The authors investigated the relevance of consequentialism in commercial space exploration as well as in the actively developing space market. The authors conclude that space expansion and colonization of space objects will lead to a revision of the foundational consequentialism provisions. Consequentialism, formed during the history of terrestrial civilization, loses its effectiveness under conditions of space commercialization. The basics of planetary thinking are different from those of cosmic thinking. Therefore, considering the meaning of the terms “cosmic expansion” and “colonization of (...) the cosmos” through the existing theory of consequentialism faces serious contradictions. There is a range of problems that are not explored in modern philosophy and ethics due to the lack of an empirical basis for philosophical analysis. (shrink)

A structure (M, $ ,...) is called quasi-o-minimal if in any structure elementarily equivalent to it the definable subsets are exactly the Boolean combinations of 0-definable subsets and intervals. We give a series of natural examples of quasi-o-minimal structures which are not o-minimal; one of them is the ordered group of integers. We develop a technique to investigate quasi-o-minimality and use it to study quasi-o-minimal ordered groups (possibly with extra structure). Main results: any quasi-o-minimal ordered group is abelian; any quasi-o-minimal (...) ordered ring is a real closed field, or has zero multiplication; every quasi-o-minimal divisible ordered group is o-minimal; every quasi-o-minimal archimedian densely ordered group is divisible. We show that a counterpart of quasi-o-minimality in stability theory is the notion of theory of U-rank 1. (shrink)

Oral history of philosophy: written format.

In this paper, we present a logic MMLS5n which is a combination of multilattice logic and modal logic S5. MMLS5n is an extension of Kamide and Shramko’s modal multilattice logic which is a multilattice analogue of S4. We present a cut-free hypersequent calculus for MMLS5n in the spirit of Restall’s one for S5 and develop a Kripke semantics for MMLS5n, following Kamide and Shramko’s approach. Moreover, we prove theorems for embedding MMLS5n into S5 and vice versa. As a result, we (...) obtain completeness, cut elimination, decidability, and interpolation theorems for MMLS5n. Besides, we show the duality principle for MMLS5n. Additionally, we introduce a modification of Kamide and Shramko’s sequent calculus for their multilattice version of S4 which (in contrast to Kamide and Shramko’s original one) proves the interdefinability of necessity and possibility operators. Last, but not least, we present Hilbert-style calculi for all the logics in question as well as for a larger class of modal multilattice logics. (shrink)

Shramko [. Truth, falsehood, information and beyond: The American plan generalized. In K. Bimbo, J. Michael Dunn on information based logics, outstanding contributions to logic...

The author argues that according to Sextus Empiricus, (a) the "sensual" nature of the phenomenon is a metaphorical notion, since it is indistinguishably extended both to sensuality and thinking; (b) the phenomenon manifest itself with irresistible force of impact, through a wide range of passive states of mind; (c) the impact of phenomena is always mediated by our ego, because all skeptic expressions are strongly correlated with the first person singular. The article proves that Descartes could not refute the “excess” (...) of skeptical doubt and make an immanent critique of skepticism without borrowing the aforementioned statements of Sextus. Such borrowing (1) has created a common ground for discussion between Descartes and skeptics; (2) made it possible for the meditator to give persuasiveness to careful observation of his own internal experience. Descartes' search for certainty in "Meditations" is entirely based on [а] evidence of "phenomena", "states of mind", "passions"; [b] refusal to agree with the "non-evident" proclaimed by Sextus Empiricus. (shrink)

In the paper we analyse the problem of axiomatizing the minimal variant of discussive logic denoted as $${\textsf {D}}_{\textsf {0}}$$ D 0. Our aim is to give its axiomatization that would correspond to a known axiomatization of the original discussive logic $${\textsf {D}}_{\textsf {2}}$$ D 2. The considered system is minimal in a class of discussive logics. It is defined similarly, as Jaśkowski’s logic $${\textsf {D}}_{\textsf {2}}$$ D 2 but with the help of the deontic normal logic (...) $$\textbf{D}$$ D. Although we focus on the smallest discussive logic and its correspondence to $${\textsf {D}}_{\textsf {2}}$$ D 2, we analyse to some extent also its formal aspects, in particular its behaviour with respect to rules that hold for classical logic. In the paper we propose a deductive system for the above recalled discussive logic. While formulating this system, we apply a method of Newton da Costa and Lech Dubikajtis—a modified version of Jerzy Kotas’s method used to axiomatize $${\textsf {D}}_{\textsf {2}}$$ D 2. Basically the difference manifests in the result—in the case of da Costa and Dubikajtis, the resulting axiomatization is pure modus ponens-style. In the case of $${\textsf {D}}_{\textsf {0}}$$ D 0, we have to use some rules, but they are mostly needed to express some aspects of positive logic. $${\textsf {D}}_{\textsf {0}}$$ D 0 understood as a set of theses is contained in $${\textsf {D}}_{\textsf {2}}$$ D 2. Additionally, any non-trivial discussive logic expressed by means of Jaśkowski’s model of discussion, applied to any regular modal logic of discussion, contains $${\textsf {D}}_{\textsf {0}}$$ D 0. (shrink)

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)

In many films, story is presented in an order different from chronological. Deviations from the chronological order in a narrative are called anachronies. Narratological theory and the evidence from psychological experiments indicate that anachronies allow stories to be more interesting, as the non-chronological order evokes curiosity in viewers. In this paper we investigate the historical dynamics in the use of anachronies in film. Particularly, we follow the cultural attraction theory that suggests that, given certain conditions, cultural evolution should conform to (...) our cognitive preferences. We study this on a corpus of 80 most popular mystery films released in 1970–2009. We observe that anachronies have become used more frequently, and in a greater proportion of films. We also find that films that made substantial use of anachronies, on average, distributed the anachronies evenly along film length, while the films that made little use of anachronies placed them near the beginning and end. We argue that this can reflect a functional difference between these two types of using anachronies. The paper adds further support to the argument that popular culture may be influenced to a significant degree by our cognitive biases. (shrink)

This article is dedicated to Nikolai O. Lossky’s intuitivism and personalism and their significance in the context of Russian philosophy. The author demonstrates how Lossky’s study of Russian philosophy influenced his work and allowed him to take a second look at a number of philosophical issues, indicating ways to develop them further. As a result of his research, Lossky discovered ideas close to his own in the works of various other Russian philosophers. Lossky became especially interested in two authors, Vladimir (...) S. Solovyov and Fyodor M. Dostoevsky. He created interpretations that examined Solovyov’s philosophy and Dostoevsky’s works from the positions of intuitivism and personalism. The study of Russian thought Lossky undertook in his book History of Russian Philosophy gave him a strong impetus for developing his own philosophical views, which were aimed at bringing philosophy and religion into closer proximity. (shrink)

The paper aims to prove the hypothesis that Sextus Empiricus’ Neo-Pyrrhonism is significantly influenced by the Cartesian meditation as a genre of philosophizing. It refutes theses about (1) the non-predicativity of Sextus’ language and about (2) Sextus’ epochê as an automatic result of the action of opposite things or statements, and it argues that both Sextus and Descartes distinguish between (a) internal (forced) agreement with clarity and (b) the personal acceptance of this agreement which depends on a volitional decision. Sextus’ (...) recognition of the clarity of appearance as appearance gives Descartes the only chance to refute the skepticism of Sextus, which is invulnerable to external criticism. Therefore, Descartes developed meditation as a special model of purely immanent criticism (the very word “skepticism” is never mentioned in the Meditations), focused on dealing with states of clarity and evidence. The author’s hypothesis is that the key elements to which this model appeals are the “history of a skeptic” set out in Outlines of Pyrrhonism and the conception of skeptical expressions. This hypothesis can be tested further by proving or disproving the thesis that the discourse of I, II, and at least partially of III Meditations is based on the pattern of skeptical expressions, focused on the internal states of the speaker, and not on clarifying the “objective” state of affairs (i.e. not on dogmatic inferences). (shrink)

An introduction to the new section "Philosophical Handbooks" from the editor-in-chief of Sententiae.

The relevance of the research reflects the unity of the requirements of the Beijing Philosophical Congress "Learning to be a man" and the anniversary report of the "Rome Club" "Come On! Capitalism, myopia, population and destruction of the planet", which the transformation processes of the socio-sphere are revealed from the standpoint the need for a radical breakdown of the spiritual and moral world of man and his worldview. The foundation of these transformations is the transition in education, as the hippocrine (...) of our knowledge, the source that quenches thirst in them to the "new Enlightenment" as a decisive factor in the learning of a person to be him. This determined the purpose and objectives of the article. The purpose of the article is to substantiate the natural and necessary character of the formation of the "new Enlightenment", to reveal the architectonics of its content. Research objectives : in the context of the goal to uncover the factors that determine the need for a transition in education to the "new Enlightenment", its qualitative difference from the Enlightenment of the 17th-18th centuries; to characterize the new content of "connectedness" in education based on the use of new information technologies; analyze the process of formation of a new spiritual and moral outlook of a specialist on the universal values of humanity; focus the learner’s attention on focusing knowledge of sustainable development as a determining factor of the global problems of mankind through the interrelation of academic disciplines; an important component presents the demand for the formation of a new integral thinking, innovative in its essence and qualitatively different from the analytical one. It is noted that the transition to the path of integral thinking contributes to the connection, coordination and organization into a single whole of the fragments of the object under study. Such thinking is characterized by stability, reliability, variability; it is original in its connections with science and education, and methodological influence on individual and social consciousness. Integral thinking reflects a qualitatively new level of intelligence. Research methods: to achieve the stated goal and constructive solution of the tasks, the article used the method of abduction, analysis and synthesis, historical and logical, synergistic approach. The results of the research: a new paradigm of education is represented – the noospheric-information one corresponding to the factuality of the “new Enlightenment”, as its ability to reproduce itself on a changing scale. The change in the scale of the socio-sphere is due to its globalization processes. The content of the “new Enlightenment” is explicated as a qualitatively new level of formation of students' sustainable knowledge based on the integral innovative type of thinking based on the information resources of society, the use of modern educational technologies, as well as on the values of society, as the quintessence of its wisdom and public intelligence. Conclusions. Thus, the formation of a "new Enlightenment" is natural and necessary. This follows from the requirements of the “learn to be human” program, as well as from the development of an internally ordered education process. “New Enlightenment” also has an attribute of uniqueness, since it does not have anything to compare with, identify; it is an objective, essential, unique phenomenon; it is single, relative, determined by the previous development of education. It is based on the processes of intellectualization, innovation, informational content, humanism and is capable of solving constructively the tasks facing society. (shrink)

The Crimea Conference is by all means an extremely complex historical event. Any attempt to estimate its role and significance without analyzing its ethical components would unavoidably result in unduly simplifying the historical reality of the time, as well as in forming erroneous assumptions that would necessarily be used in the analysis of the causes of Cold War. A thorough examination will show that as far as the ‘ethical’ issues are concerned, there are significant developments with regard to general methodology, (...) as well as its application to the sources. Generations of historians who have addressed the issue of Yalta Conference, although they have not been able to form a scientific, distinct ‘ethical’ tradition so far, have developed all the necessary prerequisites for its establishment. This is evident in the possibility of segmenting the issue in two parts on the one hand, and on the other in the availability of sufficient sources, structured databases, and selected outstanding works. Still, there are no studies about the Yalta Conference so far that address exclusively ethical issues concerning ‘good’ and ‘evil,’ ‘morality,’ ‘duty,’ and ‘honor.’ Although historiographical approaches are to a large extent dependent upon ethical viewpoints, in the case of Yalta agreements so far there have been no techniques available, so as to connect historical accounts with ideology, and historical facts with their philosophical background. In a sense, the situation is quite the same as it is with the study of prehistory: although there is an abundance of data and facts that can be primarily processed, there are no methodological guidelines, nor any devices to classify and explain them. This is also typical for any question raised about the ethics of the Yalta agreements in February 1945. (shrink)

he model theory of groups of unitriangular matrices over rings is studied. An important tool in these studies is a new notion of a quasiunitriangular group. The models of the theory of all unitriangular groups are algebraically characterized; it turns out that all they are quasiunitriangular groups. It is proved that if R and S are domains or commutative associative rings then two quasiunitriangular groups over R and S are isomorphic only if R and S are isomorphic or antiisomorphic. This (...) algebraic result is new even for ordinary unitriangular groups. The groups elementarily equivalent to a single unitriangular group UTn are studied. If R is a skew field, they are of the form UTn, for some S ≡ R. In general, the situation is not so nice. Examples are constructed demonstrating that such a group need not be a unitriangular group over some ring; moreover, there are rings P and R such that UTn ≡ UTn, but UTn cannot be represented in the form UTn for S ≡ R. We also study the number of models in a power of the theory of a unitriangular group. In particular, we prove that, for any communicative associative ring R and any infinite power λ, I = I). We construct an associative ring such that I = 3 and I) = 2. We also study models of the theory of UTn in the case of categorical R. (shrink)

In this paper, we consider modal multilattices with Tarski, Kuratowski, and Halmos closure and interior operators as well as the corresponding logics which are multilattice versions of the modal logics MNT4, S4, and S5, respectively. The former modal multilattice logic is a new one. The latter two modal multilattice logics have been already mentioned in the literature, but algebraic completeness results have not been established for them before. We present a multilattice version of MNT4 in a form of a sequent (...) calculus and prove the algebraic and neighbourhood completeness theorems for it. We extend the algebraic completeness result for the multilattice versions of S4 and S5 as well. (shrink)

Publication date: 22 December 2020 Source: International Letters of Social and Humanistic Sciences Vol. 89 Author: Oleg Tarnopolsky, Marina Kabanova The article analyzes using Content and Language Integrated Learning for teaching one of the optional humanities disciplines to Ukrainian university students of different majors. The discipline discussed in the article as an example of using CLIL methodology is “The Fundamentals of Psychology and Pedagogy” and it is in the list of optional humanities subjects for the first-year students of Alfred (...) Nobel University in Dnipro, Ukraine. However, unlike the other optional humanities disciplines, the methodology underlying this course is based on teaching the subject in English, instead of Ukrainian, following the CLIL approach widely used in the European education but still little known in Ukraine. The purpose of the paper is to expose and analyze the original methodology developed that conditioned the specific structure of the relevant course, and the specific learning activities used in it. The essence of the developed CLIL theory-based methodology and its practical application are manifested through learning activities that include students’ mini-lectures/workshop-type presentations, brainstorming, case-studies, discussions, and a learning project with its results summarized in students’ essays, abstracts, and summaries written in English. The students collect the information required for completing their tasks not only from the teacher’s lectures and the recommended literature but also by way of doing extensive Internet-search on psychological and pedagogical sites in English. All this makes CLIL in the case under discussion experiential-interactive, blended, autonomous, and cooperative. As the result, students mostly self-construct their knowledge of the discipline by way of using the target language as the tool for such self-construction. This makes the elaborated course a clear-cut case of constructivism in CLIL pedagogy. Subject Classification Numbers: PACS 01.40.-d. (shrink)

Publication date: 2 May 2019 Source: Author: Oleg Tarnopolsky The article discusses an innovative course taught to students majoring in English at Ukrainian universities. The course called “Specific Features of the English Language and English-Speaking Nations’ Cultures in the Context of International Communication” was designed to eliminate the lack of a number of issues that must be included in the curriculum of English language and culture studies to be learned by such students but which are ordinarily not included there (...) because each of them cannot make the subject matter of a separate university course and does not fit into the traditionally taught courses. The issues in question embrace: the specific role of English among other languages of international communication; World Englishes, International English and English as a lingua franca and how to choose the variety of English to be taught as a foreign language; the specifics of business negotiations in English in intercultural contexts, business presentations in English, and business telephoning in English in such contexts; communicative behavioral etiquette in intercultural communication in English; lifestyle communicative behavioral patterns of the English-speaking nations. The paper shows how teaching these issues enriches and improves the English language and culture education of English major students expanding that education and relevant practical training to fit much better the international and intercultural contexts of communication in English. (shrink)

Publication date: 30 August 2017 Source: Author: Oleg Tarnopolsky This paper analyzes a project devoted to elaborating a new textbook of English for students majoring in “Tourism.” The textbook is designed on the basis of the constructivist approach, i.e. such an organization of the teaching/learning process that ensures students’ involuntary language acquisition through participation in target language communication which is implemented when performing learning tasks modeling the professional activities of the future university graduates. Those tasks are completed in the (...) form of experiential learning activities that provide for modeling the students’ future professional activities and professional target language communication, giving them opportunities of acquiring the language involuntarily through practical experience of participating in such communication. Examples of experiential learning activities are given – those that are used in every unit of the textbook as organized in the separate parts of every such unit. (shrink)

Statistical physics cannot explain why a thermodynamic arrow of time exists, unless one postulates very special and unnatural initial conditions. Yet, we argue that statistical physics can explain why the thermodynamic arrow of time is universal, i.e., why the arrow points in the same direction everywhere. Namely, if two subsystems have opposite arrow-directions at a particular time, the interaction between them makes the configuration statistically unstable and causes a decay towards a system with a universal direction of the arrow of (...) time. We present general qualitative arguments for that claim and support them by a detailed analysis of a toy model based on the baker’s map. (shrink)

We propose that a top priority of the cerebral cortex must be the discovery and explicit representation of the environmental variables that contribute as major factors to environmental regularities. Any neural representation in which such variables are represented only implicitly (thus requiring extra computing to use them) will make the regularities more complex and therefore more difficult, if not impossible, to learn. The task of discovering such important environmental variables is not an easy one, since their existence is only indirectly (...) suggested by the sensory input patterns the cortex receives – these variables are “hidden.” We present a candidate computational strategy for (1) discovering regularity-simplifying environmental variables, (2) learning the regularities, and (3) using regularities in perceptual and decision-making tasks. The SINBAD computational model discovers useful environmental variables through a search for different, but nevertheless highly correlated functions of any kind over non-overlapping subsets of the known variables, this being indicative of some important environmental variable that is responsible for the correlation. We suggest that such a search is performed in the neocortex by the dendritic trees of individual pyramidal cells. According to the SINBAD model, the basic function of each pyramidal cell is (1) to discover and represent one of the regularity-simplifying environmental variables, and (2) to learn to infer the state of its variable from the states of other variables, represented by other pyramidal cells. A network of such cells – each cell just attending to representation of its variable – can function as a sophisticated and useful inferential model of the outside world. (shrink)

We consider relational databases organized over an ordered domain with some additional relations — a typical example is the ordered domain of rational numbers together with the operation of addition. In the focus of our study are the first-order queries that are invariant under order-preserving “permutations” — such queries are called order-generic. It has recently been discovered that for some domains order-generic FO queries fail to express more than pure order queries. For example, every order-generic FO query over rational numbers (...) with + can be rewritten without +. For some other domains, however, this is not the case.We provide very general conditions on the FO theory of the domain that ensure the collapse of order-generic extended FO queries to pure order queries over this domain: the Pseudo-finite Homogeneity Property and a stronger Isolation Property. We further distinguish one broad class of domains satisfying the Isolation Property, the so-called quasi-o-minimal domains. This class includes all the o-minimal domains, but also the ordered group of integer numbers and the ordered semigroup of natural numbers, and some other domains.An important difference of this paper from the recent series of related papers is that we generalize all the notions to the case of finitely representable database states — as opposed to finite states — and develop a general lifting technique that, essentially, allows us to extend any result of the kind we are interested in, from finite to finitely representable states. We show, however, that these results cannot be transfered to arbitrary infinite states. (shrink)

The main point for criticizing the Cartesians for Vico is the notion of method, interpreted as exceptionally discursive procedure, devoid of spontaneity and creative force which are necessary for discovering new truths. These qualities are embodied for Vico in the Latin term ingenium, loan translation of which is found in Italian (ingegno) and is absent in French. The criticism of Cartesianisn suggested by Vico does not consider the fundamental bilingualism of this philosophy and wide use of the term ingenium in (...) the corps of Descartes’ Latin works. The analysis of the latter proves that the early Descartes’ notion intuitus mentis, as well as the concept of natural light of mind are, in the end, based exactly on ingenium, but not on the discursive methodical procedures. Human soul, following Descartes, reveals its content in several hypostastes and each method of revelation corresponds to specific terminology. Soul as mens is not the same as soul as ingenium. But even the early Descartes’ study of soul is marked by peculiar nominalism, proclamation of the real existence of individual soul as a separate entity. Therefore later, stating his ego cogito, Descartes states exactly the individual substance, not thinking in general. The terminological couple ingenium/mens is not translatable already in the French texts of Descartes himself (both merge in the French esprit), however their Ukrainian translations do not consider neither this untranslatability nor obvious references of Descartes’ esprit to other Latin compliances which differ each time. The article also analyses frequency in usage of the terms ingenium and mens in early and late Descartes’ Latin works; it has been proved that the augmentation of the meaning of metaphysical problems gradually turned mens into the main subject of Descartes’ research and deactualised the problem of ingenium. (shrink)

C’est la première édition critique du Liber particularis de Michel Scot, traité cosmologique latin qui constitue la deuxième partie de son Liber introductorius, rédigé entre 1220 et 1235 environ. L’édition est effectuée sur la base du ms. Bodl. Canon. Misc. 555 (collationné avec les mss Vatican, BAV Rossi IX 11 et Milan, Ambrosiana L 92 Sup), afin de restituer une version qui circula, sous une forme relativement stable, en Italie dans la première moitié du xiv e siècle. Dans l’introduction, on (...) trouvera les données essentielles sur les manuscrits du Liber particularis, sur la place de ce traité dans l’œuvre de Michel Scot et dans le contexte intellectuel de la cour de Frédéric II, ainsi qu’un essai préliminaire visant à l’inscrire dans le développement des savoirs en Occident dans la première moitié du xiii e siècle. (shrink)

In the article, the author asserts that the transition of world history from Ancient Greece to the Middle Ages is connected precisely with the changed understanding and evaluation of the fundamental meanings of Being, but not with their replacement. The ancient paideia with all its achievements and peculiarities did not disappear in the history of culture. It transformed into the “paideia of Christ,” in which the second birth took place. After reviving in the new socio-cultural reality, Greek paideia retained its (...) fundamental meanings, which continued to be expounded through the conceptual apparatus of Christian theology in the theories of education in the Middle Ages. (shrink)

Primatological and archaeological evidence along with anthropological accounts of hunter-gatherer societies indicate that lethal between-group violence may have been sufficiently frequent during our ancestral past to have shaped our evolved behavioral repertoire. Two simulations explore the possibility that heroism (risking one's life fighting for the group) evolved as a specialized form of altruism in response to war. We show that war selects strongly for heroism but only weakly for a domain-general altruistic propensity that promotes both heroism and other privately costly, (...) group-benefiting behaviors. A complementary analytical model shows that domain-specific heroism should evolve more readily when groups are small and mortality in defeated groups is high, features that are plausibly characteristic of our collective ancestral past. (shrink)

Filtration combustion is described by Laplacian growth without surface tension. These equations have elegant analytical solutions that replace the complex integro-differential motion equations by simple differential equations of pole motion in a complex plane. The main problem with such a solution is the existence of finite time singularities. To prevent such singularities, nonzero surface tension is usually used. However, nonzero surface tension does not exist in filtration combustion, and this destroys the analytical solutions. However, a more elegant approach exists for (...) solving the problem. First, we can introduce a small amount of pole noise to the system. Second, for regularisation of the problem, we throw out all new poles that can produce a finite time singularity. It can be strictly proved that the asymptotic solution for such a system is a single finger. Moreover, the qualitative consideration demonstrates that a finger with 1 2 of the channel width is statistically stable. Therefore, all properties of such a solution are exactly the same as those of the solution with nonzero surface tension under numerical noise. The solution of the ST problem without surface tension is similar to the solution for the equation of cellular flames in the case of the combustion of gas mixtures. (shrink)

A totally ordered group G is called coset-minimal if every definable subset of G is a finite union of cosets of definable subgroups intersected with intervals with endpoints in G{±∞}. Continuing work in Belegradek et al. 1115) and Point and Wagner 261), we study coset-minimality, as well as two weak versions of the notion: eventual and ultimate coset-minimality. These groups are abelian; an eventually coset-minimal group, as a pure ordered group, is an ordered abelian group of finite regular rank. Any (...) pure ordered abelian group of finite regular rank is ultimately coset-minimal and has the exchange property; moreover, every definable function in such a group is piecewise linear. Pure coset-minimal and eventually coset-minimal groups are classified. In a discrete coset-minimal group every definable unary function is piece-wise linear 261), where coset-minimality of the theory of the group was required). A dense coset-minimal group has the exchange property ); moreover, any definable unary function is piecewise linear, except possibly for finitely many cosets of the smallest definable convex nonzero subgroup. Finally, we give some examples and open questions. (shrink)

For a quasi variety of algebras K, the Higman Theorem is said to be true if every recursively presented K-algebra is embeddable into a finitely presented K-algebra; the Generalized Higman Theorem is said to be true if any K-algebra which is recursively presented over its finitely generated subalgebra is embeddable into a K-algebra which is finitely presented over this subalgebra. We suggest certain general conditions on K under which the Higman Theorem implies the Generalized Higman Theorem; a finitely generated K-algebra (...) A is embeddable into every existentially closed K-algebra containing a finitely generated K-algebra B if and only if the word problem for A is Q-reducible to the word problem for B. The quasi varieties of groups, torsion-free groups, and semigroups satisfy these conditions. (shrink)

The article examines the place of graphic design in modern post-industrial society, extending beyond purely applied art and aspiring to play the role of an expert in the interiors of human existence, determining the social and cultural status of an individual. It is argued that graphic design, organically integrating into contexts and actively responding to the challenges of such a social-decorative phenomenon as fashion, plays a significant role in shaping taste culture. This attests to the multiplicity of ambivalent cultural manifestations (...) of graphic design. Special attention is given to identifying the functional potential of graphic design in creating cross-cutting trends that, through non-verbal means of communication, can form and maintain social and cultural unity. In connection with this, an analysis of graphic design is carried out through the prism of philosophical communication, allowing the identification of graphic design as the most effective practice of nonverbal communication and information visualization in post-industrial society. It is determined that graphic design is capable not only of generating new meanings but also of creating communicative gaps. Given this specificity, the article particularly focuses on identifying the educational and upbringing potential of graphic design. It is demonstrated that the process of creating visual images and their subsequent interpretation by consumers of graphic information depends not only on the aesthetic taste, ethical beliefs, and humanistic orientation of the designer (visualizer) but also on their educational and upbringing potential. The necessity of strengthening humanistic orientations in modern Ukrainian design and art education is emphasized. (shrink)

Martin-Löf’s type theory stems simultaneously from Frege and Russell’s logic-ontological ideas and Husserl’s phenomenology. The article examines this intermediate status of type theory using as examples Martin-Löf ’s syntactical-semantic method and the role of evidence and canonical objects in his approach. Martin-Löf borrows the syntactical-semantic method from Frege and extends it drawing on Husserl’s theory of meaning. In type theory this method leads to the identity (isomorphism) of syntax and semantics (formal logic and formal ontology). Unlike traditional formal logic the (...) type theory is an interpreted system from the very beginning. Being intuitionistic, Martin-Löf ’s theory is based on the notion of proof, not truth. From the meaning theory point of view, it is a variant of proof-theoretic semantics (Gentzen, Prawitz, Dummett) which understands meaning as an object constructed according to certain rules. So understood, the proof is based on evidence, which allows us to associate it with the theory of intentionality by Husserl. The article compares Martin-Löf ’s type theory with Husserl’s intentionality theory, especially with the latter’s noematic component. We may consider type-theoretical rules for constructing objects and operating with them as a concretization and formalization of the phenomenological notion of noema. Both are explications of the more general concept of meaning. The article discusses the interrelation between notions of sense and meaning (Sinn, Bedeutung) in Frege, Husserl and Martin-Löf. This reveals the uncertainty of Martin-Löf ’s position in relation to meaning theories of Frege and Husserl. (shrink)