The responsibility of the subjects is the most important basis of the social life. Recurrences of irresponsible behaviour on the all levels of the modern society do the problem of the purposeful cultivation of the liberty and the morality to be more actual nowadays. The liberty and the morality realized by any personality become the prerequisites of the responsibility that are so necessary for the society. Became the true reality the responsibility provides the sustainable reproduction of all system of feelings, (...) convictions and actions and raises the liberty to the higher and more deliberate stage. Responding to the changes of the time the philosophy has to be urged to clarify the idea of the closing of the social anthropology, aksiologiya and ethics. (shrink)

The question of constructing an evolutionary picture of the world based on the results obtained by extending classical mechanics is considered. The expansion of mechanics arose as a result of taking into account the role of the structure of bodies in their dynamics. It is shown that such an extension leads to the possibility of combining branches of physics, in particular, to the substantiation of the laws of thermodynamics, statistical physics, kinetics within the framework of the laws of classical mechanics. (...) It turned out that, according to the laws of classical mechanics, matter is infinitely divisible and can be represented by an infinite hierarchical structure from simple to complex. The expansion showed the existence of universal principles connecting the laws of the upper rung of the hierarchical ladder of matter with the laws of the lower rung. It is considered how they lead to the possibility of constructing a picture of the world based on the fundamental laws of nature. (shrink)

In 1933 Godel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. In this paper we give a solution to this problem. We find the logic LP of propositions and proofs and show that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic propositional logic Int via classical proofs and provides a Brouwer-Heyting-Kolmogorov style provability semantics for Int which (...) resisted formalization since the early 1930s. LP may be regarded as a unified underlying structure for intuitionistic, modal logics, typed combinatory logic and λ-calculus. (shrink)

We describe a general logical framework, Justification Logic, for reasoning about epistemic justification. Justification Logic is based on classical propositional logic augmented by justification assertions t: F that read t is a justification for F. Justification Logic absorbs basic principles originating from both mainstream epistemology and the mathematical theory of proofs. It contributes to the studies of the well-known Justified True Belief vs. Knowledge problem. We state a general Correspondence Theorem showing that behind each epistemic modal logic, there is a (...) robust system of justifications. This renders a new, evidence-based foundation for epistemic logic. As a case study, we offer a resolution of the GoldmanRed Barns in Justification Logic. Furthermore, we formalize the well-known Gettier example and reveal hidden assumptions and redundancies in Gettier’s reasoning. (shrink)

In this paper individual proofs are integrated into provability logic. Systems of axioms for a logic with operators “A is provable” and “p is a proof of A” are introduced, provided with Kripke semantics and decision procedure. Completeness theorems with respect to the arithmetical interpretation are proved.

We outline an intuitionistic view of knowledge which maintains the original Brouwer–Heyting–Kolmogorov semantics for intuitionism and is consistent with the well-known approach that intuitionistic knowledge be regarded as the result of verification. We argue that on this view coreflectionA→KAis valid and the factivity of knowledge holds in the formKA→ ¬¬A‘known propositions cannot be false’.We show that the traditional form of factivityKA→Ais a distinctly classical principle which, liketertium non datur A∨ ¬A, does not hold intuitionistically, but, along with the whole of (...) classical epistemic logic, is intuitionistically valid in its double negation form ¬¬(KA¬A).Within the intuitionistic epistemic framework the knowability paradox is resolved in a constructive manner. We argue that this paradox is the result of an unwarranted classical reading of constructive principles and as such does not have the consequences for constructive foundations traditionally attributed it. (shrink)

Justification Logic provides an axiomatic description of justifications and delegates the question of their nature to semantics. In this note, we address the conceptual issue of the logical type of justifications: we argue that justifications in the logical setting are naturally interpreted as sets of formulas which leads to a class of epistemic models that we call modular models . We show that Fitting models for Justification Logic naturally encode modular models and can be regarded as convenient pre-models of the (...) former. (shrink)

Within the article the attempt is made to study the perception of the XVIII century philosopher Hryhorii Skovoroda’s image and its philosophy through the prism of the later national identities. The fact is stressed that the statement of the issue concerning the Hryhorii Skovoroda’s image Ukrainization and the history of its solution turns out to be the consequence of the process of establishing the Ukrainian modern self-identity which started in the ХІХ century. The situation is emphasized that within “all-Russian” identity (...) one can come across its three variations: Skovoroda is a “Russian” (meaning “all-Russian”); Skovoroda is a “Malorussian” (meaning a representative of a regional variant of a “Russian” identity) and Skovoroda is a “Ukrainian” (meaning a native from the land that is called Ukraine). At the end of the ХІХ century Skovoroda’s image was interpreted within Ukrainian personal identity. The conclusion is made that during ХІХ—ХХ centuries and even nowadays two national identities for Skovoroda’s personality remain relevant: Ukrainian and Russian. The Russian one is a result of the XVIII—XIX centuries “all-Russian” syncretism state being transferred into the modern particular Russian national self-identity. The process of Hryhorii Skovoroda’s image Ukrainization (in other words its extraction from the “all-Russian” context) developed through several stages. At the beginning of the ХІХ century he was “Ukrainian” because he had a Ukrainian territorial identity and was related to Slobidska-Ukrainian province. Later he became “Ukrainian” because he represented “simple” Ukrainian people. Finally he is “Ukrainian” because he belongs to the Ukrainian ethnic nation and therefore his philosophy belongs to Ukrainian philosophical culture. (shrink)

In this paper, we provide a semantic analysis of the well-known knowability paradox stemming from the Church–Fitch observation that the meaningful knowability principle /all truths are knowable/, when expressed as a bi-modal principle F --> K♢F, yields an unacceptable omniscience property /all truths are known/. We offer an alternative semantic proof of this fact independent of the Church–Fitch argument. This shows that the knowability paradox is not intrinsically related to the Church–Fitch proof, nor to the Moore sentence upon which it (...) relies, but rather to the knowability principle itself. Further, we show that, from a verifiability perspective, the knowability principle fails in the classical logic setting because it is missing the explicit incorporation of a hidden assumption of /stability/: ‘the proposition in question does not change from true to false in the process of discovery.’ Once stability is taken into account, the resulting /stable knowability principle/ and its nuanced versions more accurately represent verification-based knowability and do not yield omniscience. (shrink)

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that are simple enough. This contradiction points to the fruitlessness of trying to solve the Logical Omniscience Problem qualitatively if the rationality of agents is to be maintained. We provide a (...) quantitative solution to the problem compatible with the two important facets of the reasoning agent: rationality and resource boundedness. More precisely, we provide a test for the logical omniscience problem in a given formal theory of knowledge. The quantitative measures we use are inspired by the complexity theory. We illustrate our framework with a number of examples ranging from the traditional implicit representation of knowledge in modal logic to the language of justification logic, which is capable of spelling out the internal inference process. We use these examples to divide representations of knowledge into logically omniscient and not logically omniscient, thus trying to determine how much information about the reasoning process needs to be present in a theory to avoid logical omniscience. (shrink)

Saul Aaron Kripke, the most influential philosopher and logician of his generation, died on September 15, 2022, at the age of 81.

The paper proves a predicate version of Solovay's well-known theorem on provability interpretations of modal logic: If a closed modal predicate-logical formula R is not valid in some finite Kripke model, then there exists an arithmetical interpretation f such that $PA \nvdash fR$ . This result implies the arithmetical completeness of arithmetically correct modal predicate logics with the finite model property (including the one-variable fragments of QGL and QS). The proof was obtained by adding "the predicate part" as a specific (...) addition to the standard Solovay construction. (shrink)

The author analyzes the transformations of Hellenic theologys content and forms in the epoch of early antique classics. The general orientation of such transformations is the generalization of mythological gods meanings into the abstract implications of the Absolute, which is not yet sacral in its full sense and not transcendent. Besides, this period is the end of the decentralization of consciousness. Cognitive limitations to the development of abstract conceptual thinking and the rational component of consciousness are removed. This processs main (...) points transform mythology into artistic and aesthetic creativity, religious consciousness, and theology. Rationalism is always critical. Critical rationalism inevitably leads to historicism. Therefore, the formation of a historical attitude strengthens at the sight of the critical approach. The world's mythological image is increasingly being questioned. Its content is being transferred to the past. Finally, the era of early classicism comes into play. It is a time when theology becomes a field of philosophical and theoretical reflection on myth and an area of its artistic and aesthetic experience. The most influential form of such an understanding of myth was the theater. The ancient theater served as a spiritual and practical form of ancient theology, a subject embodiment of theology in stage action. (shrink)

The language of the basic logic of proofs extends the usual propositional language by forming sentences of the sort x is a proof of F for any sentence F. In this paper a complete axiomatization for the basic logic of proofs in Heyting Arithmetic HA was found.

In the late nineteenth and early twentieth centuries the need to rethink the status of space and time which Kant considered to be a priori forms of sensibility was prompted by the emergence of new approaches to the methodology of scientific cognition. In neo-Kantian interpretation these cognitive forms acquire a special epistemological status, manifesting themselves in theoretical research as “pre-given” foundations of knowledge. It seems necessary to conduct a comparative analysis of two interconnected neo-Kantian concepts, of Hermann Cohen and Ivan (...) Lapshin. Studying Kant’s philosophy since his student days, Lapshin gradually came to the conclusion that the need to clarify and develop Kant’s transcendental method was dictated by the development of scientific knowledge. Indeed, the works of the Russian neo-Kantian contain echoes and polemical adjustments of Cohen’s spatio-temporal ideas. Our study has revealed common epistemological attitudes in Cohen and Lapshin: the wish to improve elements of Kantian philosophy, adjusting them to prove the possibility of scientific-theoretical cognition and of overcoming psychologism and developing the logicistic approach to the critique of cognition. Each of the two authors developed their own “mechanism” of reducing space and time to a range of intellectual procedures for the construction of the object of knowledge. In Cohen’s account space and time pre-establish the language of observation and found all scientific-theoretical work. Lapshin, on the other hand, in discussing the formal and substantive features of these categories (the introduction of “axioms” of time, the need to specify the concepts of time and space through other categories), notes that their use in scientific judgment implies an epistemological givenness of the concept of the object. This I see as a variant of solving one and the same epistemological task. I submit that Lapshin worked out an independent concept of space and time as cognitive forms that are congruent with the spirit of European neo-Kantianism and contemporary science. (shrink)

This article exposes criterial bases of the development of social quality in the USSR and Russia. The causes of the increased volatility of the state-monopoly capitalism emerging in Russia from the 1990s and in the first decade of the twenty-first century are analyzed. Characteristics of social quality such as a high proportion of low-paid employees, a low standard of living and a high economic inequality are considered. The impact of the precarity of employment on these processes is demonstrated. Risk factors (...) of precarity of employment such as type of labor contract, form of employment, working conditions and wages (in particular, volatility and discreteness of payments) are analyzed. The evaluation of scale of the precarity of employment in the formal sector in Russia is made; the distribution of workers in precarity of employment by kinds of economic activity and the deviation of their average wages are introduced. Overcoming the instability of development is linked to the transition to a society of people-humanistic socialism. (shrink)

We introduce reference structures — a basic mathematical model of a data organization capable of storing and utilizing information about its addresses. A propositional labeled modal language is used as a specification and programming language for reference structures; the satisfiability algorithm for modal language gives a method of building and optimizing reference structures satisfying a given formula. Corresponding labeled modal logics are presented, supplied with cut free axiomatizations, completeness and decidability theorems are proved. Initialization of typed variables in some programming (...) languages is presented as an example of a reference structure building. (shrink)

This book is not only a major twentieth-century contribution to Dostoevsky’s studies, but also one of the most important theories of the novel produced in our century. As a modern reinterpretation of poetics, it bears comparison with Aristotle.“Bakhtin’s statement on the dialogical nature of artistic creation, and his differentiation of this from a history of monological commentary, is profoundly original and illuminating. This is a classic work on Dostoevsky and a statement of importance to critical theory.” Edward Wasiolek“Concentrating on the (...) particular features of ‘Dostoevskian discourse,’ how Dostoevsky structures a hero and a plot, and what it means to write dialogically, Bakhtin concludes with a major theoretical statement on dialogue as a category of language. One of the most important theories of the novel in this century.” The Bloomsbury Review. (shrink)

We present a general classification of the conditions under which cognitive science, concerned, e.g. with decision making, requires the use of quantum theoretical notions. The analysis is done in the frame of the mathematical approach based on the theory of quantum measurements. We stress that quantum effects in cognition can arise only when decisions are made under uncertainty. Conditions for the appearance of quantum interference in cognitive sciences and the conditions when interference cannot arise are formulated.

In this paper the modal operator "x is provable in Peano Arithmetic" is incorporated into first-order theories. A provability extension of a theory is defined. Presburger Arithmetic of addition, Skolem Arithmetic of multiplication, and some first order theories of partial consistency statements are shown to remain decidable after natural provability extensions. It is also shown that natural provability extensions of a decidable theory may be undecidable.

The principle motivation of this work is to display the sense in which the epistemic reading of a Kripke model tacitly requires common knowledge of the model, CKM. This requirement significantly restricts the amount of epistemic situations we are able to consider. We explore possible worlds epistemic models in a general setting without CKM assumptions and show that such models can be identified with observable substructures of Kripke models. We argue that such observable models offer a new level of generality (...) and conceptual clarity in epistemic modeling. Similar analysis applies to intuitionistic models. (shrink)

This book provides an invaluable overview of the reach of logic. It provides reference to some of the most important, well-established results in logic, while at the same time offering insight into the latest research issues in the area. It also has a balance of theory and practice, containing essays in the areas of modal logic, intuitionistic logic, logic and language, nonmonotonic logic and logic programming, temporal logic, logic and learning, combination of logics, practical reasoning, logic and artificial intelligence, abduction, (...) theorem proving and goal-directed reasoning. It will be invaluable reading for researchers and graduate students in logic and computer science, and a fabulous source of inspiration for research students in search of a topic for a PhD in logic and theoretical computer science. (shrink)

This research provides an analysis of the role of ‘natural consciousness’ and ‘absolute knowledge’ in the process of establishing the notion of philosophy in Hegel’s The Phenomenology of Spirit. The author seeks to show that ‘natural consciousness’ does not disappear in the first approaches to The Phenomenology, but rather, it continues to act as the subject of the ‘experience of consciousness’ until the end. The material analysis directly related to the evolution of ‘natural consciousness’ in the first stages of ‘experience’ (...) particularly supports the hypothesis about the philosopher’s work on the book. The results obtained can be seen as a validation of the idea that the usual notions of overcoming ‘natural consciousness’ already in the first ‘experiences of consciousness’ do not correspond to its fundamental role in establishing the notion of philosophy in The Phenomenology of Spirit. It represents not only the starting point of the phenomenological movement but it is also involved in the ‘reversals of consciousness’ at every stage of the ‘experience,’ which is important to take into account for the correct evaluation of the specificity of The Phenomenology of Spirit and the comprehension of the nature of philosophical knowledge as the main result of this Hegelian work. (shrink)

The importance of the topic of the article lies in the fact that in our time there is a need for innovation of the educational process, the use of innovations in teacher self-training is therefore important teacher self-education in a pedagogical context. The purpose of the article is the need to explore and substantiate the importance of teacher self-education in a pedagogical post-historical context. The article provides a theoretical foundation of the concepts of self-education and self-development of the teacher in (...) the pedagogical context the conditions of the effectiveness of self-education of teachers in the current system of education are highlighted; the structure of readiness for self-education of teachers in a postmodern society, as the present period of modernization of education, undergoing reforms of different parties, makes higher demands on the professional competence of teachers is presented. Today it will be obvious that society needs a constantly learning mobile teacher and his improvement of personal and professional qualities. It is important to note that the training of a teacher who meets the requirements of today's professional activity is continuous, not continuous only during basic training, but also during continuing education courses and self-study, because the knowledge and skills acquired at university are no longer sufficient to solve new school problems. (shrink)

Dynamic topological logic provides a context for studying the confluence of the topological semantics for S4, topological dynamics, and temporal logic. The topological semantics for S4 is based on topological spaces rather than Kripke frames. In this semantics, is interpreted as topological interior. Thus S4 can be understood as the logic of topological spaces, and can be understood as a topological modality. Topological dynamics studies the asymptotic properties of continuous maps on topological spaces. Let a dynamic topological system be a (...) topological space X together wError: Corrupted memory profileError: read ICCBased color space profile errorith a continuous function f. f can be thought of in temporal terms, moving the points of the topological space from one moment to the next. Dynamic topological logics are the logics of dynamic topological systems, just as S4 is the logic of topological spaces. Dynamic topological logics are defined for a trimodal language with an S4-ish topological modality, and two temporal modalities, and ∗, both interpreted using the continuous function. (shrink)

ABSTRACT In 1933 Gödel introduced an axiomatic system, currently known as S4, for a logic of an absolute provability, i.e. not depending on the formalism chosen ([God 33]). The problem of finding a fair provability model for S4 was left open. The famous formal provability predicate which first appeared in the Gödel Incompleteness Theorem does not do this job: the logic of formal provability is not compatible with S4. As was discovered in [Art 95], this defect of the formal provability (...) predicate can be bypassed by replacing hidden quantifiers over proofs by proof polynomials in a certain finite basis. The resulting Logic of Proofs enjoys a natural arithmetical semantics and provides an intended provability model for S4, thus answering a question left open by Gödel in 1933. Proof polynomials give an intended semantics for some other constructions based on the concept of provability, including intuitionistic logic with its Brouwer- Heyting- Kolmogorov interpretation, ?-calculus and modal ?-calculus. In the current paper we demonstrate how the intuitionistic propositional logic Int can be directly realized by proof polynomials. It is shown, that Int is complete with respect to this proof realizability. (shrink)

Justification Logic is a family of epistemic logical systems obtained from modal logics of knowledge by adding a new type of formula t:F, which is read t is a justification for F. The principal epistemic modal logic S4 includes Tarski’s well-known topological interpretation, according to which the modality 2X is read the Interior of X in a topological space (the topological equivalent of the ‘knowable part of X’). In this paper, we extend Tarski’s topological interpretation from S4 to Justification Logic (...) systems with both modality and justification assertions. The topological semantics interprets t:X as a reachable subset of X (the topological equivalent of ‘test t confirms X’). We establish a number of soundness and completeness results with respect to Kripke topology and the real topology for S4-based systems of Justification Logic. (shrink)