Introduction. In the Russian philosophical tradition, domestic philosophical concepts are rather poorly considered at the moment. In fact, there is no coverage of regional specific features: the problems that worried and united Russian philosophers within the boundaries of one or another temporalterritorial locality. The purpose of the article is to consider the views of the Tyumen philosopher-ethicist Yuri Mikhailovich Fedorov in the context of their relevance at present and in the context of a continuous research tradition. Methods. The author proceeds (...) from the methods of hermeneutics, which are obligatory in this case, and also uses L. Laudan’s theory of research traditions, M. Foucault’s optics and the concept of permanent modernity. Scientific novelty of the research. The author clarifies Yu.M. Fedorov’s views through the specified methodology, considering his works in the context of a continuing philosophical tradition, with a special emphasis on the methods of subjectification. Results and conclusions. Taking into consideration the results of analytical reading of Yu.M. Fedorov’s key work “Universe of Morality”, it is concluded that the author’s concept, which combines the features of idealism, cosmism, structuralism, semiotics and existentialism, with some reservations (indicated in the article), suggests an adequate model of subjectification for a person of the XXI century. (shrink)

In Belnap's useful 4-valued logic, the set 2 = {T, F} of classical truth values is generalized to the set 4 = ������(2) = {Ø, {T}, {F}, {T, F}}. In the present paper, we argue in favor of extending this process to the set 16 = ᵍ (4) (and beyond). It turns out that this generalization is well-motivated and leads from the bilattice FOUR₂ with an information and a truth-and-falsity ordering to another algebraic structure, namely the trilattice SIXTEEN₃ with an (...) information ordering together with a truth ordering and a (distinct) falsity ordering. Interestingly, the logics generated separately by the algebraic operations under the truth order and under the falsity order in SIXTEEN₃ coincide with the logic of FOUR₂, namely first degree entailment. This observation may be taken as a further indication of the significance of first degree entailment. In the present setting, however, it becomes rather natural to consider also logical systems in the language obtained by combining the vocabulary of the logic of the truth order and the falsity order. We semantically define the logics of the two orderings in the extended language and in both cases axiomatize a certain fragment comprising three unary operations: a negation, an involution, and their combination. We also suggest two other definitions of logics in the full language, including a bi-consequence system. In other words, in addition to presenting first degree entailment as a useful 16-valued logic, we define further useful 16-valued logics for reasoning about truth and (non-)falsity. We expect these logics to be an interesting and useful instrument in information processing, especially when we deal with a net of hierarchically interconnected computers. We also briefly discuss Arieli's and Avron's notion of a logical bilattice and state a number of open problems for future research. (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)

This paper develops a version of Natural Logic – an inference system that works directly on natural language syntactic representations, with no intermediate translation to logical formulae. Following work by Sánchez, we develop a small fragment that computes semantic order relations between derivation trees in Categorial Grammar. The proposed system has the following new characteristics: It uses orderings between derivation trees as purely syntactic units, derivable by a formal calculus. The system is extended for conjunctive phenomena like coordination and relative (...) clauses. This allows a simple account of non-monotonic expressions that are reducible to conjunctions of monotonic ones. A decision procedure for provability is developed for a fragment of Natural Logic. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy of Music Education Review 11.2 (2003) 112-129 [Access article in PDF] Musical Aphorisms and Common Aesthetic Quandaries Yaroslav Senyshyn Simon Fraser University, Canada I have written in the style of aphorisms because their form is useful for both the sake of brevity and possible complexity. As well, they are historically significant as they have served many philosophers in the past and in our own time. Some will (...) argue that they do not say enough, but this is unfounded as in saying less there is often scope for more. Who knows perhaps academe will experiment with this mode of writing more frequently?For the sake of a sense of direction, I will borrow Russell Nieli's title to his thoughtful book on Wittgenstein's philosophy, From Mysticism to Ordinary Language, 1 to characterize the procedure of these aphorisms. Thus my initial aphorisms begin with music as a thing-in-itself, a striving toward a Kantian noumenon 2 and move toward the everyday practical concerns of music education. There are no determinate limits to a philosophy of music; unfortunately, this is also true of confusion. The following aphorisms (while hardly exhaustive of any possible gamut of music philosophy) strive to demystify some of the more common aesthetic quandaries and hopefully provide an opportunity for a wider field of discussion in music philosophy and education. [End Page 112] Music: External and Internal Inferences Sound and silence as potentiation of music precedes human existence.If music precedes existence then it can never be defined in absolute terms of thought. It remains thus even if nothingness were an all-pervasive, encompassing silence (that is, the silence of music or music as silence). 3 Silence as music in our culture may be perceived to be music by some and not necessarily by all cultures. As the sound and silence that preceded our being, it is indeed music in everlasting potentiation.In this sense sound can only be philosophically inferred as the "other," outside music, which the pre-Socratic philosophers referred to mystically and metaphorically as "the music of the spheres"; it is that music outside of us and finds its origins in sounds indirectly related to us. 4 It is what I prefer to call the Sound and Silence that define and are defined by each other in their potentiation for music. Thus this sound is music as potential or dynamis if intended to be music and perceived as such. It is also the possible music or sounds of the environment and non-humans such as whales, elephants, and monkeys. But the latter is our perception of their "music" and not necessarily their own appropriation. In the former we can use or intend the sounds of the environment to be music if these are perceived as such by at least one other person.Thus all sound is music in potentiation.The notion of a possible pre-existence of music, as stated in the first aphorism, is then defined by music as both a source and external entity.As an external inference (that is, the possibility of such) music does not communicate with us; rather, we utilize it through our own means and culture to communicate by it indirectly. It becomes our social construct and thus not an absolute notion.This source of music can be verified as it is implicit in our respective societies and world cultures.A music which possibly or inferentially precedes existence is, of necessity, part of that possible catalyst of sound waves identified by modern-day physics by which the universe may have been formed. For this reason, such notions usually appropriated by world mythologies have made it possible to worship music, perceive it as a supernatural force, or even view it is a possible cause in the big bang theory. 5Music is embodied in experience in that it is appropriated by members of extant cultures for its own particular use. We can speak of music from within our personal experiences of it. But this can only be appropriated or understood properly by others when our description of it accords with that cultural... (shrink)

У добу радикальної цивілізаційної трансформації суспільства та досягнення ним нового рівня складності, загострюється проблема віднаходження ресурсів свободи та свободи вибору людини. Обмеженість природних ресурсів спонукає людину віднаходити внутрішні, рефлексивні, інтелектуально-духовні ресурси виживання та свободи самореалізації, що дає можливість у перспективі перейти, крім іншого, до екологічної рівноваги між природою та суспільством та запобігти кліматичному колапсу людства. Цивілізаційний розвиток розширює горизонт свободи людини і, водночас, ставить її перед проблемою ресурсного забезпечення для реалізації нових можливостей свободи, одним із важливих ресурсів якої є рефлексія. (...) Здатність людини до рефлексії не є чимось, що притаманно виключно ефемерній суб’єктивності, а виявляється продовженням певних глибинних закономірностей буття, що виражаються, зокрема, у рекурсивній функції, а також у самореференції природних і соціальних процесів. Відрефлексовування людиною власного стану в аспекті свободи або несвободи є важливим чинником, що спонукає її як до самовдосконалення, так і до втілення якісно нових суспільних відносин, за яких її власна вільна самореалізація є і умовою і наслідком вільної самореалізації осіб, з якими вона взаємодіє. Напрацювання такого соціального капіталу та формування відповідних соціальних відносин є соціальною й організаційною передумовою прориву до інноваційних технологій та відновлювальної енергетики. Досягнути такого рівня вільного цивілізованого стану суспільство може лише пройшовши через «вузький коридор» (Д. Аджемоглу та Дж. Робінсон) цілеспрямованого створення відповідних соціальних інститутів і формування легітимної держави та відповідального громадянського суспільства, що відкриває можливість свободи самореалізації людини. У результаті триваючої наразі цивілізаційної трансформації має виникнути суспільство з високою синергією (А. Маслоу), важливим ресурсом якого повинно стати рефлексія другого порядку, цілеспрямоване самоуправління рефлексивними процесами, що забезпечують соціальну самоорганізацію на основі загальнолюдських цінностей. (shrink)

B. Kooi and A. Tamminga present a correspondence analysis for extensions of G. Priest’s logic of paradox. Each unary or binary extension is characterizable by a special operator and analyzable via a sound and complete natural deduction system. The present paper develops a sound and complete proof searching technique for the binary extensions of the logic of paradox.

In this paper, we present sound and complete natural deduction systems for Fitting’s four-valued generalizations of Kleene’s three-valued regular logics.

Successful reform of the higher education system in the context of COVID-19, both in a single country and in the world in the context of its development toward democratization, requires updated approaches to assessing the results of socialization of various categories of young people, and especially students. Since student age is a period of active formation of the inner need of a person to correlate his own aspirations with the interests of society, it is sensitive for the assimilation of social (...) experience, socially significant activities, and the formation of an active creative personality. Higher education in the context of COVID-19 faces an important task - to ensure the education of "vital and socially competent person who can make independent choices and make responsible decisions in various life situations" the formation of their own motives and interests. It is important how much the student as a subject of socialization, independent in the information space, what is the level of his social competence, how quickly he chooses the field of activity in which he can achieve high professionalism. The article deals with the problem of socialization of student youth in modern conditions of a higher educational institution, associated with the processes of development and education of the individual. The features, stages and socio-pedagogical conditions of successful socialization of students in the context of COVID-19 are revealed. (shrink)

Shakya Chokden's approach consists of reducing all phenomena to mind and its appearances, and then negating dualistic minds as illusory and nonexistent and establishing the non-dual jñāna transcending them as the only phenomenon existent in reality—the primordial tathāgatagarbha with all buddha-qualities complete. For him, this interpretation of tathāgatagarbha is indispensable for tantric contemplative practice and for explaining how and why that practice works. The initial identification of tathāgatagarbha as the primordially existent jñāna endowed with buddhaqualities serves as the foundation for (...) conceptually envisioning deities of the ultimate body-maṇḍala and eventually, when enough clarity is achieved, directly perceiving them by jñāna itself. Further cultivation of that self-cognizing jñāna displaying Cakrasaṃvara maṇḍala takes the practitioner through the stages of the tantric path to the eventual achievement of buddhahood qualified by the full manifestation and vision of buddha-qualities from within and by jñāna. (shrink)

Важливою характеристикою самоорганізаційної еволюції складних систем, починаючи від неорганічних, продовжуючи до органічних і завершуючи соціальними, є зростання потенціалу свободи. Ця динаміка розвитку, що набирає прискорення, продовжується в еволюції соціальних систем. Найбільш помітною названа динаміка стає у біфуркаційних періодах соціальних трансформацій. Два таких трансформаційних переходів суспільства відбулися у доцивілізаційний час. Це Когнітивна революція та Неолітична (аграрна) революція (Ю. Н. Харарі). Два інші радикальні трансформації соціуму відбулися вже після виникнення цивілізацій, які можна назвати цивілізаційними трансформаціями. Це «осьовий час» та Індустріальна революція. Аграрна (...) революція та Індустріальна революція створили матеріально-технологічні умови суттєвого нарощування свободи людини у зовнішніх її проявах. Аграрна революція сприяла виробленню достатньої кількості харчу для зростаючого населення та створенню цивілізованих форм життя. Індустріальна революція створила матеріальні засоби для достатнього життєзабезпечення та розвитку людини, збільшення ресурсу вільного часу й створення умов для свободи творчості. Індустріальна революція стала можливою у передових країнах світу, які спромоглися забезпечити низку соціально-організаційних інновацій. Н. Фергюсон такими інноваціями вважає конкуренцію, науку, власність, медицину, споживання, працю. Решта світу швидше засвоює технологічні результати та переваги більш прогресивного способу життя, однак дещо повільніше оволодіває людськими якостями та відповідними інноваційними суспільними відносинами, необхідними для створення зазначених людиновимірних досягнень цивілізації. С. Пінкер засвідчує, що решта світу у найважливіших соціальних і економічних показниках наздоганяє високоцивілізовані країни у темпах значно вищих, ніж останні розвивалися у період від початку Індустріальної революції, створюючи умови для подальшої вільної самореалізації людини. Когнітивна революція та, особливо, «осьовий час» створили рефлексивний духовно-культурний інструментарій для розширення горизонтів свободи людини на внутрішньому її плані – у сфері свідомості. Наразі у світі на глобальному рівні відбувається цивілізаційна трансформація, що співвимірна із зазначеними вище. Ця трансформація відбувається як на зовнішньому плані – у сфері технологій, так і у внутрішньому – у сфері свідомості. Останнє полягає у формуванні інституціоналізованої рефлексії другого порядку – цілеспрямованим управлінням рефлексивними процесами, нарощуванням їх ієрархічної складності та підвищенням їх ефективності. (shrink)

У ХХІ столітті, з розвитком інформаційного суспільства, невпинно зростають роль і значення свободи активної творчої особистості і відповідних рівноправних мережевих відносин, що вільно самоорганізуються. Передумовою ініціативної самоорганізації соціальної мережі є наявність у її компетентних учасників розуміння сутності суспільних процесів та смислів поточної ситуації у соціумі, а також вироблення навичок практично-організаційної діяльності. Усе це стає можливим завдяки здатності дійових осіб до соціальної рефлексії. Інтенсивна соціальна рефлексія суттєво прискорює самоорганізацію легальних соціальних мереж та породжує своєрідний мережевий катарсис, завдяки якому в учасників мережі (...) виникає відчуття солідарності та впевненості в легітимності власних дій. Телекомунікаційні інформаційні мережі Інтернет, що надбудовуються над соціальними мережами, прискорюють самоорганізацію та поліпшують якість останніх, впорядковують соціальну рефлексію, консолідують відповідні сегменти колективної мережевої свідомості, що робить учасників мережі впливовими соціальними суб’єктами. Кваліфіковане використання соціальної рефлексії в мережевих сегментах суспільства сприяють їх більшій конкурентоспроможності в сучасному світі. (shrink)

Формування рефлексії як схеми мислення та тригера практичної дії у стародавньому світі було важливим чинником виникнення феномена «вісьового часу» (К.Ясперс). У цей період виникли мораль як рефлексія та регулятор вольової діяльності, логіка як рефлексивне відслідковування істинності руху думки, демократія як рефлексивне взаємовизнання громадянами гідності один одного, монотеїстичні релігії (юдаїзм, брахманізм, веданта, християнство, деякі школи будизму), а також класична філософія. Рефлексія як компонент самосвідомості стала важливим механізмом самоорганізації ідентичності, починаючи з вісьового часу. Сократ виявив необхідність рефлексивного усвідомлення відмінності загального від одиничного (...) у процесі мислення та сприяв усвідомленню моралі як форми суспільної свідомості. Платон сформулював ідею мислення як бесіди душі із самою собою та рефлексивного осмисленного переходу від однієї ідеї до іншої у процесі мислення. Аристотель з’ясував, що відчуття, сприйняття, уява супроводжуються своєрідним сприйняттям-мисленням (усвідомленням, рефлексією), але останнє є вищим за природою, ніж перші, та, на противагу цьому, розум мислить божественне, що є однією природою з ним, і є мисленням мислення. (shrink)

У статті реконструйовано заключний етап українсько-польської війни 1918-1919 рр., зокрема травневий 1919 р. загальний наступ польського війська в Галичині. Визначено геополітичні передумови, перебіг та наслідки Чортківської операції Галицької армії в червні 1919 р., які спричинили тимчасовий перелом у ході українсько-польської війни. І хоча ця операція не закінчилася повним успіхом - визволенням Львова та території ЗУНР, однак засвідчила високий морально-бойовий дух і боєздатність особового складу Галицької армії, змусивши країни Антанти повернутися до серйозного обговорення проблеми державно-політичного статусу ЗУНР, нових східних кордонів Польщі.

This paper considers normative dimensions of the memory of Ukrainians and the problem related to the post soviet model of memory in Ukrainian society. The author emphasizes the social and cultural determinants of the process of formation and development of soviet model of memory, its conceptualization in the Soviet and Post soviet world. The analysis is centered on the clash of European and post soviet discourses in the context of the conflict of identities. The paper raises some general problems regarding (...) these discourses as well as the development of values within the antonymic memory frames in the context of its belonging to certain socio-cultural traditions, its compatibility with the dimensions of morality, the observance of Low, social responsibility, solidarity and openness too changes. Sintering the different approaches to the values, experience of formation and evolution social institutions, it also explores the role of Central European changes in the process of memory reconstruction in Ukraine. The paper considers cultural and law foundations of social reconstruction and problems related to historical foundation of different grope and communities. The article emphasizes that the lack of legal consciousness, disrespect for the law, the spread of rooted traditions of revolutionary purposefulness and the post soviet stile telephone justice are the serious obstacle for changes of post soviet frame and changes within European Union. In this context the aim of social groups is oriented to their historical memory transformation as well as the development of common European experience, symbolic and values heritage. At the same time the role of civil society as European foundation for historical changes is analyzed. (shrink)

In recent years, the study of this problem has received considerable attention in both Ukrainian and Polish historiography, which is connected, on the one hand, with the deportation of Ukrainians from Poland and Poles from Ukraine, and, on the other, with the loss of confessional presence, including property., these two denominations in Western Ukraine in 1944-1946. Both the first and the second are related to the policy of the State power of the Stalin regime. The echo of these events reminded (...) itself in the late 1980s - in the first half of the 1990s - of the apogee years of interfaith confrontation in Ukraine and still echoes today, activating these 60-year-old events. Therefore, given the Ukrainian and Polish historiography of the study, it is appropriate to cover this issue in more detail. This is the relevance of our article. In this context, the author used sources already available in our time in the archives of Lviv, Ternopil, and Ivano-Frankivsk regions, which have not yet been fully explored by researchers. This made it possible to reproduce the confessional transformations of the Roman Catholic Church and the Armenian Catholic Church in a broader and more detailed way and to show the impact on this process of state power, which was the purpose of the study. (shrink)

The article deals with the main reasons, processes and consequences of minimization of Roman Catholic network in Lviv, Ternopil and Stanislav regions in consequence of state policy in the area of religion in late Stalinism and Khrushchev periods.

The article examines the essence and relationship of aesthetic experience and aesthetic judgment. It is argued that philosophical aesthetics deals with constants that are fundamental to aesthetic experience. Such constants are phenomena and characteristics that have a fundamental ontological status in the aesthetic sphere. It was found that the ontological characteristic of aesthetic experience is that it is not reducible to “pure” rationality, that is, it is not something that is “adapted” to complete and final comprehension by the mind alone. (...) Therefore, a complete “absorption” of aesthetic experience by a certain semantic structure is impossible: such experience always goes beyond any discursive boundaries and simultaneously opens them. In addition, aesthetic experience serves as one of the means of a person’s “contact” with the world and society. Forming on the material of sensations, aesthetic experience extends from the most general ideas about the universe to the inner life of a person. The analysis also showed that the formulation of an aesthetic judgment is based on the concepts of the perfect and the imperfect. In turn, the mastery of such concepts is carried out in the process of correlating a certain aesthetic fact with the existing value scale. That is why aesthetic judgments have signs of normativity. They also create the basis for a common worldview and attitude, lay the foundation for mutual understanding between people of a certain culture. The study showed that the process of aesthetic assessment is a constant correlation of the existing state of affairs with something ideal, this is a permanent “demand” for perfection, as well as a tireless search for an opportunity to fulfill this “demand”. At the same time, ethical experience is dissociated from “pure” pragmatics, which personifies vital necessity, because the aesthetic sphere is always associated with a certain “redundancy” in human existence. Also, the results obtained in the course of the study suggested that philosophical aesthetics, which takes into account and investigates the specificity of the phenomenon of corporeality, as well as such phenomena of human existence as affective sensitivity and sensitive rationality, is able to overcome the limitation of “an-esthetic” naturalism in aesthetics. (shrink)

In the paper, we apply Kooi and Tamminga’s correspondence analysis to some conventional and functionally incomplete fragments of classical propositional logic. In particular, the paper deals with the implication, disjunction, and negation fragments. Additionally, we consider an application of correspondence analysis to some connectiveless fragment with certain basic properties of the logical consequence relation only. As a result of the application, one obtains a sound and complete natural deduction system for any binary extension of each fragment in question. With the (...) focus on exclusive disjunction we comparatively study the proposed systems. Finally, we discuss Segerberg’s systems for connectiveless and negation fragments and compare them with our systems. (shrink)

ABSTRACTThe paper deals with a problem posed by Mathieu Vidal to provide a formal representation for defective conditional in mathematics Vidal, M. [. The defective conditional in mathematics. Journal of Applied Non-Classical Logics, 24, 169–179]. The key feature of defective conditional is that its truth-value is indeterminate if its antecedent is false. In particular, we are interested in two explanations given by Vidal with the use of trivalent logics. By analysing a simple argument from plane geometry, where defective conditional is (...) in use, he gives two trivalent formal explanations for it. For both explanations, Vidal rigorously shows that trivalent logics cannot adequately represent defective conditional. Preserving Vidal's criteria of defective conditional ad max, we indicate some arguable points in his explanations and present an alternative explanation containing the original conjunction and disjunction in order to show that there are trivalent logics that might be an adequate formal explanation for defective conditional. (shrink)

Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP -language) by the addition of unary and binary connectives. Tamminga has also applied this technique to the paracomplete (...) analogue of LP, strong Kleene logic \. In this paper, we generalize these results for the negative fragments of LP and \, respectively. Thus, the method of correspondence analysis works for the logics which have the same negations as LP or \, but either have different conjunctions or disjunctions or even don’t have them as well at all. Besides, we show that correspondence analyses for the negative fragments of \ and LP, respectively, are also suitable without any changes for the negative fragments of Heyting’s logic \ and its dual \ and LP). (shrink)

Досліджуються методологічні можливості історії понять та її зв'язок з історією філософських понять і дискурс-аналізом філософських текстів. Окреслюються їхні функції у процесі культурної предикації. Наголошується на їхньому значенні при забезпеченні адекватного перекладу з мови історичної на мову актуальної культури.

The paper’s novelty is in combining two comparatively new fields of research: non-transitive logic and the proof method of correspondence analysis. To be more detailed, in this paper the latter is adapted to Weir’s non-transitive trivalent logic \({\mathbf{NC}}_{\mathbf{3}}\). As a result, for each binary extension of \({\mathbf{NC}}_{\mathbf{3}}\), we present a sound and complete Lemmon-style natural deduction system. Last, but not least, we stress the fact that Avron and his co-authors’ general method of obtaining _n_-sequent proof systems for any _n_-valent logic (...) with deterministic or non-deterministic matrices is not applicable to \({\mathbf{NC}}_{\mathbf{3}}\) and its binary extensions. (shrink)

We consider a logic which is semantically dual (in some precise sense of the term) to intuitionistic. This logic can be labeled as “falsification logic”: it embodies the Popperian methodology of scientific discovery. Whereas intuitionistic logic deals with constructive truth and non-constructive falsity, and Nelson's logic takes both truth and falsity as constructive notions, in the falsification logic truth is essentially non-constructive as opposed to falsity that is conceived constructively. We also briefly clarify the relationships of our falsification logic to (...) some other logical systems. (shrink)

In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets of (...) higher-order values. This method is based on the concept of a multilattice. If the method is applied to the set of truth values of Belnap's “useful four-valued logic”, one obtains a trilattice, and, more generally, structures here called Belnap-trilattices. As in Priest's case, it is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic. Whereas Priest's construction in terms of designated truth values always results in his Logic of Paradox, the present construction in terms of truth and falsity orderings always results in First Degree Entailment. However, it is observed that applying the multilattice-approach to Priest's initial set of truth values leads to an interesting algebraic structure of a “bi-and-a-half” lattice which determines seven-valued logics different from Priest's Logic of Paradox. (shrink)

In this paper, we introduce the notion of dual Post’s negation and an infinite class of Dual Post’s finitely-valued logics which differ from Post’s ones with respect to the definitions of negation and the sets of designated truth values. We present adequate natural deduction systems for all Post’s k-valued ) logics as well as for all Dual Post’s k-valued logics.

На основі синергетичної методології (І.Пригожин, Г.Хакен та ін.) в останню третину ХХ століття формується концепція соціальної самоорганізації, якій спочатку певною мірою був притаманний фізикалістський підхід до розуміння суспільства. На початку ХХІ століття концепція самоорганізації соціуму стає все більш людиномірною (Е.Гіденс, Н.Луман, К.Фухс, Ф.Хейліген, Ф.Шлем та ін.). Людина своєю діяльністю та комунікацією з іншими людьми продукує соціальну структуру, а остання, своєю чергою, спрямовує людську діяльність. Внаслідок цього соціальна система стає самовідтворюваною соціальною системою, а ця самовідтворюваність ґрунтується на творчій діяльності людської істоти. (...) Самоорганізація суспільства у ХХІ столітті є багатовимірною та багаторівневою. Основою самоорганізації суспільства знизу є протестні рухи, основою самоорганізації яких є самоорганізація кіберпротесту, а основою самоорганізації останнього є самоорганізація комунікації в інтернеті; остання базується на самоорганізації відповідного самоменеджменту знання і т.п. (К.Фухс). Новий підхід до ідеї самоорганізації суспільства є дуже перспективним і потребує ретельного дослідження. (shrink)

The complex of modern sociological and religious studies approaches to the analysis of religious practices in post-sectarian societies makes it possible, among other things, to characterize their biographical aspects. First of all, it is about the ways and means of displaying the "Man of Faith" in the various reference journals, which are traditionally widely represented in secular literature, and have recently become increasingly popular among denominational publications and resources. The latter promotes both the "mature" of the domestic theological centers and (...) the more open intensive work of religious organizations. But the landmark change, which radically changed the state of affairs, setting new trends and putting forward fundamentally different goals, was the emergence of new information technologies and their adaptation and use to accumulate and disseminate information about beliefs and their leaders. The most important feature of these newest electronic resources in comparison with the traditional is their potential ability to objectively integrate the information accumulated previously by society in all its diversity, to organically absorb the inheritance of the manuscript and print culture of the past. (shrink)

ABSTRACTIn this paper, we consider non-associative generalisations of Hájek's logics BL and psBL. As it was shown by Cignoli, Esteva, Godo, and Torrens, the former is the logic of continuous t-norms and their residua. Botur introduced logic naBL which is the logic of non-associative continuous t-norms and their residua. Thus, naBL can be viewed as a non-associative generalisation of BL. However, Botur has not presented axiomatization of naBL. We fill this gap by constructing an adequate Hilbert-style calculus for naBL. Although, (...) as was shown by Flondor, Georgescu, and Iorgulescu, there are no non-commutative continuous t-norms, Hájek's psBL can be viewed as BL's non-commutative generalisation. We present the logic psnaBL of psnaBL-algebras which can be viewed as naBL's non-commutative generalisation as well as psBL's non-associative generalisation and BL's both non-commutative and non-associative generalisation. (shrink)

In this paper, we introduce provability multilattice logic PMLn and multilattice arithmetic MPAn which extends first-order multilattice logic with equality by multilattice versions of Peano axioms. We show that PMLn has the provability interpretation with respect to MPAn and prove the arithmetic completeness theorem for it. We formulate PMLn in the form of a nested sequent calculus and show that cut is admissible in it. We introduce the notion of a provability multilattice and develop algebraic semantics for PMLn on its (...) basis, by the method of Lindenbaum-Tarski algebras we prove the algebraic completeness theorem. We present Kripke semantics for PMLn and establish the Kripke completeness theorem via syntactical and semantic embeddings from PMLn into GL and vice versa. Last but not least, the decidability of PMLn is shown. (shrink)

In this paper, we introduce a new four-valued logic which may be viewed as a variation on the theme of Kubyshkina and Zaitsev's Logic of Rational Agent textbf{LRA} cite{LRA}. We call our logic $ bf LIRA$. In contrast to textbf{LRA}, it has three designated values instead of one and a different interpretation of truth values, the same as in Zaitsev and Shramko's bi-facial truth logic cite{ZS}. This logic may be useful in a situation when according to an agent's point of (...) view her/his reasoning is rational, while from the external one it might be not the case. One may use textbf{LIRA}, if one wants to reconstruct an agent's way of thinking, compare it with respect to the real state of affairs, and understand why an agent thought in this or that way. Moreover, we discuss Kubyshkina and Zaitsev's necessity and possibility operators for textbf{LRA} definable by means of four-valued Kripke-style semantics and show that, due to two negations of textbf{LRA}, two more possibility operators for textbf{LRA} can be defined. Then we slightly modify all these modalities to be appropriate for $bf LIRA$. Finally, we formalize all the truth-functional $ n $-ary extensions of the negation fragment of $bf LIRA$ as well as their basic modal extension via linear-type natural deduction systems. (shrink)

The study of the problem in Ukrainian historiography, both in particular aspects of activity and in the analytical synthesis of all areas of late Protestantism, has been given wide attention. Instead, the author, while supplementing and deepening the historiography of the study, sheds light on the source data of the state archives of the Lviv, Ternopil, and Ivano-Frankivsk regions and draws upon these sources in more detail the activities of late Protestantism religious communities in Western Ukraine during the Stalinist period. (...) This enabled him not only to follow the transformational processes caused by the factors of state pressure on late Protestantism, to find out the phenomena of the inner life of the communities of the ECHB, the HVE and the ASD, but also to compare the current situation of these denominations to the years under study. Reproduction of the external and internal processes of Protestant denominations and the influence of state power on them is the goal of our study. (shrink)

Jaroslav Stotskyi. Methodological peculiarities of study of polyvector history of parishes, monasteries and eparchies of Ukrainian Greek Catholic Church. The article reveals investigation methodology of history of eparchy main activity constituents, namely history of establishment, development, integral parts of eparchy transformations – parishes, monasteries, parish communities, brotherhoods, catechetic processes, monastery religious and social institutions etc.

The paper is the Part IV of the large research, dedicated to both revision of the system of basic logical categories and generalization of modern predicate logic to functional logic. The topic of the paper is consideration of graphs of functions and relations as a derivative and definable category of ultra-Fregean logistics. There are two types of function specification: an operational specification, in which a function is first applied to arguments and then the value of the function is entered as (...) the result of such application, and a grammar specification, in which an object is first entered and then represented as a value of the function on the given arguments. Since function specifications are relations themselves (which was shown in the previous article of the series), this means that each function forms two relations: the obverse (for an operational specification) and the reverse one (for a grammatical specification). Hence, the definitions introduce two types of graphs: the obverse graph of a function, or a graph of the obverse relation formed by this function, is a set of sequences of such objects, the last of which is a value of this function on the sequence of other of these objects as arguments of the same function. Similarly, the reverse graph of a function, or the graph of the reverse relation formed by this function, is called a set of sequences of such objects, the first of which is the value of this function on the sequence of other of these objects as arguments of the same function. In the limiting case of 0-ary functions, both graphs of any such function coincide. Gottlob Frege discovered obverse graphs of functions and called them function value-ranges. He fundamentally emphasized the non-identity of functions and their graphs. Unfortunately, in set theory under the influence of Giuseppe Peano, an alternative approach was adopted, according to which functions and relations are identical to their graphs and, ultimately, to each other. We show that this approach leads to two unacceptable and, at the same time, mutually contradictory conclusions, and must therefore be rejected. (shrink)

In this book, Yaroslav Komarovski argues that the Tibetan Buddhist interpretations of the realization of ultimate reality both contribute to and challenge contemporary interpretations of unmediated mystical experience. The model used by the majority of Tibetan Buddhist thinkers states that the realization of ultimate reality, while unmediated during its actual occurrence, is necessarily filtered and mediated by the conditioning contemplative processes leading to it, and Komarovski argues that therefore, in order to understand this mystical experience, one must focus on (...) these processes, rather than on the experience itself. Komarovski also provides an in-depth comparison of seminal Tibetan Geluk thinker Tsongkhapa and his major Sakya critic Gorampa's accounts of the realization of ultimate reality, demonstrating that the differences between these two interpretations lie primarily in their conflicting descriptions of the compatible conditioning processes that lead to this realization. Komarovski maintains that Tsongkhapa and Gorampa's views are virtually irreconcilable, but demonstrates that the differing processes outlined by these two thinkers are equally effective in terms of actually attaining the realization of ultimate reality. Tibetan Buddhism and Mystical Experience speaks to the plurality of mystical experience, perhaps even suggesting that the diversity of mystical experience is one of its primary features. (shrink)

In Luminous Emptiness, Yaroslav Komarovski offers an annotated translation of three seminal works on the nature and relationship of Yogacara and Madhyamaka, by Serdok Penchen Shakya Chokden.

The review is devoted to an analysis of Nazip Khamitov’s new book “War in Ukraine and the New Humanism: David versus Goliath. Metaanthropology of history of the 21st century”, which was published in Bulgaria.

After Stalin's death, the struggle for power took place in the top of the CPSU, and in the lower echelons they took a standstill, so in 1953, in the reports of the ROC Commissioner and the Commissioner of Religious Cults, he was formally restrained.

The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...) a trilattice of truth values – a specific algebraic structure with information ordering and two distinct logical orderings, one for truth and another for falsity. Each logical order not only induces its own logical vocabulary, but determines also its own entailment relation. We consider both semantic and syntactic ways of formalizing these relations and construct various logical calculi. (shrink)