However, they are not so often considered from the perspective of natural sciences. Wittgenstein distinguishes between a name and a word. The name is on the surface, while the word affects emotions, penetrating into life. How deep does it penetrate into reality? This issue can be approached from two sides - from the linguistic point of view and from the perspective of life. Wittgenstein considers the first approach, but in this paper the second one is discussed as well. For this purpose, the authors make an analytical review of the current concepts of the clinical "therapist-patient" interaction within the "psychotherapeutic framework" in terms of the symmetry of the psychological types. They also consider the modern information model of the cell and mechanisms of information transfer within cellular structures. The study applies the methods of geometrization of logical structures and the topological comparison of structures. The authors show that concept of isomorphism raises the question of the genetic unity of the structures of language and life. [ABSTRACT FROM AUTHOR]