В прил.: Простые математические модели динамики коллективной деятельности / Л. Е. Попов, М. И. Слободской. Мозг и обучение / Б. И. Вершинин.

Zagadochnyĭ starik.--T︠S︡iolkovskiĭ v Peterburge.

Gödel logic is the extension of intuitionistic logic by the linearity axiom. Symmetric Gödel logic is a logical system, the language of which is an enrichment of the language of Gödel logic with their dual logical connectives. Symmetric Gödel logic is the extension of symmetric intuitionistic logic. The proof-intuitionistic calculus, the language of which is an enrichment of the language of intuitionistic logic by modal operator was investigated by Kuznetsov and Muravitsky. Bimodal symmetric Gödel logic is a logical system, the (...) language of which is an enrichment of the language of Gödel logic with their dual logical connectives and two modal operators. Bimodal symmetric Gödel logic is embedded into an extension of Gödel–Löb logic, the language of which contains disjunction, conjunction, negation and two modal operators. The variety of bimodal symmetric Gödel algebras, that represent the algebraic counterparts of bimodal symmetric Gödel logic, is investigated. Description of free algebras and characterization of projective algebras in the variety of bimodal symmetric Gödel algebras is given. All finitely generated projective bimodal symmetric Gödel algebras are infinite, while finitely generated projective symmetric Gödel algebras are finite. (shrink)

Representations of monadic MV -algebra, the characterization of locally finite monadic MV -algebras, with axiomatization of them, definability of non-trivial monadic operators on finitely generated free MV -algebras are given. Moreover, it is shown that finitely generated m-relatively complete subalgebra of finitely generated free MV -algebra is projective.

We define and study monadic MV-algebras as pairs of MV-algebras one of which is a special case of relatively complete subalgebra named m-relatively complete. An m-relatively complete subalgebra determines a unique monadic operator. A necessary and sufficient condition is given for a subalgebra to be m-relatively complete. A description of the free cyclic monadic MV-algebra is also given.

The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...) the automorphism groups of the free MV-algebras over finitely many generators. (shrink)

Review of the book Nemchinov, I. (2019). Malinin / Malinin: Reconstruction of the "lost biography" of Kiev professor. Vinnitsa: FOP Baranovskaya TP.

The article is devoted to the philosophical views of Swami Vivekananda, reflected in his commentary on the Yoga Sutras of Patanjali. The text under study is one of the few Indian commentaries on the Yoga Sutras translated into Russian. The object of the study is a widespread translation of the commentary, made and published by Ya. K. Popov in 1906. The popularity of yoga as a health-improving practice increases interest in its spiritual component, therefore, the study of Vivekananda's commentary on (...) the Yoga Sutras seems to be an urgent task. The purpose of this article is to analyze Vivekananda's commentary for the authenticity of the transmission of the content of the ancient text and the reflection of the teachings of the Bengali thinker. Since Vivekananda's commentary on the Yoga Sutras has not been studied by domestic orientalists, and has not received comprehensive coverage in foreign studies, the results of his analysis contain scientific novelty. Using the hermeneutical method, it is revealed that the philosopher forms a commentary on the ancient text mainly to demonstrate the basics of his teaching. Vivekananda's work expresses his Orient-centric position, as well as the author's beliefs in accordance with the provisions of yoga to his contemporary science. Since the philosopher's views are in line with Advaita Vedanta, the ontological foundations of yoga are interpreted by him according to this philosophical school. The commentary of the late XIX century anticipates modern ideas of the healing potential of yoga and the superiority of experienced knowledge of the Divine, and also demonstrates the predictive talent of the Bengali thinker. (shrink)

We prove that the m -generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the m -generated free MV-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV-algebras and special maps between them as morphisms.

The purpose of the study is to reveal the essential content of the digital environment for the provision of medical services. The article discusses various scientific approaches to the formation and development of the digital health care environment. Scientific novelty lies in the substantiation of the definition of a digital environment for the provision of medical services, which will allow developing a scientific and methodological approach to designing a digital ecosystem for the development of the regional economy based on increasing (...) the level of health preservation of citizens. As a result, the strategic directions for the development of the digital environment for the provision of medical services were identified, reflecting the global trends in the development of digital health. (shrink)

A description of the free cyclic algebra over the variety of Solovay algebras, as well as over its pyramid locally finite subvarieties is given.

Our approach bases on the explication of Rosanov’s creativity as the special intention, that implements the unspeakable Self-Selfness of Vasiliy Rosanov. The ineffability of Self-Selfness can be dialectical expressed by Rosanov through phenomena, of that consists the Rosanov’s world. This ineffability actualizes by Rosanov by means of understanding as a filled emptiness, that determinates the specialties and the structure of the understood objects. The exposition of this emptiness conditions the antinomies of Rosanov’s creativity: one sides is understanding by Rosanov the (...) closed world, other sides it corresponds with the world of things. Rosanov mythically fills the void, using the intimate personal contact with the things. We consider the creativity of Rosanov as the synthesis of both this global directions of Rosanov’s theory: the vision of understanding through things, this vision causes the special perception of things by Rosanov. The things are by Rosanov neither material objects, nor the ideal essences. This are by Rosanov the givens, inherent to the understanding. At the same time Rosanov examines the things through understanding, including it with help of the carnivalisation in his own special world. This method defines in our opinion style and content of Rosanov’s works. The thinker realizes by means of the carnivalisation the understanding, according to the concrete things, creating the special world of life (reality). For Rosanov this world is the second world. (shrink)

The intuitions of Raimundus Lullus religious metaphysics are in this article explicated according to the opportunities of the convergence between the medieval and the new time philosophy. Such approach to the creativity of the thinker is possible, because his conception is one sides associated with the mystical symbolic theologism, that is typical for the medieval tradition, over sides develops Lullus the new understanding of the infinity of the world, inherent in the newtime philosophy. This opposition conditions some of the features (...) of Lullus spiritual quest. This quest connected the respect to the past, that causes the homesickness to the lost ideals, together with the progressivity – the presentation of the future. This presentiment is by Lullus expressed as the desire to change the external world. The aim of this change is the approximation of the rational theological base – the model for the real life. Lullus experiences the combination and the unrealized synthesis of this intentions as the tragedy. The acute and intensive conflict of this intentions triggers the practical atheism, when the stimulation of the external distraction of the evil leads causes the appearance and the activation of the new evil. This disaster of life is determined with some aspects of Lullus metaphysics, in that the infinity of God is realized as the infinity of the world. The infinity of the world is by Lullus given as the rational hierarchical order, leading to the creator of the world. The tragedy of life is for Lullus the marker, that emphasizes the crisis of the medieval philosophy, that was based on the revelation. This crisis discovers the land of new philosophy. This philosophy stresses the autonomy of the human personality. (shrink)

The spiritual quest of Raymond Lull is of interest to modern philosophical discourse as occupying an intermediate position between the Middle Ages and the Renaissance and thus combining the features of these two eras in the history of the development of human thought. They are connected with the Middle Ages by theocentrism and traditionalism, and with the Renaissance by emphasizing the peculiar polyphony of the world, the predominance of plurality over unity, given in the autonomous dialogic space of the human (...) personality as a gradual immanentization of the presence of a transcendent deity, associated with the acceptance by man of the external world as the only possible one. This immanentization is carried out by Luli in the symbol of Love as the Unity of the Loving and the Beloved, explicating the thinker's introspection. The novelty of the work lies in the application of the teachings of A.F. Losev about the interpretive symbol, which made it possible to consider them as a special form of explication of the personality as its transcendence and simultaneous immanence, being a special form of introspection, which correlates with Lull's teaching about Love as a fluctuation in which the Beloved descends, and the Lover ascends. This contributes to the actualization of Lull's spiritual quest as an integrity, a unique eidos, in which each of the separate features of Raymond Lull's spiritual quest is realized in a special way, reflecting the intermediate position occupied by the thinker between the worlds of Antiquity and the Middle Ages. The proposed model of mutual positing of the "components" of Lull's teaching allows us to show one of the possibilities for the interaction of the thinker's logical system (understanding the force, its bearer and passively perceiving its beginning) and his theologically oriented personal spiritual quest as a special kind of dynamics in which the leading role is assigned to introspection as a personal intentions, a kind of mythological sub-foundation of the actual logical dimension of the thinker's teachings. (shrink)

An introduction to the basic ideas of philosophy as a science, materialism, the categories and laws of motion of nature, society and human thought, dialectics, the theory of knowledge.