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)
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)
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.
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)
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)
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.
In terms of formal deductive systems and multi-dimensional Kripke frames we study logical operations know, informed, common knowledge and common information. Based on  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)
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 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)
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 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)
The Cell Cycle Ontology (CCO) has the aim to provide a 'one stop shop' for scientists interested in the biology of the cell cycle that would like to ask questions from a molecular and/or systems perspective: what are the genes, proteins, and so on involved in the regulation of cell division? How do they interact to produce the effects observed in the regulation of the cell cycle? To answer these questions, the CCO must integrate a large amount of knowledge from (...) diverse sources; the irregularity and incompleteness of this information suggests an ontology can act as the means of this integration. The volatility and continued expansion of biological knowledge means the content and modelling of the CCO will have to be frequently changed and updated. The CCO is generated from the input data automatically once every two months. This makes it easy to change the representation to enable certain queries; incorporate new knowledge; and consistently apply design patterns across the CCO. The automatic process also allows the CCO to be delivered in a variety of representations that suit the needs of various CCO customers and the abilities of existing toolsets. In this paper we present the CCO and its characteristics of utility and flexibility, that, from our perspective, make it a beautiful ontology. (shrink)
The notion of conditional entropy is extended to noncomposite systems. The \-deformed entropic inequalities, which usually are associated with correlations of the subsystem degrees of freedom in bipartite systems, are found for the noncomposite systems. New entropic inequalities for quantum tomograms of qudit states including the single qudit states are obtained. The Araki–Lieb inequality is found for systems without subsystems.
I attempt to clarify the connection between two late texts by V.S. Solov'Ã«v: Justification of the Good and Theoretical Philosophy. Solov'Ã«v drew attention to the intrinsic connection between moral and intellectual virtues. Theoretical Philosophy is the initial -- unfinished -- sketch of the dynamism of mind seeking truth as a good. I sketch several parallels and analogies between the doctrine of moral experience set out in Justification and the account of the intellect's dynamism based on immediate certitude set out in (...) Theoretical Philosophy. Solov'Ã«v can thus be considered as a âvirtue epistemologistâ in the current meaning given to this description. I conclude by suggesting that Solov'Ã«v's position on these questions does not easily cohere with the âimpersonalismâ he appears to defend in Theoretical Philosophy. (shrink)