In today's world, the problems of culture have become world problems, as are those of the protection of the environment, the rational use of natural resources, the demographic situation, international disarmament and the prevention of war. We speak of a “cultural explosion” with regard to the very lively interest that culture arouses today and the increasing needs in this area. We can expect this development to continue, but what is the social significance of the process? What is its origin? To (...) what is it connected? (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)

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)

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)

The work aims to demonstrate that at the heart of Eriugena’s approach to Christian theology there lies a profoundly philosophical interest in the necessity of a cardinal shift in the paradigms of thinking – namely, that from the metaphysical to the dialectical one, which wins him a reputation of the ‘Hegel of the ninth century,’ as scholars in Post-Hegelian Germany called him. The prime concern of Eriugena’s discourse is to prove that the actual adoption of the salvific truth of Christ’s (...) revelation about all humans’ Sonship to God directly depends on the way the truth of God’s Oneness is consistently thought of. It is exactly the dialectic of the universal and particular which allows Eriugena both to tackle the dichotomy between being and non-being and to proceed towards raising a question how the totality of God’s being can be approached so as to let him radically reconsider a predominantly metaphysical view of creation the theological reflection traditionally relies on. According to the dialectical understanding of unity that Eriugena does adhere to, the reality of creation cannot be thought of, and therefore known, otherwise than in the way of being inseparable from the universal Principle of all. This is the Principle abandoned by nothing, unless the mind corrupted by the senses thinks otherwise and, following the metaphysical pattern of dichotomy, improperly sets the creation and its Principle apart. Restoration of the mind to the proper rational motion of recta ratio freed, as Eriugena argues, from the dictates of senses therefore becomes the way of both the epistemological breakthrough to the infinite whole and practical return from the world of finite things to living in the divine reality of creation. The work’s argument is based on the assumption of close affinity between Eriugena’s discourse and that of his Islamic contemporaries, who developed their dialectical ideas within the Mu’tazilah tradition of a philosophically disciplined approach to the truth of God’s Oneness. In particular, al-Nazzam’s engagement with Parmenides’ Periphyseon and his resistance to the danger of a dualistic interpretation of its ontology seem to provoke Eriugena’s innovative approach to Christian theology with a view to suggesting a mode of overcoming dualism as the main obstacle on the way to the Truth revealed. This vision of the meaning of Eriugena’s undertaking allows us not only to better understand the novelty of his approach to Christian theology, but also reconsider some of the key points of his discourse that seem to have become a sort of commonplace in Eriugenian studies: 1. Unlike the prevalent opinion, not the forms of the division of Nature but the modes of interpreting being and non-being are to be understood to constitute the genuine subject-matter of each book of the Periphyseon and, hence, of the five parts of his system. 2. The fourfold division of Nature is to be interpreted not as a basic structure of the system offered by Eriugena, but as a means of introducing dialectic to the body of theology by refuting Augustine’s metaphysical vision of a hierarchical model of the universe and indicating the way of resolution of the cardinally theological contradiction – God does and does not create at the same time. 3. All this gives reason to disagree with a general tendency of associating Eriugena’s work with exploration of the division of God’s Nature and to reinterpret it as an immense anti-division project to be understood as an important turn in the history of Christian thought entirely focused on the truth of God’s Oneness and human life in conformity to it. *** I affirm that this thesis is entirely my own work and has not been submitted for examination in any form elsewhere. (shrink)

The author presents the previously unknown text of the outstanding Soviet philosopher and historian of science Boris Mikhailovich Hessen. The author analyzes the report of Boris M. Hessen at the Second international Congress on the history of science and technology in London (1931). He considers as well some published works of B.M. Hessen, mainly his book on the philosophical interpretation of the theory of relativity. He argues that it is time to start introducing unpublished texts by B.M. Hessen into scientific (...) circulation. This will make the study of his work more thorough and increase the reliability of conclusions made by specialists in Hessen’s legacy. This publication offers the reader the text of B.M. Hessen, extracted from the archive: the report of B.M. Hessen at a meeting of the Presidium of the Communist Academy about the trip to the London Congress. (shrink)

The restoration of "forgotten" names to the bosom of our culture is a natural and necessary accompaniment of the political freedom beginning to make its way in our country. Free and continuous creativity is being reunited with the reader, the listener, and the participant, who had been tragically alienated from it. Our half-knowledge, intellectual arbitrariness, and opportunism are becoming clearer, more acute, and more shameful. All this is an inevitable accompaniment of one of the most prestigious and, it would seem, (...) least labor consuming trends in contemporary publishing and journal policy. The publication of texts of Russian philosophers has marked journals as different in character and mission as Novyi mir, Voprosy filosofii, Literaturnaia ucheba, Druzhba narodov, Volga, and many others. In most cases they are more or less well known works reprinted from the YMCA Press, equipped with prefaces—some better, some worse—and devoid of any sort of real intellectual commentary. (shrink)

The present study aims to elucidate whether insight problem solving could be facilitated by the cognitive component of humour. The authors take interest in whether the logical mechanisms of humour can affect how fast insight problems are solved. To that end, the authors conducted two experiments where participants solved insight problems after watching visual humorous stimuli such as videos and slideshows. The first experiment demonstrated the overall impact of facilitation by humour on insight problem solving; however, it did not show (...) any difference in how particular logical mechanisms of humour affect the solution time of insight problems. The second experiment showed that the cognitive component of humour could selectively affect insight problems whose difficulty stems from different sources. These results suggest that the cognitive component of humour, when operationalised as logical mechanisms and schema switching, contributes to solving insight problems. (shrink)

This article examines a still contentious question: how conservative and liberal elements are combined in Boris N. Chicherin’s worldview and political doctrine. It considers several points of view...

The basic tendencies in the conceptual history of the 'subject' within Russian intellectual history are presented. This backgrounds a closer analysis of S. Trubetskoj's concept of 'conciliar consciousness', including the problems and aporiae connected with it. It will be shown that and how this conception depends on assumptions from prekantian metaphysics and therefore ignores the Kantian account of subjectivity.

The basic tendencies in the conceptual history of the 'subject' within Russian intellectual history are presented. This backgrounds a closer analysis of S. Trubetskoj's concept of 'conciliar consciousness', including the problems and aporiae connected with it. It will be shown that and how this conception depends on assumptions from prekantian metaphysics and therefore ignores the Kantian account of subjectivity.

We prove here that the intuitionistic theory $T_{0}\upharpoonright + UMID_{N}$ , or even $EEJ\upharpoonright + UMID_{N}$ , of Explicit Mathematics has the strength of $\prod_{2}^{1} - CA_{0}$ . In Section I we give a double-negation translation for the classical second-order $\mu-calculus$ , which was shown in [ $M\ddot{o}02$ ] to have the strength of $\prod_{2}^{1}-CA_{0}$ . In Section 2 we interpret the intuitionistic $\mu-calculus$ in the theory $EETJ\upharpoonright + UMID_{N}$ . The question about the strength of monotone inductive definitions in (...) $T_{0}$ was asked by S. Feferman in 1982, and - assuming classical logic - was addressed by M. Rathjen. (shrink)

An instance of Stratified Comprehension ∀x₁ … ∀x n ∃y∀x (x ∈ y ↔ φ(x, x₁, …, x n )) is called strictly impredicative iff, under minimal stratification, the type of x is 0. Using the technology of forcing, we prove that the fragment of NF based on strictly impredicative Stratified Comprehension is consistent. A crucial part in this proof, namely showing genericity of a certain symmetric filter, is due to Robert Solovay. As a bonus, our interpretation also satisfies some (...) instances of Stratified Comprehension which are not strictly impredicative. For example, it verifies existence of Frege natural numbers. Apparently, this is a new subsystem of NF shown to be consistent. The consistency question for the whole theory NF remains open (since 1937). (shrink)

Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a 'definable quotient group' U/L, for some convex V-definable subgroup U of 〈Mⁿ, +〉 and a lattice L of rank n. As two consequences, we derive Pillay's conjecture (...) for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L. (shrink)

On peut distinguer trois cas de correspondances différentes entre les « scénarios schématiques » et le domaine narratif folklorico-littéraire : 1. La narration constitue la projection de la « dramaturgie de la vie » (une telle projection n’est évidemment ni directe ni complète) ;2. La structure de l’univers des personnages et la structure événementielle du narratif influencent la formation des « scénarios de la vie », en conditionnant l’apparence morphologico-compositionnelle de l’un et de l’autre ;3. La coincidence de la « (...) dramaturgie de la vie » et de la « dramaturgie de la narration»s’explique par le fait qu’elles ont des sources communes ; ces sources pourraient être les modèles mentaux de la tradition, qui dictent à un homme des « règles de comportement » d’une part, et qui s’incarnent dans la narration folklorico-littéraire d’autre part. Le « scénario schématique » possède une structure événementielle, situationnelle et actantielle. À cette structure correspond un certain niveau d’interprétation qui souvent la lie directement à la conscience religieuse et mythologique ; une telle conscience — compte tenu du fait qu’une conceptualisation globale de tous les aspects de la vie humaine caractérise le mythe — englobe, par sa nature même, les « blocs interprétatifs » pertinents pour pratiquement tous les précédents événementiels. Le « scénario schématique » est donc lié au domaine des croyances et concepts actuels, lié aussi aux systèmes de valeurs et normes éthiques, etc. ; il est possible de reconstituer nombre de ces croyances, concepts, valeurs et normes à l’aide de l’histoire vécue qui nous occupe. D’ordinaire, ces interprétations ne représentent pas le fond neutre des événements, mais un élément actif et dynamique qui agit directement sur le développement de ces événements. (shrink)

We discuss a phenomenon that appears when ‘even’ occurs in questions. Specifically, an inference of what we call “extreme ignorance” is projected onto the speaker. We argue that this effect arises when the known unlikelihood ‘even’ focuses an entire question, resulting in the focused question being the least likely to be asked. Specific implicatures then conspire to bring about the inference that the speaker does not know the answer to the question that is most expected to be known. The environments (...) explored are Wh-questions and Y/N questions, and the languages looked at primarily English, Greek, German and Russian. (shrink)

We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.

§1. Introduction. By and large, definitions of a differentiable structure on a set involve two ingredients, topology and algebra. However, in some cases, partial information on one or both of these is sufficient. A very simple example is that of the field ℝ where algebra alone determines the ordering and hence the topology of the field:In the case of the field ℂ, the algebraic structure is insufficient to determine the Euclidean topology; another topology, Zariski, is associated with the ield but (...) this will be too coarse to give a diferentiable structure.A celebrated example of how partial algebraic and topological data determines a differentiable structure is Hilbert's 5th problem and its solution by Montgomery-Zippin and Gleason.The main result which we discuss here is of a similar flavor: we recover an algebraic and later differentiable structure from a topological data. We begin with a linearly ordered set ⟨M, <⟩, equipped with the order topology, and its cartesian products with the product topologies. We then consider the collection of definable subsets of Mn, n = 1, 2, …, in some first order expansion ℳ of ⟨M, <⟩. (shrink)

Computability theorists have introduced multiple hierarchies to measure the complexity of sets of natural numbers. The Kleene Hierarchy classifies sets according to the first-order complexity of their defining formulas. The Ershov Hierarchy classifies Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^0_2$$\end{document} sets with respect to the number of mistakes that are needed to approximate them. Biacino and Gerla extended the Kleene Hierarchy to the realm of fuzzy sets, whose membership functions range in a complete lattice L. In (...) this paper, we combine the Ershov Hierarchy and fuzzy set theory, by introducing and investigating the Fuzzy Ershov Hierarchy. In particular, we focus on the fuzzy n-c.e. sets which form the finite levels of this hierarchy. Intuitively, a fuzzy set is n-c.e. if its membership function can be approximated by changing monotonicity at most n-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n-1$$\end{document} times. We prove that the Fuzzy Ershov Hierarchy does not collapse; that, in analogy with the classical case, each fuzzy n-c.e. set can be represented as a Boolean combination of fuzzy c.e. sets; but that, contrary to the classical case, the Fuzzy Ershov Hierarchy does not exhaust the class of all Δ20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varDelta ^0_2$$\end{document} fuzzy sets. (shrink)

The problem of the article is based on a long tradition of studying the category ‘antinomy‘ in the history of philosophy from antiquity until the early twentieth century. Antinomical thinking has particular importance for the spiritual life in the 20th century. The author draws attention to the fact that, for example, in the poetry of Thomas Stern Eliot antinomies and paradoxes are of philosophical and religious nature especially in then dealing with questions of reaching the Truth by rational way exclusively. (...) The basic material for studies are the works of modern Russian poets Olesya Nikolaeva, Sergei Kruglov, Timur Kibirov, Olga Sedakova and Helen Schwartz. It is shown how moral and philosophical themes and descriptions of the spiritual lives of the characters associated with the interpretation of ideas of compositions in the form of antinomies. The idea of the influence of the antinomies of thinking on aesthetics and system of images of Russian poets verses is justified. Article reveals the originality of each of the poets whose poems are analyzed in the work. The author concludes that modern poetry gives traditional antinomies personal psychological nature, but at the same time, problems and poetics of paradox are in tune with thinking of twentieth century as a whole - with its disastrous spirit, full of doubt and contradiction. (shrink)

Various connexive FDE-based modal logics are studied. Some of these logics contain a conditional that is both connexive and strict, thereby highlighting that strictness and connexivity of a conditional do not exclude each other. In particular, the connexive modal logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, cKN4, scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, cMBL, and scMBL are introduced semantically by means of classes of Kripke models. The logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} (...) \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document} and cKN4 are connexive variants of the FDE-based modal logics BK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document} and KN4 with a weak and a strong implication, respectively. The system cMBL is a connexive variant of the modal bilattice logic MBL. The latter is a modal extension of Arieli and Avron’s logic of logical bilattices and is characterized by a class of Kripke models with a four-valued accessibility relation. In the systems scBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}, scKN4, and scMBL, the conditional is both connexive and strict. Sound and complete tableau calculi for all these logics are presented and used to show that the entailment relations of the systems under consideration are decidable for finite premise set. Moreover, the logics cBK-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cBK}^-$$\end{document} and cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} are shown to be algebraizable. The algebraizability of cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} is derived from proving cMBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {cMBL}$$\end{document} to be definitionally equivalent to MBL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {MBL}$$\end{document}. All connexive modal logics studied in this paper are decidable, paraconsistent, and inconsistent but non-trivial logics. (shrink)

Neuroscience has established several brain pathways that process visual information. Distinct neural circuits analyze body appearance and movement providing information about the person’s cognitive and emotional states. The activity of the pathways depends on the salience of visual stimuli for the organism in the given circumstances. Since ballet performances are not among the crucial events for the viewer’s organism, not all viewers perceive and interpret bodily signs that express the mental state of the dancer. Treatment of the dancer as close (...) other activates the neural circuits that elaborate emotions, this enables the viewer to feel the internal state of the dancer and enrich the interpretation of the scenic action. (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)

Why does the theory of law have such a significant role in Russian liberalism, and how is this related to the state of the legal system in Russia and to the public’s legal consciousness? This intro...