The article is devoted to the applicability of Wittgenstein’s following the rule in the context of his philosophy of mathematics to real mathematical practice. It is noted that in «Philosophical Investigations» and «Remarks on the Foundations of Mathematics» Wittgenstein resorted to the analysis of rather elementary mathematical concepts, accompanied also by the inherent ambiguity and ambiguity of his presentation. In particular, against this background, his radical conventionalism, the substitution of logical necessity with the «form of life» of the community, as (...) well as the inadequacy of the representation of arithmetic rules by a language game are criticized. It is shown that the reconstruction of the Wittgenstein concept of understanding based on the Fregian division of meaning and referent goes beyond the conceptual framework of Wittgenstein language games. (shrink)

The article shows that Borisov’s direct solution to the problem of skepticism about meaning using a special type of introspection is associated with the assumption of the agent’s direct access to their own consciousness. This assumption has two complicating consequences: the analogy with Moore’s paradox and the Platonic concept of meaning. It is also shown that direct access to meaning as a way of Borisov’s direct solution of the skeptical paradox significantly uses the performativity of the speech act, narrowing the (...) scope of analysis of the original problem. The little-studied problem of distinction in the analysis of the skeptical paradox of meaningful and formalized mathematics is noted. (shrink)

The article is devoted to the comparison of two types of proofs in mathematical practice, the methodological differences of which go back to the difference in the understanding of the nature of mathematics by Descartes and Leibniz. In modern philosophy of mathematics, we talk about conceptual and formal proofs in connection with the so-called Hilbert Thesis, according to which every proof can be transformed into a logical conclusion in a suitable formal system. The analysis of the arguments of the proponents (...) and opponents of the Thesis, “conceptualists” and “formalists”, is presented respectively by the two main antagonists – Y. Rav and J. Azzouni. The focus is on the possibility of reproducing the proof of “interesting” mathematical theorems in the form of a strict logical conclusion, in principle feasible by a mechanical procedure. The argument of conceptualists is based on pointing out the importance of other aspects of the proof besides the logical conclusion, namely, in introducing new concepts, methods, and establishing connections between different sections of meaningful mathematics, which is often illustrated by the case of proving Fermat’s Last Theorem (Y. Rav). Formalists say that a conceptual proof “points” to the formal logical structure of the proof (J. Azzouni). The article shows that the disagreement is based on the assumption of asymmetry of mutual translation of syntactic and semantic structures of the language, as a result of which the formal proof loses important semantic factors of proof. In favor of a formal proof, the program of univalent foundations of mathematics In. Vojevodski, according to which the future of mathematical proofs is associated with the availability of computer verification programs. In favor of conceptual proofs, it is stated (A. Pelc) that the number of steps in the supposed formal logical conclusion when proving an “interesting” theorem exceeds the cognitive abilities of a person. The latter circumstance leads the controversy beyond the actual topic of mathematical proof into the epistemological sphere of discussions of “mentalists” and “mechanists” on the question of the supposed superiority of human intelligence over the machine, initiated by R. Penrose in his interpretation of the Second Theorem of Goedel, among whose supporters, as it turned out, was Goedel himself. (shrink)

The article discusses the V.V. Tselishchev’s original and unique systematic study of the specific and extremely complicated problems of Gödel results regarding the question of artificial intelligence essence. Tselishchev argues that the reflexive property should be considered not only as an advantage of human reasoning, but also as an objective internal limitation that appears in case of adding Gödel sentence to a theory to build a new theory. The article analyzes so-called mentalistic Gödel’s argument for fundamental superiority of human intelligence (...) over machine one and the non-algorithmic nature of natural thinking. The discussion about the Gödel argument is not entirely speculative, but contains new knowledge. An example of such knowledge are the results of R. Smullyan levels of computers “awareness,” which are may be interpreted in a psychophysical sense. The concept of “zero level of intelligence” is proposed for such a reflexive property as “awareness of selfconsciousness.” Reflexive ranks below the awareness of self-consciousness can be considered negative levels of thinking in the sense that the intelligence, being reduced to them, significantly loses its completeness. Even self-consciousness turns out to be a negative level of thinking, since, according to Smullyan, the subject of self-consciousness is unaware of the type of thought to which he belongs. A thought experiment is proposed that allows us to establish the distribution of the properties of Smullyan stability and normality and to answer the question “Does an intuitive belief in the truth of a formal proof affect the truth of a proposition being proved?” According to intuitionism, the most unpleasant epistemic property is instability: beliefs that are not based on deep intuitions have no value. According to the constructivist philosophy of mathematics, instability is a less negative property than abnormality: the fact that high-ranking beliefs cannot be immersed to the very foundations is not significant because violation of truth due to lowering the rank of reflection is not critical. (shrink)

This set reprints volumes that were orginally published by Routledge and Kegan Paul Ltd. in 1953. Landmark volumes at the time of their original publication, these titles do not merely expound the theoretical constructions of Russian philosophers, but also relate these constructions to the general conditions of Russian life. Volume One examines the historical conditions of the development of philosophy in Russia and explores the general features of Russian philosophy. It also surveys the principal works on the history of Russian (...) philosophy. Volume Two includes biographies and examination of the themes of the following philosophers; Vladimir Solovyov, V.D. Kudryavtsev, N.F. Fyodorov and Later Hegelians such as Chicherin, Debolski and Bakunin. This volume also provides analysis of various schools of thought in Russian philosophy in the twentieth century, for example; Neo-Leibzianism, Modern Positivism and New-Marxism to name but a few. (shrink)

Purpose. The knowledge influence analysis on the formation process of new anthropological images of man in the contexts of scientific achievements and innovative technologies is the basis of this study. It involves the solution of the following tasks: 1) explication of the ontological content of knowledge in the anthropo-cultural senses of the epoch; 2) analysis of the knowledge influence on the process of forming a new type of man; 3) characteristics of the modern anthropological situation in the context of digital (...) culture; 4) substantiation of interrelation of phatic communication with post-truth society in the dimensions of anthropo-social transformations of the present. Theoretical basis. Ontological content of knowledge determines the anthropo-cultural context of the epoch by forming a system of intellectual, value, social meanings of human life. The assertion of new anthropological types of man is caused by the changes in social and cultural space in the context of the growing influence of achievements in scientific knowledge and technology. Digital revolution as the process of expanding the possibilities of informational-digital reality, the substitution of knowledge for information gives rise to Homo digitalis – the digital man. He focuses on phatic communication, which in its intellectual meaninglessness is commensurate with the anthropological dimensions of post-truth society. Originality. It is substantiated that Homo digitalis is the result of a complex set of heterogeneous effects of scientific knowledge, which in modern post-truth conditions appears as different communicative practices. A condition for the formation of a new anthropological type of man in the perspective of scientific and technological progress is the affirmation of ethical wisdom. Conclusions. Knowledge in the process of evolution of socio-cultural life acquires constitutive significance for the process of formation of anthropological situations that manifest themselves in new images of man. Today, he is commensurate with the demands of digital culture, in which human life practices are increasingly becoming information and digital clusters embedded in the reality of a post-truth society. The means of overcoming the passivity of digital man is the formation of a new anthropological type based on a rethinking of the value system. (shrink)

Purpose. The purpose of the study is to outline the links between individual and collective dimensions of the human worldview. This purpose requires solving two tasks: to update philosophical ideas formed by reflection on human and community worldview; to identify and generalize the relationship of singular and general in the context of the problem of human worldview. Theoretical basis. The study is based on philosophical reflections about manifestations of singular and general worldviews. Such reflections appeared in European philosophy quite a (...) long time ago. Ukrainian and foreign philosophical discourse considers both measures of the worldview. And a role of the carrier of worldview plays either human or society. We can see that in researches of S. Krymskyi, I. Nadolniy, V. Popov, N. Rozhanska, V. Tabachkovskyi, V. Shynkaruk, V. Poythress, D. Rousseau, D. Billingham, C. Gianolla and others. However the links between individual and collective dimensions of worldview are not clearly outlined. It is possible to note the research of V. Popov who focuses on the problem of socio-collective and individual dimensions of worldview. But the scientist focuses more on the use of the concept of worldview in these two meanings. Human as a social being interacts with worldviews of other individuals. That is why we can speak of two dimensions of the worldview function: individual and collective. This problem became topical due to acuteness of the links between human and society in modern life. Originality. The author outlined key links between individual and collective dimensions of human worldview functioning. The study identified a role of human as a carrier of the worldview in formation of collective worldview. Conclusions. Human as a worldview carrier plays a key role in formation of collective worldview. In philosophical discourse thoughts about links between individual and collective worldviews are different and sometimes conflicting. We have a discussion problem of uniformity and diversity of collective worldview. Collective worldview is showed as a circulation of different ideas and views of individuals. But collective worldview is showed as a whole system of individual views too. Collective worldview manifests as integrated phenomenon because it is based on common worldviews of individuals. At the same time the human is influenced by collective worldview in particularly as a past generation heritage. (shrink)

Questions connected with the admissibility of rules of inference and the solvability of the substitution problem for modal and intuitionistic logic are considered in an algebraic framework. The main result is the decidability of the universal theory of the free modal algebra imageω extended in signature by adding constants for free generators. As corollaries we obtain: there exists an algorithm for the recognition of admissibility of rules with parameters in the modal system Grz, the substitution problem for Grz and for (...) the intuitionistic calculus H is decidable, intuitionistic propositional calculus H is decidable with respect to admissibility . A semantical criterion for the admissibility of rules of inference in Grz is given. (shrink)

Purpose. To analyse the philosophical and psychological contexts of social expectations of personality, to form general scientific provisions, to reveal the properties, patterns of formation, development and functioning of social expectations as a process, result of reflection and construction of social reality. Theoretical basis of the study is based on the phenomenology of E. Husserl, the social constructivism philosophy of L. S. Vygotskiy, P. Berger, T. Luckmann, K. J. Gergen, ideas of constructive alternativeism of G. Kelly, psychology of social expectations (...) of a personality as the unity of the mental process, mental state and properties of expectations. Originality. Social expectations of personality are considered as philosophical and psychological dimensions of the study, presented by analysing expectations in social constructivism, externalizing, building a model of the expected future. The authors clarified some theoretical and methodological aspects of the study of patterns of social expectations in the reflection and construction of social reality. The role of social institutions in the formation of expectations is outlined. The poly-aspect of the investigated problems is shown. It is substantiated that formation, realization of social expectations in organization of interaction of personality and social environment is possible in the presence of subject, object and content of activity. Conclusions. Social expectations influence social behaviour and determine the behaviour of an individual, small contact group, community, or large mass of people. Social expectations are able to set specific requirements, norms, sanctions, ideals that participants of the process must follow or must not violate. The philosophical dimension of the study integrates the ontological, epistemological, axiological preconditions for the formation and realization of the social ideal, represented by the study of the expected future in the forms of utopia, eschatology and thanatology. Psychological dimension of the study has a sufficiently developed content orientation from the psychological content parameters of social expectations to the role of expectations in social institutions and various spheres of human life. Systematic, actionable, self-regulatory, and subjective approaches have constituted a verified system of interpreting the social expectations of personality as a process, a result of the reflection and construction of social reality. The topic of social expectations of personality is far from being completed, in our opinion it is promising to create a deeper philosophical concept of social expectations of the personality. The specific topics are of particular relevance in the context of socio-political uncertainty, domination of the mass consciousness, loss of national and cultural identity. (shrink)

Purpose. The paper considers the fear of social alienation of love. It is within the limits of psychoanalytic epistemology, the analysis of which will be presented in the article, the tendencies to monotony and universal solutions with an emphasis on ensuring the objectivity of the problem of gender alienation, to be more exact, the fear of love, which causes the gender process, are viewed most reliably. In view of the above the purpose of the paper is to investigate the conceptual (...) contradictions associated with the reconstruction of basic measurements of the fear of alienation of love within different ideological approaches; to reveal the most significant contradictions that manifest themselves in the differences between secular and religious frames; to determine a philosophical and fundamental foundation for the types of fear: metaphysical, transcendental and social, which to some extent have influenced the development of a gender tradition. The paper investigates the fear of alienation of love, not as an instinct or psychological experience, or as a social factor, but as a correlation between the functional types of fear and the peculiarities of social and cultural processes, and it acts as a dependence of the European societies on the various functional forms of fear of love that influence the processes of social transformations. Theoretical basis. The authors determine that in the gender approach the subject, who is cognized, has specific desires and interests. The process of cognation is local, contextual, in which physiologically and spiritually the fear of alienation of love is closely linked to the conditions of existence of people, with the arrangement of social and individual life. In modern civilization, true love with some exceptions, is fleeting. It is now hindered by the burdens of life, and ideological settings, which go only from the "I", and not from the common "I and You", contributing to frustration and alienation. Originality. The emphasis is placed on the fact that the fear of alienation of love, as a way of identifying the essential characteristics of "I", acts as an existential, which concentrates on the sense-life range of problems. The range of problem in a single topic is in the "point I", surrounded by gender boundaries, it contains as a condition for its manifestation the personality distancing – free or forced consolidation and assertion of the autonomy of the individual. Alienation of love as an existential admits in the register of the intimate, intentional for self-perception, internal state to organize and identify with the "authentic I". Conclusions. The article establishes that gender identity under the conditions of modern socio-psychological crisis is associated with forming a special "picture of fear, anxiety, loneliness" as a part of that internal and external world, generated by alienation from society. The fear of alienated love acts as the essential existential of human being, which is a necessary existential condition of the existential tension that occurs as an antipode and a characteristic of courage, asceticism, and the "beginning of wisdom". The considered phenomenon of the fear of alienation of love is interpreted as the result of the ontological and gender alienation of a person who has lost a sense of security and plunged into a continuous interindividual rivalry. (shrink)

We are demonstrating that the Luttinger model with short range interaction can be treated as a type of Fermi liquid. In line with the main dogma of Landau’s theory one can define a fermion excitation renormalized by interaction and show that in terms of these fermions any excited state of the system is described by free particles. The fermions are a mixture of renormalized right and left electrons. The electric charge and chirality of the Landau quasi-particle is discussed.

We consider structural completeness in modal logics. The main result is the necessary and sufficient condition for modal logics over K4 to be hereditarily structurally complete: a modal logic λ is hereditarily structurally complete $\operatorname{iff} \lambda$ is not included in any logic from the list of twenty special tabular logics. Hence there are exactly twenty maximal structurally incomplete modal logics above K4 and they are all tabular.