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)

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)

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)

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.

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)

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.

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)

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)

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)

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)

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

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

The 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 urgency of the topic is due to the lack of research on the problem of the school curriculum with regard to the special elective course "Fundamentals of Christian ethics", its curriculum, the professionalism of teachers, the role of students in education, certain religious uniqueness in polyconfessional Ukraine, and comparison with religious studies in public, private or church schools of some Western European countries.

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)

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 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 development of recursion theory motivated Kleene to create regular three-valued logics. Remove it taking his inspiration from the computer science, Fitting later continued to investigate regular three-valued logics and defined them as monotonic ones. Afterwards, Komendantskaya proved that there are four regular three-valued logics and in the three-valued case the set of regular logics coincides with the set of monotonic logics. Next, Tomova showed that in the four-valued case regularity and monotonicity do not coincide. She counted that there are (...) 6400 four-valued regular logics, but only six of them are monotonic. The purpose of this paper is to create natural deduction systems for them. We also describe some functional properties of these logics. (shrink)

In the paper a theory of relevant properties is developed. The theory permits us to distinguish between properties that are relevant to an object and the properties that are irrelevant to it. Predication is meaningful only if a property is relevant to an object. On the base of introducing a special negative type of predication as opposed to usual sentential negation, a new notion of generalization for properties is defined. Context-free, as weIl as context-depended relevance of properties are considered.

In this paper I reject the normative interpretation of logic and give reasons for a realistic account based on the ontological treatment of logical values.

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)

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)

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 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)

The article deals with the Aristotelian doctrine of induction and its influence on the theory of induction of Al-Farabi. Inductive syllogisms of antiquity and the Middle Ages are compared with modern inferences by induction.

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 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)

I highlight the importance of the notion of falsity for a semantical consideration of intuitionistic logic. One can find two principal (and non-equivalent) versions of such a notion in the literature, namely, falsity as non-truth and falsity as truth of a negative proposition. I argue in favor of the first version as the genuine intuitionistic notion of falsity.

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

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

The 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 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.