This paper considers non-standard analysis and a recently introduced computational methodology based on the notion of ①. The latter approach was developed with the intention to allow one to work with infinities and infinitesimals numerically in a unique computational framework and in all the situations requiring these notions. Non-standard analysis is a classical purely symbolic technique that works with ultrafilters, external and internal sets, standard and non-standard numbers, etc. In its turn, the ①-based methodology does not use any of these (...) notions and proposes a more physical treatment of mathematical objects separating the objects from tools used to study them. It both offers a possibility to create new numerical methods using infinities and infinitesimals in floating-point computations and allows one to study certain mathematical objects dealing with infinity more accurately than it is done traditionally. In these notes, we explain that even though both methodologies deal with infinities and infinitesimals, they are independent and represent two different philosophies of Mathematics that are not in a conflict. It is proved that texts :539–555, 2017; Gutman and Kutateladze in Sib Math J 49:835–841, 2008; Kutateladze in J Appl Ind Math 5:73–75, 2011) asserting that the ①-based methodology is a part of non-standard analysis unfortunately contain several logical fallacies. Their attempt to show that the ①-based methodology can be formalized within non-standard analysis is similar to trying to show that constructivism can be reduced to the traditional Mathematics. (shrink)

Successful interactions between people are dependent on rapid recognition of social cues. We investigated whether head direction – a powerful social signal – is processed in the absence of conscious awareness. We used continuous flash interocular suppression to render stimuli invisible and compared the reaction time for face detection when faces were turned towards the viewer and turned slightly away. We found that faces turned towards the viewer break through suppression faster than faces that are turned away, regardless of eye (...) direction. Our results suggest that detection of a face with attention directed at the viewer occurs even in the absence of awareness of that face. While previous work has demonstrated that stimuli that signal threat are processed without awareness, our data suggest that the social relevance of a face, defined more broadly, is evaluated in the absence of awareness. (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)

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)

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)

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)

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 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)

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)

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.

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)

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)

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.

According to Suszko’s Thesis, there are but two logical values, true and false. In this paper, R. Suszko’s, G. Malinowski’s, and M. Tsuji’s analyses of logical twovaluedness are critically discussed. Another analysis is presented, which favors a notion of a logical system as encompassing possibly more than one consequence relation. [A] fundamental problem concerning many-valuedness is to know what it really is. [13, p. 281].

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)

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)

A modal extension of multilattice logic, called modal multilattice logic, is introduced as a Gentzen-type sequent calculus \. Theorems for embedding \ into a Gentzen-type sequent calculus S4C and vice versa are proved. The cut-elimination theorem for \ is shown. A Kripke semantics for \ is introduced, and the completeness theorem with respect to this semantics is proved. Moreover, the duality principle is proved as a characteristic property of \.

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 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)

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 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 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.

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 this paper, bi-intuitionistic multilattice logic, which is a combination of multilattice logic and the bi-intuitionistic logic also known as Heyting–Brouwer logic, is introduced as a Gentzen-type sequent calculus. A Kripke semantics is developed for this logic, and the completeness theorem with respect to this semantics is proved via theorems for embedding this logic into bi-intuitionistic logic. The logic proposed is an extension of first-degree entailment logic and can be regarded as a bi-intuitionistic variant of the original classical multilattice logic (...) determined by the algebraic structure of multilattices. Similar completeness and embedding results are also shown for another logic called bi-intuitionistic connexive multilattice logic, obtained by replacing the connectives of intuitionistic implication and co-implication with their connexive variants. (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)

The aggravation of the global environmental and military-political crisis has become evidence that the postmodern era has ended and the time has come for post-postmodern and profound civilizational transformation, the technological base of which is renewable energy and artificial intelligence; the main social environment is distributed capitalism (J. Rifkin) and social networks; and the main driving forces and mechanisms of social self-organization are humanity, competitiveness and double reflection (E. Giddens). Since humanity has not yet fully actualized the basic values of (...) survival and development and has not paid enough attention to the problem of climate catastrophe, more drastic measures to mitigate it will be implemented in the process of its deployment (A. Honnacker) and in the difficult conditions of military-political opposition to democracy and authoritarianism. One of the main rational worldview and practical guidelines of post-postmodernism is classical Pragmatism, which is based on human experience, an important element of which should be scientific knowledge, which is confirmed experimentally. Societies that are dominated by pragmatic and democratic egalitarian relations that promote human self-realization and creative freedom can channel natural aggressiveness into competition to improve the well-being of all its members. The ruling elite in totalitarian societies, in which man is humiliated and exploited, and in which aggressiveness accumulates due to polarization into upper and lower classes of the population, may start wars in order to prevent self-destruction from within, directing aggression outwards against other countries. Therefore, the global community in today's conditions needs to expand the worldview and orientation horizon of every citizen of the world from the everyday concerns of life support to the understanding and actualization of the absolute values of survival and development of humanity. Pragmatism, from a purely methodological point of view, is aimed at ensuring that a person is guided by life experience in his activity and cognition, putting forward certain hypotheses regarding his own activity and cognition, simultaneously and/or later experimentally testing these hypotheses on the basis of practical results. Thanks to the pragmatist approach, a person increasingly experiments with the choice of innovative behavior models and avoids predetermined outdated life guidelines and ideological grand narratives. Based on her own experience and online social communication with other people, he or she is convinced of the effectiveness of certain value models of behavior that have not only a socio-economic, but also a moral dimension. A pragmatist approach focused on global human values of survival and development is an important tool that should ensure urgent civilizational transformation and the avoidance of destructive environmental and military-political disasters. In the conditions of modern civilizational transformation, survival is possible only with a radical intensification of the development of human-centered social self-organization. (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)

Останніми роками у світі прискорюється процес заміщення старих технологій на сучасні, пов’язані насамперед з відновлювальною енергетикою та штучним інтелектом, що неминуче призведе до перевороту у суспільних відносинах та до кардинальних змін у ідентичності. Реструктуризація ідентичності веде і до зміни практичних орієнтацій суб’єктів, до переосмислення ними власного місця у світі та взаємовідносин з Іншими. За антропним принципом науки, поза іншим, будь-яка система за посередництвом самореферентних процесів прагне самоорганізуватися з метою самозбереження та передбачає існування Спостерігача. На рівні живих систем код ДНК забезпечує (...) природну ідентичність організму. У суспільному житті ідентичність забезпечує саморегуляцію взаємовідносин індивіда та Інших в контексті суспільного середовища. Протягом історії людства ідентичність ускладнюється та є чинником самоорганізації суспільних відносин. Поняття ідентичності починає формуватися ще з античного соціуму, починаючи з «вісьового часу» та виникнення рефлексивної моралі (Сократ, Аристотель, Конфуцій, Будда та ін.); продовжується цей процес і у філософії Нового часу та у класичній німецькій філософії у вигляді поняття рефлексивного духу, трансцендентальної аперцепції, рефлексивної самосвідомості; зазначені феномени розглядалися по суті справи як внутрішній живий механізм самоконструювання ідентичності (Р. Декарт, Т. Гобс, П. Гасенді, І. Кант, І. Фіхте, Г. Гегель). Ю. Габермас, спираючись на Л. Кольберга, Е. Еріксона, Ж. Піаже, пов’язав рівень розвитку ідентичності з рівнями та етапами розвиненості моральної свідомості. Мислителі та практикуючі філософи кінця ХХ – початку ХХІ століть (К. Вілбер, Ф. Лалу та ін.) в умовах сучасного технологічного та соціоорганізаційного вибуху виявляють та досліджують нові типи множинної гуманізованої ідентичності. (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)

Self-organization of modern society more and more reveals as self-organization of social networks. This become obvious thanks to the appearance of informational web of internet that finish building over social networks as such. Socialcommunicative practice of networks strengthens their self-organizing and selfregulative aspect of their activity. Social researchers create the theoretic ground that allows to analyze phenomenon of network. F. de Saussure investigated the language as a web of notions which exists in network of social-communicated ties. P. Blau and R. (...) Emerson realized that when actors interact and communicate they create the network of social ties. The idea of social networks influenced upon M. Castells, who assumes that structure of modern society penetrates by multitude of communicative ties and become more and more similar to the network.J.L. Moreno considered that in horizontal communication networks formed confidence, solidarity and social capital and mutual support of men. B. Kollanyi, Sz. Molnar and L. Szekely notice that in network society increases the role and significance of personal moral position of man, and growth of his social capital in result of equal communication and other reasons. The increased intensity of communication and reflection is a important factor of self-organization of social networks. (shrink)

Jaśkowski's discussive (discursive) logic D2 is historically one of the first paraconsistent logics, i.e., logics which 'tolerate' contradictions. Following Jaśkowski's idea to define his discussive logic by means of the modal logic S5 via special translation functions between discussive and modal languages, and supporting at the same time the tradition of paracomplete logics being the counterpart of paraconsistent ones, we present a paracomplete discussive logic D2p.

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)

The purpose of this article is to offer a specific perspective on Puritan philosophy. Most of the early American philosophy of the Puritans dealt with theological issues, the main topics of philosophical speculation were the ideas of God, salvation, freedom, and others. However, there were some ideas, the presence of which is an important factor, which until now has been little taken into account. This factor is the genuine interest of the Puritans in the natural sciences. Both in England and (...) in America, there were favorable conditions for the new natural philosophy proclaimed by Francis Bacon, this natural philosophy offered a new type of thought. The English philosopher struggled with obstacles in the way of research, one of which was infallible authority, for example, the authority of Aristotle. One of the most curious facts about the colonial life of American settlers is the construction of Harvard College, which from the first days, preserved and increased knowledge. Among the sciences taught was astronomy, which indicates the interest of the Puritans in the study of space. The most important change in the scientific worldview of the times of the first colonies in North America was the adoption of the heliocentric system of Nicolaus Copernicus to replace the geocentric system of Ptolemy, which had existed for many centuries. Among the first books printed in the colonies were mainly religious texts, but there were also scientific ones, for example, astronomical almanacs and catalogs appeared. The information in these books helped in observing the heavenly bodies, for which the first optical instruments, telescopes, were used. Several decades after the first settlers in Plymouth, the first telescope appeared in America thanks to John Winthrop Jr. Taken together, these facts show that in addition to religious reflections, American Puritan thinkers were also interested in cosmological problems. (shrink)

Засобами логіки комунікації історичних логік і методології історико-філософської міжкультурної комунікації аналізується культурна предикація як концепт історико-філософського дискурсу. Звертається увага на функціювання культурної предикації в контексті методологічної комунікації як інформаційної взаємодії конкуруючих методологій, їхніх інструментів і стратегій. Здійснюється конкретний аналіз ситуації застосування методологічної комунікації в межах історико-філософської комунікації як різновиду міжкультурної комунікації. В результаті методологічний і процесуальний дискурси історії філософії постають складниками специфічного історико-філософського комплексу.

Kooi and Tamminga's correspondence analysis is a technique for designing proof systems, mostly, natural deduction and sequent systems. In this paper it is used to generate sequent calculi with invertible rules, whose only branching rule is the rule of cut. The calculi pertain to classical propositional logic and any of its fragments that may be obtained from adding a set of rules characterizing a two-argument Boolean function to the negation fragment of classical propositional logic. The properties of soundness and completeness (...) of the calculi are demonstrated. The proof of completeness is conducted by Kalmár's method. Most of the presented sequent-calculus rules have been obtained automatically, by a rule-generating algorithm implemented in Python. Correctness of the algorithm is demonstrated. This automated approach allowed us to analyse thousands of possible rules' schemes, hundreds of rules corresponding to Boolean functions, and to nd dozens of those invertible. Interestingly, the analysis revealed that the presented proof-theoretic framework provides a syntactic characteristics of such an important semantic property as functional completeness. (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 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)

This article analyzes the historical development of the philosophical logic syntax from the standpoint of the unity of historical and logical methods. According to this perspective, there are three types of logical syntax: the elementary subject-predicate, the modified definitivespecificative, and the standard propositional-functional. These types are generalized in the grammatical and mathematical styles of logical syntax. The main attention is paid to two scientific revolutions in elementary subject-predicate syntax, which led to the emergence of modified definitive-specific and standard propositional-functional syntaxes (...) and created the syntactic conditions for the development of contemporary philosophical logic. The specifics of contemporary philosophical logic and the methodological possibilities of its application to philosophical discourse are studied. The article aims to reevaluate the undeservedly forgotten systems of philosophical logic of the continental tradition, created by such prominent representatives as Aristotle, G.W.F. Hegel, and E. Husserl, and to actualize these logics in the context of contemporary philosophical culture. The potential of the above-mentioned logics is not fully involved in the philosophical discourse of modernity, primarily because they primarily used an imperfect elementary subject-predicate syntax and modified definitive-specificative syntax as its slightly improved version. Both syntaxes have one thing in common: the grammatical style of sentence structure. Nevertheless, they also have one common flaw – a high dependence on grammar formalism. As a result, the interaction between these syntaxes and Frege’s standard propositional-functional syntax is impossible, because the latter is based on mathematical formalism, which operates on the philosophical logic of the analytic tradition. The article substantiates the way to solve this problem by constructing a modified subject-predicate syntax of contemporary philosophical logic. This syntax provides information interaction between Aristotle’s elementary subject-predicate syntax, and Frege’s standard propositional-functional syntax based on Hegel’s modified definitive-specificative syntax. The proposed solution to this problem can create new opportunities for complementarity and mutual enrichment between the philosophical logic of continental and analytical traditions. The theoretical basis for the construction and study of contemporary philosophical logic is a functional analysis of contemporary symbolic logic, which improves the grammatical analysis of traditional formal logic. Functional-grammatical analysis is a way to rehabilitate the philosophical logic of the continental tradition. The novelty of this paper lies in the substantiation of the modified subjectpredicate syntax of contemporary philosophical logic. It makes it possible to establish a dialogue between continental and analytical traditions, which is designed to promote the further development of philosophy. (shrink)

There are two implicit semantic postulates underlying modern predicate logic. Hence predicate logic is not semantically neutral. The author proposes to take semantically neutral languages, which have no predicate categorial structure but replace the notion of predicate with general notion of function. Some function calculi for different semantics are demonstrated.

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)

The article presents a historical and philosophical study of the main philosophical ideas of the American thinker of the Puritan era, John Cotton (1585–1652). The renowned thinker worked as a priest both in England and in the American colonies. He was known as an outstanding theologian and Puritan philosopher of the Massachusetts Bay Colony. The future philosopher received his education at Trinity College and Emmanuel College in Cambridge. His reputation was associated with his ability to preach and his knowledge of (...) theology, but his views also contained a place for philosophical reflections. He was a supporter of Puritan philosophy and was opposed to Catholicism, which was reflected in his works. In addition, he opposed the Anglican Church, which he considered insufficiently separated from Catholicism. However, in his philosophy of religion, there was a desire to purify faith from unnecessary burden. His ideas and views on religion made it possible to create the Puritan movement, which placed great emphasis on personal faith and rejected many customs and rituals that were considered unnecessary. On the one hand, J. Cotton was a critic of the church institution, but on the other hand, he did not support separation from it. He maintained a balance in his views and believed that the expulsion of his ideological opponent, Roger Williams, was related to the danger of his ideas. He believed that man cannot save himself and depends on God's grace. The American thinker took part in important polemical discussions in the American colonies, where his religious philosophy determined the settlers' way of life. He was a supporter of philosophical dialogue and believed that truth arises only in dialogue. (shrink)

The problem of relations between the Apostolic Capital and the Soviet state in the interwar period and the interstate Bolshevik authorities and the Ukrainian Greek Catholic Church in 1944-1945 has been widely and comprehensively covered in Ukrainian and foreign historiography. The author, in order to reproduce the two vectors of one problem in a holistic way, synthesized them into a single complex, setting up specific aspects: state – Church – relations. And when, in the 1920s and 1930s, the Soviet authorities (...) carried out a brutal struggle against religion, it is natural that the Apostolic See opposed this lawlessness. (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)

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)