We prove that an intermediate predicate logic characterized by a class of finite partially ordered sets is recursively axiomatizable iff it is "finite", i.e., iff it is characterized by a single finite partially ordered set. Therefore, the predicate logic LFin of the class of all predicate Kripke frames with finitely many possible worlds is not recursively axiomatizable.

An intermediate predicate logic L is called finite iff it is characterized by a finite partially ordered set M, i.e., iff L is the logic of the class of all predicate Kripke frames based on M. In this paper we study axiomatizability of logics of this kind. Namely, we consider logics characterized by finite trees M of a certain type (levelwise uniform trees) and establish the finite axiomatizability criterion for this case.

We propose a new, rather simple and short proof of Kripke-completeness for the predicate variant of Dummett's logic. Also a family of Kripke-incomplete extensions of this logic that are complete w.r.t. Kripke frames with equality (or equivalently, w.r.t. Kripke sheaves [8]), is described.

The Kripke-completeness and incompleteness of some intermediate predicate logics is established. In particular, we obtain a Kripke-incomplete logic (H* +A+D+K) where H* is the intuitionistic predicate calculus, A is a disjunction-free propositional formula, D = x(P(x) V Q) xP(x) V Q, K = ¬¬x(P(x) V ¬P(x)) (the negative answer to a question of T. Shimura).

The completeness w.r.t. Kripke frames with equality (or, equivalently, w.r.t. Kripke sheaves, [ 8 ] or [4, Sect. 3.6]) is established for three superintuitionistic predicate logics: ( Q - H + D *), ( Q - H + D *&K), ( Q - H + D *& K & J ). Here Q - H is intuitionistic predicate logic, J is the principle of the weak excluded middle, K is Kuroda’s axiom, and D * (cf. [ 12 ]) is a (...) weakened version of the well-known constant domains principle D . Namely, the formula D states that any individual has ancestors in earlier worlds, and D * states that any individual has $${\neg\neg}$$ -ancestors (i.e., ancestors up to $${\neg\neg}$$ -equality) in earlier worlds. In particular, the logic ( Q - H + D *& K & J ) is the Kripke sheaf completion of ( Q - H + E & K & J ), where E is a version of Markov’s principle (cf. [ 12 ]). On the other hand, we show that the logic ( Q - H + D *& J ) is incomplete w.r.t. Kripke sheaves. (shrink)

An example of finite tree Mo is presented such that its predicate logic (i.e. the intermediate predicate logic characterized by the class of all predicate Kripke frames based on Mo) is not finitely axiomatizable. Hence it is shown that the predicate analogue of de Jongh - McKay - Hosoi's theorem on the finite axiomatizability of every finite intermediate propositional logic is not true.

Recent studies in semantics of modal and superintuitionistic predicate logics provided many examples of incompleteness, especially for Kripke semantics. So there is a problem: to find an appropriate possible- world semantics which is equivalent to Kripke semantics at the propositional level and which is strong enough to prove general completeness results. The present paper introduces a new semantics of Kripke metaframes' generalizing some earlier notions. The main innovation is in considering "n"-tuples of individuals as abstract "n"-dimensional vectors', together with some (...) transformations of these vectors. Soundness of the semantics is proved to be equivalent to some non- logical properties of metaframes; and thus we describe the maximal semantics of Kripke- type. (shrink)

In [Ono 1987] H. Ono put the question about axiomatizing the intermediate predicate logicLFin characterized by the class of all finite Kripke frames. It was established in [ Skvortsov 1988] thatLFin is not recursively axiomatizable. One can easily show that for any finite posetM, the predicate logic characterized byM is recursively axiomatizable, and its axiomatization can be constructed effectively fromM. Namely, the set of formulas belonging to this logic is recursively enumerable, since it is embeddable in the two-sorted classical (...) predicate calculusCPC 2. Thus the logicLFin is II 2 0 -arithmetical.Here we give a more explicit II 2 0 -description ofLFin: it is presented as the intersection of a denumerable sequence of finitely axiomatizable Kripke-complete logics. Namely, we give an axiomatization of the logicLB n P m + characterized by the class of all posets of the finite height m and the finite branching n. A finite axiomatization of the predicate logicLP m + characterized by the class of all posets of the height m is known from [Yokota 1989]. We prove thatLB n P m + =,B n being the propositional axiom of the branching n. (shrink)

The article is devoted to the analysis of the?Pussy riot? case and the peculiarities of Russian postsecularism. Special emphasis is placed on the phenomenon of post-secular hybrids, i.e. the overcoming of the situation of social differentiation between religion and other social subsystems. It is claimed that the materials of the trial against?Pussy riot? make evident the appearance in Russia of at least three post-secular hybrids: 1) the blending of religion and politics; 2) installation of religious norms into the public order (...) of the secular state; 3) significance of confessional legal experts as part of the new?ideological state apparatus?. Slucaj?Pusi rajot? postao je glavni religijski, ako ne i drustveno-politicki dogadjaj u Rusiji u 2012. godini. Autor ce na osnovu analize materijala koji se odnosi na navedeni slucaj i diskusije koje su potom usledile, pokusati da pokaze specificnosti ruskog iskustva desekularizacije i prelaza prema novoj situaciji postsekularizma. Kroz prizmu sudjenja ucesnicima pank molebana bice razmotreni postsekularni hibridi nastali kao rezultat desekularizacije, u kojima su cudnovato isprepleteni religijski i svetovni elementi. Radi se o tri postsekularna hibrida: ukrstanju religijske i sekularne sfere, ukrstanju religije i javnog poretka i pojavi konfesionalnih religiologa - eksperata. (shrink)

The second order intuitionistic propositional logic characterized by the class of all “principal” Kripke frames is non-recursively axiomatizable, as well as any logic of a class of principal Kripke frames containing every finite frame.

A method for constructing continua of logics squeezed between some intermediate predicate logics, developed by Suzuki [8], is modified and applied to intervals of the form [L, L+ ¬¬S], where Lis a predicate logic, Sis a closed predicate formula. This solves one of the problems from Suzuki's paper.

ABSTRACT A simple method of axiomatizing every finite intermediate propositional logic by a finite set of axioms with the minimal number of variables is proposed. The method is based on Jankov's characteristic formulas.

The article discusses the main features of the Russian philosophy of war that developed in the first third of the 20th century. The author shows that in Russia, the philosophy of war did not develop as a separate broad line of research but limited itself to only a few meaningful, but rather brief, experiments. Nevertheless, many Russian philosophers left deep, well-founded reasoning about war, which can be reconstructed as a consistent system of views. One of its features is the shift (...) in the focus of considering armed violence from the sociological and political to the anthropological and ethical; the focus is not on war as a social phenomenon, but on the human’s position in war. In this regard, the attitude to war in Russian philosophy is paradoxical. On the one hand, war brings a lot of evil in the form of death of many people and destruction, but, on the other hand, it promotes to the manifestation of the best moral qualities in people, up to selflessness and heroism. Armed violence seems to be a tragedy of the Christian conscience, and each participant must independently find a justification for his participation in the war. Based on the conditions of a difficult moral choice, personal, existential justification may come from the idea that people cannot commit violence with a clear conscience. In this case, the person choosing to participate in a war perceives the battle as his own guilt that should be expiated. (shrink)

Book Commentary:A.Yu. Korobov-Latyntsev. Philosopher and War. On Russian Military Philosophy. Moscow: Russkaya filosofiya, 2020.

This paper studies a class of infinite-valued predicate logics. A sufficient condition for axiomatizability of logics from that class is given.

Intermediate prepositional logics we consider here describe the setI() of regular informational types introduced by Yu. T. Medvedev [7]. He showed thatI() is a Heyting algebra. This algebra gives rise to the logic of infinite problems from [13] denoted here asLM 1. Some other definitions of negation inI() lead to logicsLM n (n ). We study inclusions between these and other systems, proveLM n to be non-finitely axiomatizable (n ) and recursively axiomatizable (n ). We also show that formulas in (...) one variable do not separateLM from Heyting's logicH, andLM n (n ) from Scott's logic (H+S). (shrink)

The scientific article is devoted to the actual problem of scientific interaction of scientists all over the world by developing the representation of a scientific journal on the Internet. This article describes the status of managing a scientific journal in the digital world. Modern software platforms intended for automation of preparation and publication of electronic scientific journals are presented. The analysis and comparison of several software platforms. The advantages of using open source journal systems are given. The choice of OJS3 (...) platform is substantiated and a short generalized algorithm for its use is outlined. (shrink)

Syrien im 1.-7. Jahrhundert nach Christus. Edited by Dmitrij Bumazhnov and Hans Reinhard Seeliger. Studien und Texte zu Antike und Christentum, vol. 62. Tübingen: Mohr Siebeck, 2011. Pp. viii + 284. €64.

The article dedicated to the 200th anniversary of Dmytro Vasyliovych Pospiekhov, a philosopher, psychologist, theologian and translator, for the first time in the scientific literature, highlights the milestones of his academic biography and more than 50 years of professor’s tenure at the Department of Philosophy of Kyiv Theological Academy. Based on the analysis of a significant array of printed sources and archival documents, memories of colleagues and students of Dmytro Pospiekhov, the content and specifics of his educational, administrative, editorial and (...) publishing, translation activities at the Academy were revealed for the first time; his important role in the training of professional philosophers, the development of philosophical education and the spread of philosophical knowledge in the East Slavic territories was proven. Paying special attention to Dmytro Pospiekhov’s methods of teaching of philosophical disciplines, the author emphasizes his lecturing methodology, innovative for the theological academies of the time, as well as the heuristic, religious, educational, and moral impact on the students. A special emphasis is placed on Dmytro Pospiekhov’s scientific and editorial activities, his biographical and bibliographic studies, his role in the preservation and studying of the heritage of prominent philosophers and theologians of Kyiv Theological Academy of the 1820s‒1840s: Archpriest Ivan Skvortsov, Archimandrite Theophanes, Sylvestr Hohotskyi. Analyzing Dmytro Pospiekhov’s printed works for the first time, the author reveals the content and significance of his theological and philosophical study of the Book of Wisdom, which emphasizes the direct connection of this Judaic source to the philosophical teachings of Philo of Alexandria, Plato, and the Stoics. The author also draws attention to the significant research potential of Dmytro Pospiekhov’s manuscript heritage, linking it with the study of the prospects of determining his role in the development of psychological science in theological academies and the expansion of modern scientific ideas about the content and specifics of teaching of philosophical disciplines in Kyiv of the second half of the 19th Century. (shrink)

The essay examines the three main epiphanic experiences in The Brothers Karamazov and shows how Dostoevskij's treatment of these experiences may offer a guide to spiritual renewal. The three experiences are Alësha's vision of the resurrected Zosima and transfigured Christ, Dmitrij's vision of the suffering babe, and Ivan's vision of the devil (which serves as a counter example to the first two). By examining the content of each of these visions, as well as the parallels and variations in the (...) scenes leading up to these visions, this essay seeks to explore Dostoevskij's understanding of transformational revelatory experience. (shrink)

The essay examines the three main epiphanic experiences in The Brothers Karamazov and shows how Dostoevskij’s treatment of these experiences may offer a guide to spiritual renewal. The three experiences are Alësha’s vision of the resurrected Zosima and transfigured Christ, Dmitrij’s vision of the suffering babe, and Ivan’s vision of the devil (which serves as a counter example to the first two). By examining the content of each of these visions, as well as the parallels and variations in the (...) scenes leading up to these visions, this essay seeks to explore Dostoevskij’s understanding of transformational revelatory experience. (shrink)

This essay analyzes the recent appearance in Russian letters of ultra-nationalist fantasies about the restoration of Russia’s imperial or totalitarian status. This new trend has its roots not only in the increasingly patriotic tone of Russian society and politics, but also in the dynamics of the literary field itself. ‘Imperialist writers’ such as Aleksandr Prokhanov and Pavel Krusanov have both revived and reacted against postmodern themes and motifs from earlier decades. Relying on the legacy of sots-art and stiob , the (...) ‘imperialists’ advance a new model in Russia’s postmodern tradition, one that is balanced on the very borderline between irony and ideological militancy. In playing the game of ambiguous fanaticism, these writers have been able to attract the attention of a broad and diverse public, and have moved from an intellectual periphery into the cultural mainstream. (shrink)