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

In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic both with one (...) (A. Urquhart, G. Priest, A. Tamminga) and two designated values (G. Priest, B. Kooi, A. Tamminga). The purpose of this paper is to provide natural deduction systems for weak and intermediate regular logics both with one and two designated values. (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.

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)

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)

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

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

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

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)

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)

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)

The goal of this paper is to propose correspondence analysis as a technique for generating the so-called erotetic calculi which constitute the method of Socratic proofs by Andrzej Wiśniewski. As we explain in the paper, in order to successfully design an erotetic calculus one needs invertible sequent-calculus-style rules. For this reason, the proposed correspondence analysis resulting in invertible rules can constitute a new foundation for the method of Socratic proofs. Correspondence analysis is Kooi and Tamminga's technique for designing proof systems. (...) In this paper it is used to consider sequent calculi with non-branching, invertible rules for the negation fragment of classical propositional logic and its extensions by binary Boolean functions. (shrink)

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

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

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

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

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

Pietruszczak (Bull Sect Log 38(3/4):163–171, 2009) proved that the normal logics K45 , KB4 (=KB5), KD45 are determined by suitable classes of simplified Kripke frames of the form ⟨W,A⟩ , where A⊆W. In this paper, we extend this result. Firstly, we show that a modal logic is determined by a class composed of simplified frames if and only if it is a normal extension of K45. Furthermore, a modal logic is a normal extension of K45 (resp. KD45; KB4; S5) if (...) and only if it is determined by a set consisting of finite simplified frames (resp. such frames with A≠∅; such frames with A=W or A=∅; such frames with A=W). Secondly, for all normal extensions of K45, KB4, KD45 and S5, in particular for extensions obtained by adding the so-called “verum” axiom, Segerberg’s formulas and/or their T-versions, we prove certain versions of Nagle’s Fact (J Symbol Log 46(2):319–328, 1981) (which concerned normal extensions of K5). Thirdly, we show that these extensions are determined by certain classes of finite simplified frames generated by finite subsets of the set N of natural numbers. In the case of extensions with Segerberg’s formulas and/or their T-versions these classes are generated by certain finite subsets of N. (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)

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)

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)

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

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)

B a c k g r o u n d. According to the genre characteristics, the article is a form of publicizing analytical conclusions from the experience of research in the field of the history of philosophy in the local community of philosophers of Ukraine. The material for understanding was supplied from the environment of educational and scientific professional activity of the authors and was based on the long experience of using a certain type of historical and philosophical sources, which (...) even now constitute the main resource of sources of Ukrainian philosophical education. The article explores the concept of "physical object" in the context of the history of philosophy and examines its relevance for philosophical reflections. It is noted that the variety of interpretations of the term in the history of philosophy creates the need for new methods of revealing its essence M e t h o d s. Problems with establishing the authenticity and verifiability of such sources prompted the search for methods and techniques of source studies in related fields of knowledge, in particular analytical philosophy and philosophy of science. The article uses an analytical approach based on the study of historical and philosophical sources. Methods of source studies are used to solve problems related to the authenticity and reliability of sources R e s u l t s. With this in mind, the purpose of scientific research was to justify the appropriateness of using such a phenomenon as a "physical object" in historical-philosophical research. It was established that, despite the significant unusualness of the presence of a terminological counterpart to this phenomenon in the historical-philosophical realm, its implementation and application has significant creative potential. C o n c l u s i o n s. After a concise inquiry, the authors have reached a consensus that, in contemporary research on the history of philosophy within the Ukrainian philosophical community, it is pertinent and essential to develop a methodology. This methodology should be founded on the imperative of establishing the initial point for comprehensively studying the philosophical primary source, treating it as a "physical object". (shrink)

The article is devoted to the philosophy of cosmology, its history and contemporary conditions, the tradition of studying and modern trends in teaching this discipline in higher education in Ukraine. There is problem of defining the subject of philosophy of cosmology, there are similar and different motifs with modern astrophysics, cosmology on the one hand, and, with the history of philosophy and modern philosophy on the other hand. The change in the subject of the philosophy of cosmology in the history (...) of philosophy and science has been studied in this article. A modern state of the philosophy of cosmology in modern philosophical education is demonstrated. (shrink)

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.

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

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.

In modern science, an important feature is a fact that interdisciplinary research is becoming more popular. This is due to the mutual interest of different areas of science to the methods and principles of other areas. The article is devoted to the study of the possibility of dialogue between physical cosmology and transcendental philosophy. Transcendental philosophy provides an interesting look at the problem of subject-object relations in which the object depends on the observer. The possibility of science using a specific (...) transcendental method in the field of astrophysics has been studied. This possibility is due to the specifics of astronomical objects that exist for the observer as phenomena that do not correspond to reality in time and space. The article emphasizes the conventional concept of realism in modern science. The interdisciplinary dialogue of American and Ukrainian philosophical cosmology with its methods and physical cosmology with its objects promotes mutual development. (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)

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

Russell B. The Art of Rational Conjecture // The Art of Philosophizing and Other Essays. — New York : Philosophical Library, 1968.

The historic figure of the prominent ecclesiastical figure of the princely Rus-Ukraine, the associate of the ruler of the Galician principality, Yaroslav Osmomysl, Bishop Kosmi, was always in the sight of historians, religious scholars, archaeologists and art historians. True, its reading was usually done in the context of the study of the history of the origin of the Galician diocese in the middle of the 12th century. The problem of the founding of this diocese has a rather significant historiography. (...) In the middle of the nineteenth century, thanks to the search of the Lviv priest A. Petrushevich, it was possible to establish the main stages of its ancient history. In the years 1854-1860, about. A. Petrushevich published the "Galician Historical Collection", which contained his articles on the Galician Cathedral Church, its bishops and metropolitans. The history of the diocese was investigated in the second half of the nineteenth century. Yu Peles, M. Tikhomirov and I. Rudovich. Important pages about her past were supplemented in the twentieth century. historians M. Hrushevsky, I. Nazarko, K. Panas, S.Mudry, Yu.Fedorov, Z. Fedunkov, religious scholars - S.Kyyak and I.Skochilas, archaeologists Y.Pasternak, V.Petegirich, Yu.Lukomsky, art historians Pelensky, M. Figol, V. Vuytsik. During this time, a whole body of research has been created, which is dedicated to the study of the imprint of the Galician bishop Cosmi. He is represented by the scientific works of M. Hrushevsky, P. Gaydukov, Y.Pasternak, R.Michailova, V. Yanin. (shrink)

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

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

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)

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)

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

In 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)

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].