Книга предназначена для философов, правоведов и специалистов по естественным наукам, а также для заинтересованных читателей.

In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4-valued logic to the set 16 to be the power-set of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN 3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is (...) asserted, d — incoming data is denied, and u — incoming data is neither asserted nor denied, that corresponds to the answer “don’t know”. In so doing, the power-set of 3, that is the set 8 is considered. It turns out that there are not three but four orderings naturally defined on the set 8 that form the tetralattice EIGHT 4 . Besides three ordering relations mentioned above it is an extra uncertainty ordering. Quite predictably, the logics generated by a –order (truth order) and d –order (falsity order) coincide with first-degree entailment. Finally logic with two kinds of operations ( a –connectives and d –connectives) and consequence relation defined via a –ordering is considered. An adequate axiomatization for this logic is proposed. (shrink)

We explore a possibility of generalization of classical truth values by distinguishing between their ontological and epistemic aspects and combining these aspects within a joint semantical framework. The outcome is four generalized classical truth values implemented by Cartesian product of two sets of classical truth values, where each generalized value comprises both ontological and epistemic components. This allows one to define two unary twin connectives that can be called “semi-classical negations”. Each of these negations deals only with one of the (...) above mentioned components, and they may be of use for a logical reconstruction of argumentative reasoning. (shrink)

In their useful logic for a computer network Shramko and Wansing generalize initial values of Belnap’s 4-valued logic to the set 16 to be the power-set of Belnap’s 4. This generalization results in a very specific algebraic structure — the trilattice SIXTEEN3 with three orderings: information, truth and falsity. In this paper, a slightly different way of generalization is presented. As a base for further generalization a set 3 is chosen, where initial values are a — incoming data is asserted, (...) d — incoming data is denied, and u — incoming data is neither asserted nor denied, that corresponds to the answer “don’t know”. In so doing, the power-set of 3, that is the set 8 is considered. It turns out that there are not three but four orderings naturally defined on the set 8 that form the tetralattice EIGHT4. Besides three ordering relations mentioned above it is an extra uncertainty ordering. Quite predictably, the logics generated by a–order and d–order coincide with first-degree entailment. Finally logic with two kinds of operations and consequence relation defined via a–ordering is considered. An adequate axiomatization for this logic is proposed. (shrink)

A peculiarity of early medieval geometrical texts was that alongside Euclid's Elements they transmitted remnants of the corpus of Roman land surveyors and metaphysical digressions extraneous to geometry proper. Rather than dismissing these additions as irrelevant, this essay attempts to elucidate the cultural grounds for the indiscriminate mixture of the three disciplines -- geometry, surveying, and metaphysics. Inquiry into the broader context of early medieval culture suggests that neither geometry nor surveying was treated as an independent discipline. Texts on geometry (...) and surveying were studied mainly because they were thought to provide good opportunities for enlarging the scope of meditation on spiritual subjects. Accordingly, the main concern of this essay is to show how Christian symbolism influenced both the composition and the study of geometrical texts. The essay is based on a wide range of sources: treatises on geometry and surveying, pictorial representations of Creation, and philosophical literature in which geometry was used in arguments about ontological doctrines. (shrink)

We discuss several problems in quasiclassical physics for which approximate solutions were recently obtained by a new method, and which can also be solved by novel versions of the Born–Oppenheimer approximation. These cases include the so-called bouncing ball modes, low angular momentum states in perturbed circular billiards, resonant states in perturbed rectangular billiards, and whispering gallery modes. Some rare, special eigenstates, concentrated close to the edge or along a diagonal of a nearly rectangular billiard are found. This kind of state (...) has apparently previously escaped notice. (shrink)

There is a productive and suggestive approach in philosophical logic based on the idea of generalized truth values. This idea, which stems essentially from the pioneering works by J.M. Dunn, N. Belnap, and which has recently been developed further by Y. Shramko and H. Wansing, is closely connected to the power-setting formation on the base of some initial truth values. Having a set of generalized truth values, one can introduce fundamental logical notions, more specifically, the ones of logical operations and (...) logical entailment. This can be done in two different ways. According to the first one, advanced by M. Dunn, N. Belnap, Y. Shramko and H. Wansing, one defines on the given set of generalized truth values a specific ordering relation (or even several such relations) called the logical order(s), and then interprets logical connectives as well as the entailment relation(s) via this ordering(s). In particular, the negation connective is determined then by the inversion of the logical order. But there is also another method grounded on the notion of a quasi-field of sets, considered by Białynicki-Birula and Rasiowa. The key point of this approach consists in defining an operation of quasi-complement via the very specific function g and then interpreting entailment just through the relation of set-inclusion between generalized truth values. In this paper, we will give a constructive proof of the claim that, for any finite set V with cardinality greater or equal 2, there exists a representation of a quasi-field of sets isomorphic to de Morgan lattice. In particular, it means that we offer a special procedure, which allows to make our negation de Morgan and our logic relevant. (shrink)

This volume offers a wide range of both reconstructions of Nikolai Vasiliev’s original logical ideas and their implementations in the modern logic and philosophy. A collection of works put together through the international workshop "Nikolai Vasiliev’s Logical Legacy and the Modern Logic," this book also covers foundations of logic in the light of Vasiliev’s contradictory ontology. Chapters range from a look at the Heuristic and Conceptual Background of Vasiliev's Imaginary Logic to Generalized Vasiliev-style Propositions. It includes works which cover Imaginary (...) and Non-Aristotelian Logics, Inconsistent Set Theory and the Expansion of Mathematical Thinking, Plurivalent Logic, and the Impact of Vasiliev's Imaginary Logic on Epistemic Logic. The Russian logician, Vasiliev, was widely recognized as one of the forerunners of modern non-classical logic. His "imaginary logic" developed in some of his work at the beginning of 20th century is often considered to be one of the first systems of paraconsistent and multi-valued logic. The novelty of his logical project has opened up prospects for modern logic as well as for non-classical science in general. This volume contains a selection of papers written by modern specialists in the field and deals with various aspects of Vasiliev's logical ideas. The logical legacy of Nikolai Vasiliev can serve as a promising source for developing an impressive range of philosophical interpretations, as it marries promising technical innovations with challenging philosophical insights. (shrink)

In this paper, I attempt to offer a general outline of my views on the origin and evolution of language. I do not pretend in any way to a completely new conception of language evolution. It seems to me that all the most important and productive hypotheses about the origin of language have already been made before, and it is only a matter of putting the pieces of the puzzle together correctly. As far as I can see it, the evolution (...) of language is directly related to the embedded and embodied emotional types, which served as the basis for the subsequent categorization of perceived objects, and thus laid the ground for the formation of first an internal language (of thought), and then an external verbal language. Consistent with this, the paper is organized as follows. In the Introduction I briefly describe the problem I am facing in this article and outline a plan for solving it. Next section comprises a survey of relevant empirical findings related primarily to the processing and understanding of abstract terms and concepts. In my view, it supports the idea of the close connection of abstract terms proceeding, and thus language comprehension, with emotional states. The third section provides relevant theoretical considerations of the relationship between emotions, cognition, and language. Consistently considering various theories of emotions and concepts of language formation, I pay attention to the connection between affective states and language as a sign system. In the fourth section, my views are presented directly. In so doing, I illustrate my approach with a telling example that shows how, in the course of evolution, embedded and embodied emotional responses and reactions could become the building blocks first for the internal language of thought, and then for the external natural language. (shrink)

We consider a family of logical systems for representing entailment relations of various kinds. This family has its root in the logic of first-degree entailment formulated as a binary consequence system, i.e. a proof system dealing with the expressions of the form \, where both \ and \ are single formulas. We generalize this approach by constructing consequence systems that allow manipulating with sets of formulas, either to the right or left of the turnstile. In this way, it is possible (...) to capture proof-theoretically not only the entailment relation of the standard four-valued Belnap’s logic, but also its dual version, as well as some of their interesting extensions. The proof systems we propose are, in a sense, of a hybrid Hilbert–Gentzen nature. We examine some important properties of these systems and establish their completeness with respect to the corresponding entailment relations. (shrink)

In this paper we present a solution of the axiomatization problem for the Fmla-Fmla versions of the Pietz and Rivieccio exactly true logic and the non-falsity logic dual to it. To prove the completeness of the corresponding binary consequence systems we introduce a specific proof-theoretic formalism, which allows us to deal simultaneously with two consequence relations within one logical system. These relations are hierarchically organized, so that one of them is treated as the basic for the resulting logic, and the (...) other is introduced as an extension of this basic relation. The proposed bi-consequences systems allow for a standard Henkin-style canonical model used in the completeness proof. The deductive equivalence of these bi-consequence systems to the corresponding binary consequence systems is proved. We also outline a family of the bi-consequence systems generated on the basis of the first-degree entailment logic up to the classic consequence. (shrink)

The relationship between formal logic and informal reasoning has always been a hot topic. In this paper, we propose another possible way to bring it up inspired by connexive logic. Our approach is based on the following presupposition: whatever method of formalizing informal reasoning you choose, there will always be some classically acceptable deductive principles that will have to be abandoned, and some desired schemes of argument that clearly are not classically valid. That way, we start with a new version (...) of connexive logic which validates Boethius’ Theses and quashes their converse from right to left. We provide a sound and complete axiomatization of this logic. We also study the implication-negation fragment of this logic supplied with Boolean negation as a second negation. (shrink)

The aim of the present paper is to introduce a system, where the epistemic state of an agent is represented truth-functionally. In order to obtain this system, we propose a four-valued logic, that we call the logic of rational agent, where the fact of knowing something is formalized at the level of valuations, without the explicit use of epistemic knowledge operator. On the basis of this semantics, a sound and complete system with two distinct truth-functional negations is provided. These negations (...) allow us to express the statements about knowing or not knowing something at the syntactic level. Moreover, such a system is applied to the analysis of knowability paradox. In particular, we show that the paradox is not derivable in terms of the logic of rational agent. (shrink)

We consider an example of four valued semantics partially inspired by quantum computations and negation-like operations occurred therein. In particular we consider a representation of so called square root of negation within this four valued semantics as an operation which acts like a cycling negation. We define two variants of logical matrices performing different orders over the set of truth values. Purely formal logical result of our study consists in axiomatizing the logics of defined matrices as the systems of binary (...) consequence relation and proving correctness and completeness theorems for these deductive systems. (shrink)

I FORMS AND PROBLEMS OF CULTURE INTEGRATION AND METHODS OF THEIR STUDY I. Culture Integration And Culture Unity — A Dark Problem Is every culture an ...

The article characterizes the substantial level of sacralization of values in the spiritual culture of the Greater Altai. The main emphasis is placed on identifying the grounds for the sacralization of values. It is established that the world order is one of the bases of sacralization and simultaneously performs the function of consolidating cultural carriers. The key thesis of the research is the thesis that spiritual culture cannot be fully comprehended without reference to sacred values. In addition, the sacralization of (...) values is considered as a condition for ensuring spiritual security and continuity of values and norms between generations of cultural carriers. The assessment of the spiritual potential of the culture of the Greater Altai is of great importance. The main conclusions of the study are the following provisions: 1) the sacralization of key values is carried out at the essential or substantial level, while the stages of sacralization are mainly "tied" to the religious and mythological development of culture and its value-normative system; 2) sacralization encompasses those value structures that acquire importance in human existence and are a factor in the integration of cultural carriers and their generations; 3 sacralization is the process of identifying specific value-semantic structures – they are attributed symbolic meaning, and they are also correlated with certain cultural codes, signs and texts. (shrink)

Il'in's classic work is the most impassioned and cogent work by a Russian jurist on the rule of law. The product of nearly four decades of labor, which could not be published in the former Soviet Union, this revised edition places the work in the context of developments since its first English translation in 2013. The text is accompanied by one of Il'in's early and influential articles on law and power, a bibliography devoted to his life and work, and informed (...) introductory essays about his contribution to the rule of law dialogue, the origins and transformations of the concept of legal consciousness and the fascinating history of his treatise on that subject. x, 403 pp. Ivan Aleksandrovich Il'in (Доктор государственных наук) [1883-1954], sometime professor, Moscow Lomonosov State University, is one of the most widely-read legal philosophers of the twentieth century in post-Soviet Russia. William E. Butler is the John Edward Fowler Distinguished Professor of Law, Penn State Dickinson Law; Emeritus Professor of Comparative Law, University College London; and author of numerous works on post-Soviet legal systems, including Russian Law and Legal Institutions (3d ed.; 2021). Philip T. Grier, who has written extensively on Hegel and Il'in and translated Il'in's principal treatise on Hegelianism, is the Emeritus Thomas Bowman Professor of Philosophy and Religion at Dickinson College, Carlisle, Pennsylvania. Paul Robinson is a professor at the University of Ottawa. (shrink)

This paper is focused on the ways of expressing trust and distrust in financial institutions represented in the language and speech culture of the population of the Lipetsk region. Based on 55 semi-structured interviews of three generations (centennials, millennials, elder generations) living in rural and urban settlements, issues of understanding and interpretation of financial institutions, features of trust, positive and negative experiences of interaction with various financial institutions were analyzed. The use of the constructivism made it possible to interpret trust (...) as an internal component of the practices of an agent involved in the current financial situation. The study showed that in regions with an average standard of living, an average level of financial culture and the dominance of a conservative model of financial behaviour, the difference between generations is less noticeable against the backdrop of a significant difference between residents of rural and urban settlements. The analysis of interviews with three generations of residents of the region showed that the conservative model of financial behaviour continues to be reproduced in the speech culture of the informants, where banks and insurance organizations remain the most trustworthy. The images of financial institutions, represented in the language of the interviews, revealed a high level of resentment associated with the experience of past events (the collapse of the USSR, privatization). The content analysis revealed the image of the state as a “collector of payments”, and to a lesser extent, a “helper” supporting a person in his relationship with financial institutions. (shrink)

The article pays special attention to the identification of the heuristic potential of theoretical and methodological approaches to the study of spiritual culture, which has a pronounced ethnoregional specificity. In this case, we mean the spiritual culture of the Greater Altai. A value-normative approach and a systematic approach are considered, and other research perspectives are evaluated. The key point is to assess the possibilities of applying an interiorization approach that allows us to present a specific ethno-regional culture in its integrity (...) and unity of meanings. This approach is proposed to be used to study the processes of sacralization and symbolization of human individual and collective existence, occurring through the experience of cultural bearers. This perspective of the study is aimed at conceptualizing experience, but also involves an appeal to traditions, rituals, religion and mythology. However, their analysis is carried out precisely through an assessment of experience. The main methodology of the research is related to the need to present the ethnoregional culture of the Greater Altai in its value-semantic and holistic development. The main results of the study are the following provisions formulated in the article: 1) the problematization of the study of ethnoregional culture unfolds in the direction of its value-semantic reception, which implies the use of an appropriate angle of study; 2) the specificity of ethnoregional culture is formed not only in the ratio of its traditional values and norms, but also in establishing the foundations of its integrity and consistency, therefore, for analysis, such an approach is important, which allows you to reveal these points; 3) to assess the identity of culture, its systemic integrity, it is necessary to use an interiorization approach aimed at identifying the trinity of God - World - Man in the spiritual culture of the Greater Altai; 4) the social and existential experience of cultural bearers, and not only, for example, religion and mythology, should be the subject of research within the framework of the proposed interiorization the approach. (shrink)

The subject of the research in this article are certain aspects of the "philosophy of culture" of the prominent thinker, theologian, historian of Russian thought Georgy Vasilyevich Florovsky, which influenced the evolution of his worldview. Special attention is paid to the facts of the "European" period of his biography, the analysis of his "Eurasian" works, as well as his assessments of the philosophical concepts of some Russian thinkers and calls for the conversion of the process of cultural creativity to spiritual (...) principles. Particular attention is paid to the content of the discussion that unfolded between G.V. Florovsky, N.S. Trubetskoy and (in absentia) N.Ya. Danilevsky on the problem of the status of "universal culture" and the mutual influences of cultures. The study reveals the philosophical nuances of the evolution of G. Florovsky's views as a "Eurasian" author based on his own works and the assessments contained therein. Scientific literature often emphasizes the influence of Eurasian ideology on G. Florovsky, expressed, in particular, in his ideas about culture and cultural creativity. However, based on the analysis of the material presented in the article, the author comes to the conclusion that G.V. Florovsky, although he was a member of the Eurasian circle, on some significant issues differed from the main direction of development of the Eurasian ideology presented by E. Trubetskoy. (shrink)

The modern world is confronted with a series of global problems, exacerbated by technological advancements. In this context, concerns arise in the public consciousness regarding the potential of artificial intelligence (AI) to surpass humans in intellectual and creative activities. The topic of AI creativity becomes pertinent and sparks debates within the scientific community regarding its creative potential. In response to these challenges, members of the Club of Rome in 2018 propose the concept of a new Enlightenment and the principle of (...) balance as a response to the demands of technological development. These ideas underscore the need for a balanced approach to technical progress, taking into account global values and ethical principles. I explore the definitions of creativity and AI, formulate criteria for assessing creativity, and analyse recent achievements in modelling creative processes in AI. I also focus on the utilisation of various algorithms for implementing diverse forms of creative activities, including text, image and music generation. Additionally, I present diverse opinions of researchers regarding creativity in AI. To systematise these perspectives, I propose a classification which allows their ranking. The conclusion emphasises that currently the issue of evaluating the creative potential of AI lacks a definitive solution, underscoring the relevance of further research. The future outlook may alter this situation, prompting the necessity to focus on predicting potential consequences of technological developments and developing mechanisms for controlling AI activities; humans, after all, bear responsibility for AI actions. Such an approach aligns with the concept of a new Enlightenment which seeks a balance between technological advancements and the preservation of global harmony. (shrink)

The objective of this study is to identify inimitable examples of the introduction of aesthetic content into the Western European metaphysical tradition, as it was embodied in Kant's understanding of the world concept of philosophy, which has certain aesthetic connotations. In the article, the author analyzes new stages of the movement towards the world concept of philosophy, on which the aesthetic meaning of the basic structures of transcendentalism is explicitly or implicitly realized: the art of schematism as a world concept (...) of epistemology; the world concept of art as an organ of understanding artistic works. In addition, this discussion becomes particularly relevant when they seek to reveal how much the concept of schematism allows us to advance to the explanation of the world concept of philosophy. The work reveals how Kant reproduces the definition of the world concept of philosophy according to a certain model, while posing the problem of the typical embodiment of the idea, the ideal of the philosopher as a model. In this connection, a new complication of aesthetic analysis is being carried out in order to show how the world concept of philosophy was personified and presented as if in the ideal of the philosopher as a model. Therefore, the paradox of the world concept of philosophy lies in the fact that we have to talk about a sample of what does not yet exist. The author reproduces a transcendental language that will reveal the movement of aesthetic thought into the center of the world concept of philosophy, where the traditional artistic technique of personification of the philosopher's ideal as a model is performed, where the contemplation of meaning is transferred into the universality of the concept, into the contours of metaphysics. (shrink)

The aim of the study is to clarify the aesthetic concept of color perception from the phenomenological reasoning of Edmund Husserl. Today, the orientation diagram of the field of phenomenological research is formed in various zones: from theological to naturalistic. In which of these zones the structures of the phenomenological analysis of color are located is not an easy question. The coloristic region is constituted according to the degree of consciousness, including aesthetic consciousness. It is extremely difficult to meet with (...) the phenomenon of color, if only because its obviousness is fulfilled only by the fervor of the contemplative consciousness with its aesthetic pathos, a consciousness that distinguishes between, as it were, the reality of transcendent color and the aesthetic "continent of givens". We are talking, as Husserl would say, about the halo of consciousness, referring to the essence of perception performed in the mode of turning to the beauty of color. For the first time, approaches to the study of such a complex phenomenological topic as the description of a coloristic attitude, the eidetics of color experiences in Husserl's philosophy are outlined, the significance of its development for the comprehension of aesthetic and artistic consciousness is revealed. The main conclusions of the study are related to the philosophical interpretation of the idea of color as included in phenomenology in the experience of philosophical surprise, which turns into the acquisition of the essence of "phenomenological color" in general, and in aesthetics it is directly correlated with the appearance of its structures on the horizon of the harmonic synthesis of acts of perceptual performance in the imagination, "primordial giving visions" of color, with the creation of a picture coloristic impressions as cognitive emotions, reduced pure color perception, with an understanding of how art makes the very conditions of color visibility obvious, how its artistic synthesis is made, in the structure of which correlation analysis can see an analogue of a priori empiricism – this fundamental characteristic of purely Husserl synthesis and method revealed in domestic studies. (shrink)

V glavakh kollektivnoi| monografii predstavleny kont︠s︡eptualʹnye razrabotki problem, znachimykh dli︠a︡ filosofii nachala novogo stoletii︠a︡. Ėtot krug problem okhvatyvaet vse oblasti sovremennoi| filosofii--ot ontologii i filosofii nauki do filosofii logiki i politiki. Sovremennye ot︠s︡enki i razvitie poluchai︠u︡t idei analiticheskoi| filosofii, ėkzistent︠s︡ializma, fenomenologii, strukturalizma s ikh orientat︠s︡iei| na prikladnye sfery. Kniga adresovana kak spet︠s︡ialistam, tak i vsem tem, kto proi︠a︡vli︠a︡et interes k sostoi︠a︡nii︠u︡ i problematike sovremennoi| otechestvennoĭ filosofii.