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)

The article attempts to raise a question and give an answer to it regarding the evaluation of the philosophical creativity of Hermann Cohen, the German-Jewish thinker of the late XIX - early XX century. Moreover, following the philosophical style of Cohen himself, the question posed and discussed in the article is not idle, but it contains a hypothesis that forms our answer in a certain way. It is important to identify the difficulties and intellectual determinants that prevent the formation of (...) a clear and unambiguous answer. At the same time these difficulties contain an initiating moment for opening a philosophical debate. The historical and philosophical reasons that make the very beginning of the discussion of the question more complex, are considered. The article, of course, cannot claim to be an exhaustive answer on such a fundamental topic, which is contained in the designated question. But the article itself, and the articles following it in the section devoted to the work of Herman Cohen, may be indicate that the time for this discussion has come. (shrink)

We prove that if I is a partially ordered set in a countable transitive model M of ZFC then M can be extended by a generic sequence of reals a i , i ∈ I, such that ℵ M 1 is preserved and every a i is Sacks generic over $\mathfrak{M}[\langle \mathbf{a}_j: j . The structure of the degrees of M-constructibility of reals in the extension is investigated. As applications of the methods involved, we define a cardinal invariant to distinguish (...) product and iterated Sacks extensions, and give a short proof of a theorem (by Budinas) that in ω 2 -iterated Sacks extension of L the Burgess selection principle for analytic equivalence relations holds. (shrink)

The article deals with the notion of the genetic code and its metaphorical understanding as a “language”. In the traditional view of the language metaphor of the genetic code, combinations of nucleotides are signs of amino acids. Similarly, words combined from letters represent certain meanings. The language metaphor of the genetic code, 171–200, 2011) assumes that the nucleotides stay in the analogy to letters, triples to words and genes to sentences. We propose an application of mathematical linguistic methods on the (...) notion of the genetic code. We provide quantitative analysis of mRNA strings and natural language texts. This analysis is sensitive to the detection of the code units hierarchy. We also take into consideration a representative quantitative analysis of DNA, RNA and proteins. Our analysis of mRNA confirms an assumption that the design of the genetic code cannot analogize DNA bases and letters. The notion of the letter is much more appropriate if analogized with triplets or amino acids, 187–191, 2017). (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 examines the social theory of Lester Frank Ward, one of the most significant representatives of early American social theory, with particular attention to his conception of the state, which can be described as Hegelian. The first part of the paper gives a brief overview of early American social theory: its basic features, the issues that were the focus of attention during this period in the development of sociology in the US, and its most significant representatives. The basic features (...) of Ward’s social theory are then presented and examined in more detail. It is pointed out that it is: conceptual and essentially based on the natural sciences; based on the distinction between pure and applied sociology; systematic; supportive of progressive and pro-social reforms. It was directed against the individualist tradition. His theory was based on the belief that the human mind can direct social progress and that the order based on social inequalities, which is a product of the laissez-faire doctrine, cannot guarantee freedom and prosperity. The fundamental institution capable of doing so is the state. Therefore, the central part of this paper is devoted to his conception of the state and makes a comparison with Hegel’s theory of the ethical state contained in Hegel’s philosophy of objective spirit – philosophy of law and philosophy of history. It concludes by pointing out that Ward’s theory indicated the general direction of development of social circumstances towards the era of collectivism, and was also atypical of American social theory in some of its features. (shrink)

Key premises of the target article by Juslin & Vll (J&V) are challenged. It is also shown that most of the six proposed by the authors as underlying the induction of emotion by music involve nonmusical proximal causes. As a replacement for the state of being-moved is proposed.

We consider games over a finite alphabet with Gurevich-Harrington's winning conditions and restraints as in Yakhnis-Yakhnis . The game tree, the Gurevich-Harrington's kernels of the winning condition and the restraints are defined by finite automata. We give an effective criterion to determine the winning player and an effective presentation of a class of finite automata defined winning strategies.Our approach yields an alternative solution to the games considered by Büchi and Landweber . The BL algorithm is an important tool for solving (...) effectively presented games. The differences between the BL and our algorithms are as follows. Our algorithm is uniformly applicable to winning sets that correspond to boolean combinations of BL winning conditions, while the BL algorithm requires a transformation of such boolean combinations into a single BL condition. Our algorithm directly applies to a larger class of game trees for a given game alphabet than does the BL one. We describe Büchi-Landweber's class of winning conditions in a more transparent way by using finite automata and Gurevich-Harrington's form of winning conditions. Our algorithms that determine the winner of the game and find a winning strategy, are based on a translation of the events in the game in terms of the transition table of the automaton representing the game. This automaton differs from the ones that represent BL winning conditions. Both algorithms need further investigation.The algorithm determining the winner in the game, can be used as a verifier of concurrent programs. This is because programs can be viewed as strategies in Gurevich-Harrington's games and program specifications could be regarded as winning conditions for such games. The algorithm which finds a winning strategy could be used as a basis for automated concurrent program design.The present paper is a sequel to Annals of Pure and Applied Logic 48 277–297. (shrink)

Philosophy of Science; Ukraine; Polysytemic nature of theories; Practical theories; Subsystems of a theory.

Una pandemia ha golpeado a millones de familias en el mundo. Este problema global parecía que cuestionaba todas nuestras formas de vida. No obstante, los malos hábitos y las viejas estructuras corruptas comenzaron a aprovecharse de esta situación. Y la corrupción volvió a la escena, en la sobrevaloración de medicamentos o equipos médicos, en la mala repartición de víveres o de dinero, en el cobro de dinero por ingreso a una unidad de cuidado intensivo, aprovecharse de su posición política para (...) vacunarse antes, etc. ¿Se ha normalizado la corrupción en la vida nacional? (shrink)

In continuation of our study of HST, Hrbaek set theory (a nonstandard set theory which includes, in particular, the ZFC Replacement and Separation schemata in the st--language, and Saturation for well-orderable families of internal sets), we consider the problem of existence of elementary extensions of inner "external" subclasses of the HST universe.We show that, given a standard cardinal , any set R * generates an "internal" class S(R) of all sets standard relatively to elements of R, and an "external" class (...) L[S(R)] of all sets constructible (in a sense close to the Gödel constructibility) from sets in S(R). We prove that under some mild saturation-like requirements for R the class L[S(R)] models a certain -version of HST including the principle of +-saturation; moreover, in this case L[S(R)] is an elementary extension of L[S(R)] in the st--language whenever sets R R satisfy the requirements. (shrink)

We propose that black holes may serve as a physical substratum for intelligent beings, based on(1) The descriptions of brain and psyche are complementary to each other, as internal and external observers of a black hole in the Susskind-t'Hooft's schema.(2) There is an aspect of the inner structure of a black hole that is isomorphic to the structure of the human subjective domain in the psychological model of reflexion.(3) Both black holes and the brain-psyche system have a facet that can (...) be represented using thermodynamic concepts.(4) Both lend themselves to a holographic description. (shrink)

In a recent paper, Ferraris, Lee and Lifschitz conjectured that the concept of a stable model of a first-order formula can be used to treat some answer set programming expressions as abbreviations. We follow up on that suggestion and introduce an answer set programming language that defines the mean- ing of counting and choice by reducing these constructs to first-order formulas. For the new language, the concept of a safe program is defined, and its semantic role is investigated. We compare (...) the new language with the concept of a disjunc- tive program with aggregates introduced by Faber, Leone and Pfeifer, and discuss the possibility of implementing a frag- ment of the language by translating it into the input language of the answer set solver DLV. The language is also compared with cardinality constraint programs defined by Syrjänen. (shrink)

There is given the proof of strict embedding of Leniewski's elementary ontology into monadic second-order calculus of predicates providing a formalization of the class of all formulas valid in all domains (including the empty one). The elementary ontology with the axiom S (S S) is strictly embeddable into monadic second-order calculus of predicates which provides a formalization of the classes of all formulas valid in all non-empty domains.

General historical introduction (concerning the law of historical development) -- Concerning the three types of philosophy -- Principles of organic logic : characterization -- Of integral knowledge point of departure and method of organic logic -- Principles of organic logic (continuation) : concept of the absolute : basic definitions according to the categories of the existent, essence, and being -- Principles of organic logic (continuation) : relative categories that define idea as an entity.

We commend Arbib for his original proposal that a mirror neuron system may have participated in language origins. However, in our view he proposes a complex evolutionary scenario that could be more parsimonious. We see no necessity to propose a hand-based signing stage as ancestral to vocal communication. The prefrontal system involved in human speech may have its precursors in the monkey's inferior frontal cortical domain, which is responsive to vocalizations and is related to laryngeal control.

The Russian academic theological tradition, scarcely known to the West, was the only milieu wherein the development of philosophy of religion in the pre-revolutionary Russia was under way. Philosophical investigation of the phenomenon of religion was being elaborated in the apologetic context, i.e. in critical analysis of non-theistic conceptions of the origin and essence of religion, and the figure of Friedrich Schleiermacher, with his reduction of religion firstly to cosmic feelings and later to the feeling of the ontological dependence, occupied (...) an invariable place in this analysis. The paper deals with critical comments on Schleiermacher’s Speeches on Religion and Christian Faith made by Victor Kudryavtsev-Platonov and his followers, which are being parsed in turn, as well as with historical links of the later Schleiermacher with phenomenology of religion and typological affinities of the earlier Schleiermacher with the theology of religious pluralism. (shrink)

In this article ‡ we show how the universe of HST, Hrbaček set theory admits a system of subuniverses which keep the Replacement, model Power set and Choice, and also keep as much of Saturation as it is necessary. This gives sufficient tools to develop the most complicated topics in nonstandard analysis, such as Loeb measures.

This article discusses the connection between the ideas of Fyodor M. Dostoevsky and Vladimir S. Solovyov on the need for cultural and moral transformation of those who would claim to participate in...

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...

We prove, in ZFC,the existence of a definable, countably saturated elementary extension of the reals.

Trata-se de discutir a centralidade do trabalho como categoria de reconhecimento através da problematização de sua natureza disciplinar. Isto nos levará a um duplo movimento: primeiro, a categoria de trabalho em Marx será relida à luz não apenas da temática da espoliação econômica da mais-valia, mas também da espoliação psíquica das relações de estranhamento entre sujeito e objeto; segundo, as modificações recentes no mundo do trabalho e as modalidades de sofrimento psíquico a elas associadas serão interpretadas a partir do impacto (...) social de tal forma de espoliação. (shrink)

People are remarkably smart: They use language, possess complex motor skills, make nontrivial inferences, develop and use scientific theories, make laws, and adapt to complex dynamic environments. Much of this knowledge requires concepts and this study focuses on how people acquire concepts. It is argued that conceptual development progresses from simple perceptual grouping to highly abstract scientific concepts. This proposal of conceptual development has four parts. First, it is argued that categories in the world have different structure. Second, there might (...) be different learning systems that evolved to learn categories of differing structures. Third, these systems exhibit differential maturational course, which affects how categories of different structures are learned in the course of development. And finally, an interaction of these components may result in the developmental transition from perceptual groupings to more abstract concepts. This study reviews a large body of empirical evidence supporting this proposal. (shrink)

Philosopher Vladimir Jankélévitch has only recently begun to receive his due from the English-speaking world, thanks in part to discussions of his thought by Jacques Derrida, Emmanuel Lévinas, and Paul Ricoeur. His international readers have long valued his unique, interdisciplinary approach to philosophy’s greatest questions and his highly readable writing style. Originally published in 1967, Le Pardon, or Forgiveness, is one of Jankélévitch’s most influential works. In it, he characterizes the ultimate ethical act of forgiving as behaving toward the (...) perpetrator as if he or she had never committed the action, rather than merely forgetting or rationalizing it—a controversial notion when considering events as heinous as the Holocaust. Like so many of Jankélévitch’s works, Forgiveness transcends standard treatments of moral problems, not simply generating a treatise on one subject but incorporating discussions of topics such as free will, giving, creativity, and temporality. Translator Andrew Kelley masterfully captures Jankélévitch’s melodic prose and, in a substantive introduction, reviews his life and intellectual contributions. Forgiveness is an essential part of that legacy, and this indispensable English translation provides key tools for understanding one of the great Western philosophers of the twentieth century. (shrink)

This report of the roundtable that took place on 25 November 2021 at The Peoples’ Friendship University of Russia attempts to explain the obvious growth of interest in Neo-Kantian philosophy in general and the philosophy of the head of the Marburg School of Neo-Kantianism, Hermann Cohen, in particular. In their contributions, the participants in the discussion demonstrated that the current interest in Neo-Kantianism does not solely or even largely have to do with the history of philosophy but rather with the (...) relevance of many of the ideas of Marburg Neo-Kantianism for the modern theory of cognition, the philosophy of culture, ethics and the philosophy of religion. The course of the discussion highlighted the relevance of Cohen’s theory of cognition based on logic and rationality. The main outcome of the discussion was the conviction that the potential of many of Cohen’s ideas has yet to be fully tapped and there are grounds for considering them to be heralds of a new philosophy which, in many of its features, is only maturing. (shrink)