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)

This text is a classic of Lenin - his essay explores materialism and its relation to capitalism and how Communism can get over this psychological wish for material and empirical ownership.

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)

Interdisciplinary studies of science form a “living” organism, in which every part performs its function and is connected with other parts. Philosophy of science plays a role of the “think-tank” of that organism. It is a generator of the sense that connects the functions of its separate parts into a systematic unity. It can be called the consciousness of science. Metaphilosophy of science is related to philosophy of science in the same way as philosophy of science itself is related to (...) science. Within metaphilosophy of science the propensity of philosophy of science to self-reflection is implemented. Metaphilosophy of science makes relevant the issues that relate to the philosophical significance of the processes taking place in the so-called “trading zone” (in the sense of P. Galison). These trading zone is a place where scientists, science-of-science theorists and philosophers exchange their ideas. The interaction between philosophy and metaphilosophy of science takes place in the course of a competition among various philosophical interpretations of the results received within the studies of these “trading” processes. Institutional, methodological, historical and culturological studies get a philosophical interpretation and become the source of metaphilosophical ideas. Metaphorically, one may say, that metaphilosophy of science is the self-consciousness of philosophy of science. The very idea that metaphilosophy of science is a participant of the process occurring in the “trading zone” puts an end to a meaningless pile of “metalevels” that very often characterize philosophical discussions of science. (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)

Physicalism as a metaphysical or ontological concept has maintained a dominant position since the second half of the last century to the present day. The claim that everything is physically constituted often accompanies microphysical reductionism, which assumes the existence of fundamental laws to which everything is reducible. In this context, a question regarding the status and possible autonomy of the laws of special sciences arises. The article focuses on the basic philosophical discussions between the strong, weak, and non-reductive physicalism that (...) treat the laws of special sciences in different ways, but none of which can be considered sufficiently convincing and successful. The article seeks to prove the existence of a universal mechanism that leads to the emergence of new and complex entities and regulations of their behaviour, thus justifying the autonomous status of special sciences and laws. (shrink)

This paper examines Gadamer's and Davidson's dialogical models of interpretation. It shows them to be comparable, but importantly dissimilar with respect to the kind of agreement they require for communication to be possible. It is argued that this difference entails different concepts of alterity: they model not only how we talk, but implicitly who we can intelligibly talk to. Another important contribution of this paper is to uncover a distinction in Gadamer between two kinds of agreement missed so far by (...) all commentators. The final section of this paper defends a second thesis, namely that the degree of agreement required by the models is proportional to the conceptual difference it can make intelligible. Hence, the extent of graspable cultural difference is not only an empirical matter, but is entailed by our choice of model. (shrink)

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)

What do we learn when we find out that an argument is logically incorrect? If logically incorrect means the same as not logically correct, which in turn means not having a valid logical form, it seems that we do not learn anything too useful—an argument which is logically incorrect can still be conclusive. Thus, it seems that it makes sense to fix a stronger interpretation of the term under which a logically incorrect argument is guaranteed to be wrong. In this (...) paper, we show that pinpointing this stronger sense is much trickier than one would expect; but eventually we reach an explication of the notion of logical incorrectness which we find non-trivial and viable. (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.

Name der Zeitschrift: Cognitive Linguistics Jahrgang: 26 Heft: 1 Seiten: 95-111.

This book assesses how Vatican II opened up the Catholic Church to encounter, dialogue, and engagement with other world religions. Opening with a contribution from the President of the Pontifical Council for Interreligious Dialogue, Cardinal Jean-Louis Tauran, it next explores the impact, relevance, and promise of the Declaration Nostra Aetate before turning to consider how Vatican II in general has influenced interfaith dialogue and the intellectual and comparative study of world religions in the postconciliar decades, as well as the contribution (...) of particular past and present thinkers to the formation of current interreligious and comparative theological methods. Additionally, chapters consider interreligious dialogue vis-à-vis theological anthropology in conciliar documents; openness to the spiritual practices of other faith traditions as a way of encouraging positive interreligious encounter; the role of lay and new ecclesial movements in interreligious dialogue; and the development of Monastic Interreligious Dialogue. Finally, it includes a range of perspectives on the fruits and future of Vatican’s II’s opening to particular faiths such as Judaism, Islam, Hinduism, and Buddhism. (shrink)

L’article aborde le sujet souvent débattu du rapport entre le détermi­nisme stoïcien et la morale pour rouvrir la question de la notion d’assentiment. Dans ce but, il réexamine les sources pour montrer deux choses : que les inter­prétations dites compatibilistes ont raison dans leur effort général pour montrer que les stoïciens restent déterministes quand ils présentent leur psychologie de l’action et défendent l’idée de responsabilité, mais qu’en même temps elles vont trop loin quand elles affirment – dans un effort de (...) systématisation de la stratégie stoïcienne – que l’assentiment est le simple effet de la rencontre du caractère particulier de l’agent et de l’impression sensorielle. En essayant de restituer l’ac­cent que les stoïciens ont mis sur l’assentiment, l’article indique que c’est égale­ment là que réside l’ambigüité de leur psychologie de l’action, qui a contribué au paradoxe dans l’interprétation du stoïcisme : ce dernier a été dès l’origine, d’un côté, une inspiration pour ceux qui ont voulu argumenter en faveur de la liberté de l’action humaine, et de l’autre, le sujet de la critique pour la réfutation de la liberté de l’action. Dans son ensemble l’interprétation proposée est négative dans le sens où elle veut montrer comment ne pas comprendre l’assentiment, pour ouvrir la possibilité de l’examiner de nouveau, ce qui pourrait montrer enfin que l’ambigüité mentionnée est par conséquent l’expression du plus grand potentiel philosophique de la conception stoïcienne de la raison. (shrink)

The paper is a critical reaction to a research paper that appeared in Argumentation. It suggests that Goodman’s delineation of the concept of argument for purposes of disciplines like logic is unsatisfactory in several respects. Identifying arguments as sets of propositions is highly problematic. Moreover, Goodman’s delineation is excessively vague and it may commit us to the claim that sequences of sentences which are commonly treated as expressing arguments do not, in fact, represent arguments.

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 article deals with McTaggartś paradox of time from an ontological point of view. There are two basic approaches which are usually taken in solving McTaggartś paradox. The most commonly adopted in analytic philosophy is the rejection of the flow of time as a myth. This position leads to the extreme statement that the world is intrinsically tenseless. The other is the view that temporal passage is a genuine feature of the world and is consistent with an ontology of concrete (...) events. The author endeavours to support the latter position with a discussion of a non-spatial conception of time. This conception is based on the present being conceived as a "moving Now". (shrink)

The authors consider the important problem of creative expression of a musician-teacher for modern musical pedagogy. Based on the analysis of research literature, the content and functions of creative expression in musical and performing activities are revealed. It is characterized by the aesthetic nature of creative self-expression, internal harmony of will, emotional and intellectual intents of self-expression.

The aim of this article is to compare two models of reality construction and their applicability to explain the various effects of the digitalization process. The evolution of the constructivist ideas about reality is reconstructed in the context of the dispute among realists and constructivists, which was one of the most significant events in the epistemology and philosophy of science of the 20th century. The author points out the differences between the intellectual and the social construction of reality, and carries (...) out a comparative analysis of the philosophical theories and concepts describing the aforementioned alternatives. The intellectual construction of reality, which often takes place in theoretical physics at different stages of its development, is also analyzed. Particular consideration is given to the philosophic-scientific contexts generated by the sociology of knowledge, the theory of speech acts, and the actor-network theory. The article also shows a distinction between the construction and the constitution of reality. The constitution of reality within various types of non-theoretical thinking, fixed using the means and methods of phenomenological philosophy of science, allows identifying and describing the main contexts through which the word reality acquires significance and is endowed with meaning in the present-day intellectual and social practices. Special attention is paid to the concepts of virtual reality and digital reality. The features of the intellectual construction of virtual reality are described. The difference between the intellectual and the social construction of digital reality is substantiated as between two alternative practices, which determine the meaning, and the prospects of digitalization. This distinction may be of particular interest to those who design digital platforms and implement digitalization in various areas of human life and society, especially in as education, legal procedure, management, economics, and business. Today, when partly spontaneous, partly controlled digitalization is taking place in these spheres, the results of this study make it possible not only to understand the logic of the changes taking place but also to apply forecasting and planning methods actively, i.e., constructing the digital reality. (shrink)

This article aims to discuss the gestural character of Chopin’s pianistic writing. We will focus on the set of Etudes pour piano. We expect to show how the notion of musical expression in Romanticism is dependent of a notion of expressive body always in the limit of decomposition. This could show us how musical expression is a privileged space for a better understanding of the dialectical relationship between form and formless.

The purpose of the study is to reveal the essential content of the digital environment for the provision of medical services. The article discusses various scientific approaches to the formation and development of the digital health care environment. Scientific novelty lies in the substantiation of the definition of a digital environment for the provision of medical services, which will allow developing a scientific and methodological approach to designing a digital ecosystem for the development of the regional economy based on increasing (...) the level of health preservation of citizens. As a result, the strategic directions for the development of the digital environment for the provision of medical services were identified, reflecting the global trends in the development of digital health. (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)

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.