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)

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)

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.

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)

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 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)

An aesthetic distinction between good music and the good in music is crucial for a philosophy of music education. Ultimately, it is not the music's fault, as it were, that someone may view it as being 'not good' in either a social or aesthetic context. Regardless of how music is colored it remains an entity unto itself and thus untouched by our pronouncements. Wittgenstein's Philosophical Investigations recognized the falseness of such propositions as biased pronouncements taking the form of bad 'x' (...) or good 'x.' Thus we may seek the good within the music if we know how to define what we mean by that. This approach allows music to be conceptualized and framed in a meaningful educational context. In such a way Plato and Aristotle attempted a conceptualization of the 'good' and the 'ungood' in the music of their time, as did Adorno in the preceding century. Although this context still does not allow pronouncements of music as good or bad, it does allow a seeking of its educational utility and unlimited potentiality in the name of an aesthetic and moral understanding. (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)

The paper is Part III of the large research, dedicated to both the revision of the system of basic logical categories and the generalization of modern predicate logic to functional logic. We determinate and contrapose modern Fregean logistics and proposed by the author ultra-Fregean logistics, next we describe values and arguments of functions, arguments of relations, relations themselves, sets (classes), and subsets (subclasses) as derivative categories (concepts) of ultrafregean logistics. Logistics is a part of metalogic, independent of semantics. Fregean logictics (...) is a metalogical theory, based on the quadruple <particular (individual), predicate, equality, sequence>; it generates predicate logic. Ultrafregean logictics is based on the quadruple <particular, function, representation, sequence>, where the notion of a function is a generalization of the notion of a predicate and the notion of representation is a generalization of the notion of equality; this logictics generates functional logic. For the completely correct denotation of the functional values, we need the Churchian symbolics with parenthesis. Predicates are usually identified with relations. A relation is the derived and even definable category of ultra-Fregean logictics. Namely, relations are representations by functions (of one of their arguments). We show that Frege could really establish this definition and the notion (category) of representation but, unfortunately, rejected this course of thought. Next, we show that every n-ary relation can be resolved for some of its arguments via some (n-1)-ary function. A set, or class, is a derived and not definable category of ultra-Fregean logistics. The universal way to introduce the sets is Frege’s abstraction principle. We formulate this principle for functional logic and show that the notion of a set is quantified, so there is the dual existential notion of a nonempty subset, involved by the same abstraction principle. (shrink)

To some extent, the current Russian-Ukrainian may be described as a conflict between two visions of nation, respectively, ethnic and civic models. Putin believes that a language defines a nation. In his understanding, since many Ukrainians are Russian speakers, they are Russians. His perception of Ukraine is anachronistic. He has failed to notice Ukraine's radical transformation since it gained independence. The current Ukrainian identity has a strong civic component. Its core is represented by a new urban middle class with a (...) new set of values. Sustainability of this identity largely depends on longevity and results of the war. (shrink)

The famous “slingshot argument” developed by Church, Gödel, Quine and Davidson is often considered to be a formally strict proof of the Fregean conception that all true sentences, as well as all false ones, have one and the same denotation, namely their corresponding truth value: the true or the false . In this paper we examine the analysis of the slingshot argument by means of a non-Fregean logic undertaken recently by A.Wóitowicz and put to the test her claim that the (...) slingshot argument is in fact circular and presupposes what it intends to prove. We show that this claim is untenable. Nevertheless, the language of non-Fregean logic can serve as a useful tool for representing the slingshot argument, and several versions of the slingshot argument in non-Fregean logics are presented. In particular, a new version of the slingshot argument is presented, which can be circumvented neither by an appeal to a Russellian theory of definite descriptions nor by resorting to an analogous “Russellian” theory of λ–terms. (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)

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)

I would like to start my paper with the following statement of Barry Smith: “Relevance logic has become ontologically fertile.”.

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)

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

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)

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)

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

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)

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)

In this article the questions under discussion are the properties of Descartes’s application of the first rule of his method, which requires not to agree with anything that could give rise to doubt. It is well known that Descartes came to the conclusion that only the truth “I think, therefore I am” is undoubted. The article examines the logical status of this truth and reveals that it is an entimeme where the major premise is unstated. An analysis of Descartes’s works (...) shows that the premise that he does not explicitly express is the proposition “If I think, therefore I exist, and if I do not think, then I do not exist.” It follows that Descartes’ complete syllogism would be like this: “I exist if and only if I think; I think; therefore, I exist.” In this paper, the discussion focuses on the proof of the certainty of the position “I exist,” proposed by St Augustin in his treatise The City of God. St Augustin proves the proposition “I am deceived that I exist” to be false in every possible interpretation. Hence the position “I exist” is true in every possible interpretation. According to Descartes, the only undoubted statements are those that are kept within the limits of “I think,” or within the limits of inner experience, while the data of external experience are always dubious. Thus, the statement “I walk” is not obvious, since it can only seem to me that I am walking. At the same time, the judgment “It seems to me that I walk” is undoubtedly. Ancient sceptics also believed that the data of internal experience are doubtless, and the data of external experience are not due to the fact that all objects of the external world are in fact not what they seem to be. However, there is a significant difference between the ancient sceptical approach and that of Descartes. I put forward the view that the ancient sceptics, although they are convinced that the things of the external world are not what they seem, still surely believe that each item in that world exists. But Descartes surpassed both ancient sceptics and academics in their scepticism, since he doubted the very existence of the external world. He was able to imagine that he exists exclusively as a thinking entity with no body, no world around him, and no space to store that world. It is by the fact that Descartes doubts the existence of the external world that he has cleared the way for transcendental philosophy and phenomenology. (shrink)

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.

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)

In this paper, we study logical systems which represent entailment relations of two kinds. We extend the approach of finding ‘exactly true’ and ‘non-falsity’ versions of four-valued logics that emerged in series of recent works [Pietz & Rivieccio (2013). Nothing but the truth. Journal of Philosophical Logic, 42(1), 125–135; Shramko (2019). Dual-Belnap logic and anything but falsehood. Journal of Logics and their Applications, 6, 413–433; Shramko et al. (2017). First-degree entailment and its relatives. Studia Logica, 105(6), 1291–1317] to the case (...) of infectious logics, namely to the case of Deutsch's logic Sfde introduced in Deutsch [Relevant analytic entailment. The Relevance Logic Newsletter, 2(1), 26–44; The completeness of S. Studia Logica, 38(2), 137–147]. The particular systems obtained in this way are Setl and Snfl. We present them in the form of sequent calculi and prove corresponding soundness and completeness theorems. We illuminate the connection between Setl, Snfl and two well-known systems, strong Kleene three-valued logic K3 and Priest's Logic of Paradox LP. This connection allows us to investigate the characterisation of the entailment relations associated with Setl and Snfl as well as to introduce the notion of ‘infectious analogue’ of a certain logic. We also study implicative extensions of Setl and Snfl and prove soundness and completeness theorems for them as well. (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.

In this paper, we introduce the notions of connexive and bi-intuitionistic multilattices and develop on their base the algebraic semantics for Kamide, Shramko, and Wansing’s connexive and bi-intuitionistic multilattice logics which were previously known in the form of sequent calculi and Kripke semantics. We prove that these logics are sound and complete with respect to the presented algebraic structures.

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