An algorithm recognizing admissibility of inference rules in generalized form (rules of inference with parameters or metavariables) in the intuitionistic calculus H and, in particular, also in the usual form without parameters, is presented. This algorithm is obtained by means of special intuitionistic Kripke models, which are constructed for a given inference rule. Thus, in particular, the direct solution by intuitionistic techniques of Friedman's problem is found. As a corollary an algorithm for the recognition of the solvability of logical equations (...) in H and for constructing some solutions for solvable equations is obtained. A semantic criterion for admissibility in H is constructed. (shrink)

We find an explicit basis for all admissible rules of the modal logic S4. Our basis consists of an infinite sequence of rules which have compact and simple, readable form and depend on increasing set of variables. This gives a basis for all quasi-identities valid in the free modal algebra ℱS4 of countable rank.

Our investigation is concerned with the finite model property with respect to admissible rules. We establish general sufficient conditions for absence of fmp w. r. t. admissibility which are applicable to modal logics containing K4: Theorem 3.1 says that no logic λ containing K4 with the co-cover property and of width > 2 has fmp w. r. t. admissibility. Surprisingly many, if not to say all, important modal logics of width > 2 are within the scope of this theorem–K4 itself, (...) S4, GL, K4.1, K4.2, S4.1, S4.2, GL.2, etc. Thus the situation is completely opposite to the case of the ordinary fmp–the absolute majority of important logics have fmp, but not with respect to admissibility. As regards logics of width ≤ 2, there exists a zone for fmp w. r. t. admissibility. It is shown that all modal logics A of width ≤ 2 extending S4 which are not sub-logics of three special tabular logics have fmp w.r.t. admissibility. (shrink)

The main result of this paper is the following theorem: each modal logic extendingK4 having the branching property belowm and the effective m-drop point property is decidable with respect to admissibility. A similar result is obtained for intermediate intuitionistic logics with the branching property belowm and the strong effective m-drop point property. Thus, general algorithmic criteria which allow to recognize the admissibility of inference rules for modal and intermediate logics of the above kind are found. These criteria are applicable to (...) most modal logics for which decidability with respect to admissibility is known and to many others, for instance, to the modal logicsK4,K4.1,K4.2,K4.3,S4.1,S4.2,GL.2; to all smallest and greatest counterparts of intermediate Gabbay-De-Jong logicsD n; to all intermediate Gabbay-De-Jong logicsD n; to all finitely axiomatizable modal and intermediate logics of finite depth etc. Semantic criteria for recognizing admissibility for these logics are offered as well. (shrink)

This paper offers a brief analysis of the unification problem in modal transitive logics related to the logic S4 : S4 itself, K4, Grz and Gödel-Löb provability logic GL . As a result, new, but not the first, algorithms for the construction of ‘best’ unifiers in these logics are being proposed. The proposed algorithms are based on our earlier approach to solve in an algorithmic way the admissibility problem of inference rules for S4 and Grz . The first algorithms for (...) the construction of ‘best’ unifiers in the above mentioned logics have been given by S. Ghilardi in [ 16 ]. Both the algorithms in [ 16 ] and ours are not much computationally efficient. They have, however, an obvious significant theoretical value a portion of which seems to be the fact that they stem from two different methodological approaches. (shrink)

We study the problem of finding a basis for all rules admissible in the intuitionistic propositional logic IPC. The main result is Theorem 3.1 which gives a basis consisting of all rules in semi-reduced form satisfying certain specific additional requirements. Using developed technique we also find a basis for rules admissible in the logic of excluded middle law KC.

The aim of this paper is to look from the point of view of admissibility of inference rules at intermediate logics having the finite model property which extend Heyting's intuitionistic propositional logic H. A semantic description for logics with the finite model property preserving all admissible inference rules for H is given. It is shown that there are continuously many logics of this kind. Three special tabular intermediate logics λ, 1 ≥ i ≥ 3, are given which describe all tabular (...) logics preserving admissibility: a tabular logic λ preserves all admissible rules for H iff 7λ has width not more than 2 and is not included in each λ. MSC: 03B55, 03B20. (shrink)

The paper studies Barwise's information frames and answers the John Barwise question: to find axiomatizations for the modal logics generated by information frames. We find axiomatic systems for (i) the modal logic of all complete information frames, (ii) the logic of all sound and complete information frames, (iii) the logic of all hereditary and complete information frames, (iv) the logic of all complete, sound and hereditary information frames, and (v) the logic of all consistent and complete information frames. The notion (...) of weak modal logics is also proposed, and it is shown that the weak modal logics generated by all information frames and by all hereditary information frames are K and K4 respectively. To develop general theory, we prove that (i) any Kripke complete modal logic is the modal logic of a certain class of information frames and that (ii) the modal logic generated by any given class of complete, rarefied and fully classified information frames is Kripke complete. This paper is dedicated to the memory of talented mathematician John Barwise. (shrink)

In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on [6] we introduce formal axiomatic systems for common information logics and prove that these systems are sound and complete. Analyzing the common information operation we show that it can be understood as greatest open fixed points for knowledge formulas. Using obtained results we explore monotonicity, omniscience problem, and inward monotonocity, describe their connections and give dividing examples. Also (...) we find algorithms recognizing these properties for some particular cases. (shrink)

This article seeks to clarify the concept of progress in philosophy. It treats progress as a kind of development. But not every development is a progress. When we talk about progress, what really matters is the direction of development. In some cases it is relatively easy to reach agreement about this direction. But not in the case of philosophy, if we abstract it from the obvious and the trivial, like the number of books on philosophy. As a result, the article (...) concludes that there cannot be progress in philosophy. Instead we see a continual multiplication of interpretations. (shrink)

My dear Aleksandr!I have finally found some quiet time for a slow and attentive read of your article “The Beginning of the Black Notebooks.”1 I very much liked the article, especially for your trul...

The paper discusses various aspects of the concept of “cultural memory” coined by Jan Assmann and related both to the problem of determining the categories of culture that became the first objects of philosophical reflection in the era of the Axial Age and to the issues of the modern crisis of the ideology of globalism and multiculturalism. Using the example of some categories of an archaic myth that have not lost their cultural and social relevance at present, the variability of (...) the genesis of philosophy in various civilizations of the epoch of the “Axial Age” is demonstrated - both those in which it arises as an independent form of worldview and those where this process stops at the stage of a highly speculative myth. Special attention is paid to the cultural and social aspects of memory and recollection of the past as forms of spiritual “resistance” to external cultural influences and the preservation of religious and ethnic identity, which is equally relevant both during the genesis of philosophy and in modern post-industrial society during the crisis of globalist ideology and the philosophy of multiculturalism. (shrink)

This article analyzes the issues associated with the publication of Martin Heidegger’s Black Notebooks. We attempt to explain the very publication of this document as a kind of experiment the philo...

In this paper we summarise the constraints that low-redshift data—such as supernovae Ia, baryon acoustic oscillations and cosmic chronometers —are able to set on the concordance model and its extensions, as well as on inhomogeneous but isotropic models. We provide a broad overlook into these cosmological scenarios and several aspects of data analysis. In particular, we review a number of systematic issues of SN Ia analysis that include magnitude correction techniques, selection bias and their influence on the inferred cosmological constraints. (...) Furthermore, we examine the isotropic and anisotropic components of the BAO data and their individual relevance for cosmological model-fitting. We extend the discussion presented in earlier works regarding the inferred dynamics of cosmic expansion and its present rate from the low-redshift data. Specifically, we discuss the cosmological constraints on the accelerated expansion and related model-selections. In addition, we extensively talk about the Hubble constant problem, then focus on the low-redshift data constraint on \ that is based on CC. Finally, we present the way in which this result compares to the high-redshift \ estimate and local measurements that are in tension. (shrink)

Based on some materials from the A.V. Florovsky's Foundation in the Archive of the Russian Academy of Sciences, the author of the article reconstructs a little-known page from the history of academic and philosophical life of the Russian migr, that is the history of the Philosophical Society at the Russian Free University in the 1930s-1940s, including during the Nazi occupation of Czechoslovakia. It is justified that the reconstruction of the history of Russian philosophical institutions can set a new research perspective (...) that allows us to consider the history of Russian philosophy as a process of formation and development of institutionalized forms of production, reproduction and translation of philosophical knowledge, which would allow to create a new historical and philosophical cross-section of Russian thought, complementing traditional approaches to the historiography of Russian philosophy. The article reveals new aspects of the scientific activity of N.O. Lossky and I.I. Lapshin, who played a key role in the work of the Philosophical Society. In addition, the analysis of archival materials made it possible to identify and reconstruct new facts from the creative biography of such thinkers of Russian emigration as S.L. Frank, E.V. Spektorsky, B.P. Vysheslavtsev, G.V. Florovsky. Russian Free University's Philosophical Society report for 1941 is given as an appendix to the article, as well as the reconstruction of the problems of the circle for the study of the Russian national idea. It is concluded that scientific and philosophical activity at the RSU was carried out through an extensive network of scientific societies, associations, circles and seminars, which allowed developing a wide variety of issues - aesthetics, the history of Russian and Western philosophy, philosophical problems of Russian literature and history, the Russian national idea. (shrink)

The paper explores the significance of the Chinese concept of harmony for establishing a stable and efficient global governance. The author assumes that to meet demands of the emerging global community this concept should be assessed in the context of two other important notions: “commonality” and “similarity” or “sharing”. The merging of these concepts has been a real basis of the Chinese tradition and it can serve as a foundation of a new global order based on the principle of synergy.

The article discusses the concept of political Gnosticism, developed by the philosopher Eric Voegelin. This concept is one of the main elements of Voegelin’s political philosophy, in which he answers the question about the essence of modern politics. Voegelin believes that modernity is the result of the historical victory of the ideology of “Gnosticism”. The historical roots of Gnosticism, says Voegelin, should not be sought in late antiquity, but in the Middle Ages. Based on the ideas of Christian mystics, such (...) as Joachim of Flore, an ideology of Gnosticism was formed, which spread in the Western world and became a powerful political force. This force accomplished the “great Gnostic revolution” and shaped modern society. Examples of modern Gnostic regimes are progressivism, positivism, Marxism, psychoanalysis, communism, fascism, National Socialism. Modern political science is not able to give a critical understanding of Gnosticism, since it itself is a product of Gnostic ideology. Therefore, modern political science needs to restore its fundamental principles, which were established by ancient philosophers, the founders of the philosophy of politics. Voegelin calls this the reteoretisation of political science. The author of the article analyzes the theoretical and historical grounds of Voegelin’s concept and concludes that one of the sources of his theory of political Gnosticism is Hegel’s doctrine of unhappy consciousness. The article also proves that Voegelin’s concept of Gnosticism is not identical with historical Gnosticism. The author also analyzes the reasons why political science of the twentieth century did not accept this concept and did not draw conclusions from criticism of political science in the work “New Science of Politics” by Voegelin. The article concludes that the changes that are taking place in the modern world force us to reconsider and overestimate Voegelin’s concept, which, in our opinion, has great heuristic potential. (shrink)

The article is devoted to Leo Strauss’s critique of Hegel’s political philosophy. The author holds this topic relevant in the context of the crisis of modern political science. To understand the causes and nature of this crisis, it is necessary to pay attention to alternative philosophical and political theories of the XX century. Leo Strauss’s philosophy of politics is just such an alternative theory. Strauss made a radical critique of modern political philosophy, which he saw as an important part of (...) the project of modern civilization. Strauss stresses that Hegel became one of the most prominent philosophers who participated in the creation of modern science and the modern world. The author considers the main critical arguments of Strauss, evaluates their validity and their significance for the Straussian conservative revolution in philosophy. The author pays special attention to the question of Hegel’s role in the break with classical political philosophy. Strauss accused Hegel that he had taken all the major steps that led to this rupture. Hegel, according to Strauss, secularized political thinking, which led to the loss of universal Christian values. The consequence of this secularization was the dominance of positivism in political philosophy. Hegel’s philosophy of history, according to Strauss, is relativism. Hegel’s historicism and progressivism are contradictory and inconsistent. Strauss also accuses Hegel of abandoning the philosophical esoteric art of writing. The article draws attention to the fact that Strauss recognized the importance of Hegel as an outstanding thinker of his time. Strauss viewed Hegel’s philosophy as a kind of intermediate link between classical philosophy and modern positivism. The author concludes that for Strauss the critique of Hegel’s political philosophy became an important element of his project of restoration of classical political philosophy. The article uses little-known materials from Strauss’s lectures in 1958 and 1965. (shrink)

The notion of Ausersein/outbeing, proposed by Alexius Meinong, was for a long time in the shadow of the principle of the Ausersein of a pure object, which made it possible to make non-existent objects part of a judgment. This principle was adopted by many followers of Meinong within the framework of analytical philosophy, but the very concept of Ausersein was almost totally ignored. When it’s become an object of research, there appeared several interpretations of it. It was interpreted either as (...) a way of describing the ontological status of non-existent objects, or as a basic property of all objects without exception. Dale Jacquette suggests interpreting Ausersein as extraontology, i.e. a metasemantic category that includes all items. In this article, we will analyse the arguments of modern interpreters of this notion and try to find out which interpretation is most correct. (shrink)

At the beginning of the twentieth century, Russian Marxism, which was rapidly gaining intellectual and political influence, faced the need to develop its ethical concepts, since the “atheistic ethics,” represented by the philosophy of Russian narodniki and European social democrats, were found to be ideologically unacceptable. The subject of this article is an attempt to comprehend the moral problems addressed in the heterogeneous circles of Russian Marxism in the first three decades of the twentieth century. The concepts introduced by A. (...) Bogdanov, L. Aksel’rod, and A. Lunacharsky played a critical role in this context. If Bogdanov proclaimed historical legality and morality as such to be forms of ideological consciousness that would be abolished in the course of social evolution, then Aksel’rod sought to defend and justify a universalist understanding of morality, faced with the need to reconcile this understanding with the key provisions of historical materialism. Lunacharsky, finally, found himself in an equally difficult situation, trying to reconcile the position of the self-sufficiency of the Marxist worldview with the obvious, as it seemed to him, need for its “ethical supplement” and finding a solution in peculiar identification of the ethical and the aesthetic. These attempts reflect a peculiarity of the development of Russian Marxism. In the field of ethics, in particular, it followed a path that could be described as one of narrowing interpretations‚ as a result of which a more heuristically simple and unambiguous version of the theory was created. (shrink)

The review reveals the basic conceptions elaborated by one of the major Russian modern sociologists Zh.T. Toshchenko in his new research. The reviewer argues that the book’s author thoroughly examines the various methodological grounds for identifying the essential characteristics of social dynamics. At the same time, the reviewer focuses on the further development of the theory of modern society, proposed by the book’s author. Thus, Zh.T. Toshchenko, who spent many years researching social deformations, formulates an important concept – the concept (...) of a society of trauma as the third modality of social development along with evolution and revolution. The book offers a fundamentally new view of social life, there is a holistic, systematic approach to all its processes and phenomena. The reviewer concludes that the new book of the social theorist Zh.T. Toshchenko is a significant contribution to sociological theory, since it develops ideas about the state and prospects of Russian society, gives accurate assessments of all social processes. (shrink)

In this paper1 we study admissible consecutions in multi-modal logics with the universal modality. We consider extensions of multi-modal logic S4n augmented with the universal modality. Admissible consecutions form the largest class of rules, under which a logic is closed. We propose an approach based on the context effective finite model property. Theorem 7, the main result of the paper, gives sufficient conditions for decidability of admissible consecutions in our logics. This theorem also provides an explicit algorithm for recognizing such (...) consecutions. Some applications to particular logics with the universal modality are given. (shrink)

The aim of this book is to present the fundamental theoretical results concerning inference rules in deductive formal systems. Primary attention is focused on: admissible or permissible inference rules the derivability of the admissible inference rules the structural completeness of logics the bases for admissible and valid inference rules. There is particular emphasis on propositional non-standard logics (primary, superintuitionistic and modal logics) but general logical consequence relations and classical first-order theories are also considered. The book is basically self-contained and special (...) attention has been made to present the material in a convenient manner for the reader. Proofs of results, many of which are not readily available elsewhere, are also included. The book is written at a level appropriate for first-year graduate students in mathematics or computer science. Although some knowledge of elementary logic and universal algebra are necessary, the first chapter includes all the results from universal algebra and logic that the reader needs. For graduate students in mathematics and computer science the book is an excellent textbook. (shrink)

For over a century, Haeckel's Gastraea theory remained a dominant theory to explain the origin of multicellular animals. According to this theory, the animal ancestor was a blastula‐like colony of uniform cells that gradually evolved cell differentiation. Today, however, genes that typically control metazoan development, cell differentiation, cell‐to‐cell adhesion, and cell‐to‐matrix adhesion are found in various unicellular relatives of the Metazoa, which suggests the origin of the genetic programs of cell differentiation and adhesion in the root of the Opisthokonta. Multicellular (...) stages occurring in the complex life cycles of opisthokont protists (mesomycetozoeans and choanoflagellates) never resemble a blastula. Here, we discuss a more realistic scenario of transition to multicellularity through integration of pre‐existing transient cell types into the body of an early metazoon, which possessed a complex life cycle with a differentiated sedentary filter‐feeding trophic stage and a non‐feeding blastula‐like larva, the synzoospore. Choanoflagellates are considered as forms with secondarily simplified life cycles. (shrink)

We study unification problem and problem of admissibility for inference rules in minimal Johanssonsʼ logic J and positive intuitionistic logic IPC+. This paper proves that the problem of admissibility for inference rules with coefficients is decidable for the paraconsistent minimal Johanssonsʼ logic J and the positive intuitionistic logic IPC+. Using obtained technique we show also that the unification problem for these logics is also decidable: we offer algorithms which compute complete sets of unifiers for any unifiable formula. Checking just unifiability (...) of formulas with coefficients also works via verification of admissibility. (shrink)

We investigate logical consequence in temporal logics in terms of logical consecutions. i.e., inference rules. First, we discuss the question: what does it mean for a logical consecution to be 'correct' in a propositional logic. We consider both valid and admissible consecutions in linear temporal logics and discuss the distinction between these two notions. The linear temporal logic LDTL, consisting of all formulas valid in the frame 〈L, ≤, ≥〉 of all integer numbers, is the prime object of our investigation. (...) We describe consecutions admissible LDTL in a semantic way—via consecutions valid in special temporal Kripke/Hintikka models. Then we state that any temporal inference rule has a reduced normal form which is given in terms of uniform formulas of temporal degree 1. Using these facts and enhanced semantic techniques we construct an algorithm, which recognizes consecutions admissible in LDTL. Also, we note that using the same technique it follows that the linear temporal logic L (N) of all natural numbers is also decidable w.r.t. inference rules. So, we prove that both logics LDTL and L (N) are decidable w.r.t. admissible consecutions. In particular, as a consequence, they both are decidable (Known fact), and the given deciding algorithms are explicit. (shrink)

The paper aims at providing the multi-modal propositional logic LTK with a sound and complete axiomatisation. This logic combines temporal and epistemic operators and focuses on m odeling the behaviour of a set of agents operating in a system on the background of a temporal framework. Time is represented as linear and discrete, whereas knowledge is modeled as an S5-like modality. A further modal operator intended to represent environment knowledge is added to the system in order to achieve the expressive (...) power sufficient to describe the piece of information available to the agents at each moment in the flow of time. (shrink)

We prove that a propositional Linear Temporal Logic with Until and Next has unitary unification. Moreover, for every unifiable in LTL formula A there is a most general projective unifier, corresponding to some projective formula B, such that A is derivable from B in LTL. On the other hand, it can be shown that not every open and unifiable in LTL formula is projective. We also present an algorithm for constructing a most general unifier.

The paper deals with a temporal multi-agent logic TMAZ, which imitates taking of decisions based on agents' access to knowledge by their interaction. The interaction is modelled by possible communication channels between agents in special temporal Kripke/hintikka-like models. The logic TMAZ distinguishes local and global decisions-making. TMAZ is based on temporal Kripke/hintikka models with agents' accessibility relations defined on states of all possible time clusters C(i) (where indexes i range over all integer numbers Z). The main result provides a decision (...) algorithm for TMAZ (so, we prove that TMAZ is decidable). This algorithm also solves the satisfiability problem. In the final part of the paper, we consider the admissibility problem for inference rules in TMAZ, and show that this problem is decidable for TMAZ as well. (shrink)

Our paper aims to investigate inference rules for Nelson’s logics and to discuss possible ways to determine admissibility of inference rules in such logics. We will use the technique offered originally for intuitionistic logic and paraconsistent minimal Johannson’s logic. However, the adaptation is not an easy and evident task since Nelson’s logics do not enjoy replacement of equivalences rule. Therefore we consider and compare standard admissibility and weak admissibility. Our paper founds algorithms for recognizing weak admissibility and admissibility itself – (...) for restricted cases, to show the problems arising in the course of study. (shrink)