A Turing degreedis the degree of categoricity of a computable structure${\cal S}$ifdis the least degree capable of computing isomorphisms among arbitrary computable copies of${\cal S}$. A degreedis the strong degree of categoricity of${\cal S}$ifdis the degree of categoricity of${\cal S}$, and there are computable copies${\cal A}$and${\cal B}$of${\cal S}$such that every isomorphism from${\cal A}$onto${\cal B}$computesd. In this paper, we build a c.e. degreedand a computable rigid structure${\cal M}$such thatdis the degree of categoricity of${\cal M}$, butdis not the strong degree of categoricity (...) of${\cal M}$. This solves the open problem of Fokina, Kalimullin, and Miller [13].For a computable structure${\cal S}$, we introduce the notion of the spectral dimension of${\cal S}$, which gives a quantitative characteristic of the degree of categoricity of${\cal S}$. We prove that for a nonzero natural numberN, there is a computable rigid structure${\cal M}$such that$0\prime$is the degree of categoricity of${\cal M}$, and the spectral dimension of${\cal M}$is equal toN. (shrink)

We work with weakly precomplete equivalence relations introduced by Badaev. The weak precompleteness is a natural notion inspired by various fixed point theorems in computability theory. Let E be an equivalence relation on the set of natural numbers $$\omega $$, having at least two classes. A total function f is a diagonal function for E if for every x, the numbers x and f(x) are not E-equivalent. It is known that in the case of c.e. relations E, the weak precompleteness (...) of E is equivalent to the lack of computable diagonal functions for E. Here we prove that this result fails already for $$\Delta ^0_2$$ equivalence relations, starting with the $$\Pi ^{-1}_2$$ level. We focus on the Turing degrees of possible diagonal functions. We prove that for any noncomputable c.e. degree $${\textbf{d}}$$, there exists a weakly precomplete c.e. equivalence E admitting a $${\textbf{d}}$$ -computable diagonal function. We observe that a Turing degree $${\textbf{d}}$$ can compute a diagonal function for every $$\Delta ^0_2$$ equivalence relation E if and only if $${\textbf{d}}$$ computes $${\textbf{0}}'$$. On the other hand, every PA degree can compute a diagonal function for an arbitrary c.e. equivalence E. In addition, if $${\textbf{d}}$$ computes diagonal functions for all c.e. E, then $${\textbf{d}}$$ must be a DNC degree. (shrink)

The survey contains a detailed discussion of methods and results in the new emerging area of online “punctual” structure theory. We also state several open problems.

A structure is automatic if its domain, functions, and relations are all regular languages. Using the fact that every automatic structure is decidable, in the literature many decision problems have been solved by giving an automatic presentation of a particular structure. Khoussainov and Nerode asked whether there is some way to tell whether a structure has, or does not have, an automatic presentation. We answer this question by showing that the set of Turing machines that represent automata-presentable structures is ${\rm{\Sigma (...) }}_1^1 $-complete. We also use similar methods to show that there is no reasonable characterisation of the structures with a polynomial-time presentation in the sense of Nerode and Remmel. (shrink)

We prove an effective version of the Lopez-Escobar theorem for continuous domains. Let $Mod(\tau )$ be the set of countable structures with universe $\omega $ in vocabulary $\tau $ topologized by the Scott topology. We show that an invariant set $X\subseteq Mod(\tau )$ is $\Pi ^0_\alpha $ in the Borel hierarchy of this topology if and only if it is definable by a $\Pi ^p_\alpha $ -formula, a positive $\Pi ^0_\alpha $ formula in the infinitary logic $L_{\omega _1\omega }$. As (...) a corollary of this result we obtain a new pullback theorem for positive computable embeddings: Let $\mathcal {K}$ be positively computably embeddable in $\mathcal {K}'$ by $\Phi $, then for every $\Pi ^p_\alpha $ formula $\xi $ in the vocabulary of $\mathcal {K}'$ there is a $\Pi ^p_\alpha $ formula $\xi ^{*}$ in the vocabulary of $\mathcal {K}$ such that for all $\mathcal {A}\in \mathcal {K}$, $\mathcal {A}\models \xi ^{*}$ if and only if $\Phi (\mathcal {A})\models \xi $. We use this to obtain new results on the possibility of positive computable embeddings into the class of linear orderings. (shrink)

Computably enumerable equivalence relations received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility \. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the \ case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by \ on the \ equivalence relations. (...) A special focus of our work is on the existence of infima and suprema of c-degrees. (shrink)

We investigate effective categoricity for polymodal algebras. We prove that the class of polymodal algebras is complete with respect to degree spectra of nontrivial structures, effective dimensions, expansion by constants, and degree spectra of relations. In particular, this implies that every categoricity spectrum is the categoricity spectrum of a polymodal algebra.

A major theme in the study of degree structures of all types has been the question of the decidability or undecidability of their first order theories. This is a natural and fundamental question that is an important goal in the analysis of these structures. In this paper, we study decidability for theories of upper semilattices that arise from the theory of numberings. We use the following approach: given a level of complexity, say \, we consider the upper semilattice \ of (...) all \-computable numberings of all \-computable families of subsets of \. We prove that the theory of the semilattice of all computable numberings is computably isomorphic to first order arithmetic. We show that the theory of the semilattice of all numberings is computably isomorphic to second order arithmetic. We also obtain a lower bound for the 1-degree of the theory of the semilattice of all \-computable numberings, where \ is a computable successor ordinal. Furthermore, it is shown that for any of the theories T mentioned above, the \-fragment of T is hereditarily undecidable. Similar results are obtained for the structure of all computably enumerable equivalence relations on \, equipped with composition. (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)

Limitwise monotonic sets and functions constitute an important tool in computable structure theory. We investigate limitwise monotonic numberings. A numbering ν of a family is limitwise monotonic (l.m.) if every set is the range of a limitwise monotonic function, uniformly in k. The set of all l.m. numberings of S induces the Rogers semilattice. The semilattices exhibit a peculiar behavior, which puts them in‐between the classical Rogers semilattices (for computable families) and Rogers semilattices of ‐computable families. We show that every (...) Rogers semilattice of a ‐computable family is isomorphic to some semilattice. On the other hand, there are infinitely many isomorphism types of classical Rogers semilattices which can be realized as semilattices. In particular, there is an l.m. family S such that is isomorphic to the upper semilattice of c.e. m‐degrees. We prove that if an l.m. family S contains more than one element, then the poset is infinite, and it is not a lattice. The l.m. numberings form an ideal (w.r.t. reducibility between numberings) inside the class of all ‐computable numberings. We prove that inside this class, the index set of l.m. numberings is ‐complete. (shrink)

The paper studies Heyting algebras within the framework of computable structure theory. We prove that the class _K_ containing all Heyting algebras with distinguished atoms and coatoms is complete in the sense of the work of Hirschfeldt et al. (Ann Pure Appl Logic 115(1-3):71-113, 2002). This shows that the class _K_ is rich from the computability-theoretic point of view: for example, every possible degree spectrum can be realized by a countable structure from _K_. In addition, there is no simple syntactic (...) characterization of computably categorical members of _K_ (i.e., structures from _K_ possessing a unique computable copy, up to computable isomorphisms). (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 limit computable 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. In this paper, we combine the Ershov Hierarchy and fuzzy set (...) theory, by introducing and investigating the Fuzzy Ershov Hierarchy. (shrink)

Mereological theories are based on the binary relation “being a part of”. The systematic investigations of mereology were initiated by Leśniewski. More recent authors (including Simons, Casati and Varzi, Hovda) formulated a series of first‐order mereological axioms. These axioms give rise to a plenitude of theories, which are of great philosophical interest. The paper considers first‐order mereological theories from the point of view of computable (or effective) algebra. Following the approach of Hirschfeldt, Khoussainov, Shore, and Slinko, we isolate two important (...) computability‐theoretic properties P (namely, degree spectra of structures, and effective dimensions), and consider the following problem: for a given mereological theory T, is it true that its models can realize every possible variant of the property P? If the answer is positive, then we say that the theory T is ‐universal. We obtain the following results about known mereological theories. Any theory T which is weaker than Extensional Closure Mereology (CEM) is ‐universal. A similar fact is true for the theory GM2. On the other hand, any theory stronger that CEM + (C) + (G) is not ‐universal. In particular, General Extensional Mereology is not ‐universal. (shrink)

We investigate the complexity of embeddings between bi-embeddable structures. In analogy with categoricity spectra, we define the bi-embeddable categoricity spectrum of a structure A as the family of Turing degrees that compute embeddings between any computable bi-embeddable copies of A; the degree of bi-embeddable categoricity of A is the least degree in this spectrum (if it exists). We extend many known results about categoricity spectra to the case of bi-embeddability. In particular, we exhibit structures without degree of bi-embeddable categoricity, and (...) we show that every degree d.c.e above 0(α) for α a computable successor ordinal and 0(λ) for λ a computable limit ordinal is a degree of bi-embeddable categoricity. We also give examples of families of degrees that are not bi-embeddable categoricity spectra. (shrink)

For a non-zero natural number n, we work with finitary $$\Sigma ^0_n$$ -formulas $$\psi (x)$$ without parameters. We consider computable structures $${\mathcal {S}}$$ such that the domain of $${\mathcal {S}}$$ has infinitely many $$\Sigma ^0_n$$ -definable subsets. Following Goncharov and Kogabaev, we say that an infinite list of $$\Sigma ^0_n$$ -formulas is a $$\Sigma ^0_n$$ -classification for $${\mathcal {S}}$$ if the list enumerates all $$\Sigma ^0_n$$ -definable subsets of $${\mathcal {S}}$$ without repetitions. We show that an arbitrary computable $${\mathcal {S}}$$ (...) always has a $${{\mathbf {0}}}^{(n)}$$ -computable $$\Sigma ^0_n$$ -classification. On the other hand, we prove that this bound is sharp: we build a computable structure with no $${{\mathbf {0}}}^{(n-1)}$$ -computable $$\Sigma ^0_n$$ -classifications. (shrink)

The complexity of equivalence relations has received much attention in the recent literature. The main tool for such endeavour is the following reducibility: given equivalence relations R and S on natural numbers, R is computably reducible to S if there is a computable function f:ω→ω that induces an injective map from R-equivalence classes to S-equivalence classes. In order to compare the complexity of equivalence relations which are computable, researchers considered also feasible variants of computable reducibility, such as the polynomial-time reducibility. (...) In this work, we explore Peq, the degree structure generated by primitive recursive reducibility on primitive recursive equivalence relations with infinitely many equivalence classes. In contrast with all other known degree structures on equivalence relations, we show that Peq has much more structure: e.g., we show that it is a dense distributive lattice. On the other hand, we also offer evidence of the intricacy of Peq, proving, e.g., that the structure is neither rigid nor homogeneous. (shrink)

This paper studies algorithmic learning theory applied to algebraic structures. In previous papers, we have defined our framework, where a learner, given a family of structures, receives larger and larger pieces of an arbitrary copy of a structure in the family and, at each stage, is required to output a conjecture about the isomorphism type of such a structure. The learning is successful if there is a learner that eventually stabilizes to a correct conjecture. Here, we analyze the number of (...) mind changes that are needed to learn a given family K. We give a descriptive set-theoretic interpretation of such mind change complexity. We also study how bounding the Turing degree of learners affects the mind change complexity of a given family of algebraic structures. (shrink)

We combine computable structure theory and algorithmic learning theory to study learning of families of algebraic structures. Our main result is a model-theoretic characterization of the learning type InfEx_\iso, consisting of the structures whose isomorphism types can be learned in the limit. We show that a family of structures is InfEx_\iso-learnable if and only if the structures can be distinguished in terms of their \Sigma^2_inf-theories. We apply this characterization to familiar cases and we show the following: there is an infinite (...) learnable family of distributive lattices; no pair of Boolean algebras is learnable; no infinite family of linear orders is learnable. (shrink)

In previous work, we have combined computable structure theory and algorithmic learning theory to study which families of algebraic structures are learnable in the limit (up to isomorphism). In this paper, we measure the computational power that is needed to learn finite families of structures. In particular, we prove that, if a family of structures is both finite and learnable, then any oracle which computes the Halting set is able to achieve such a learning. On the other hand, we construct (...) a pair of structures which is learnable but no computable learner can learn it. (shrink)

In the corporate social responsibility literature, the principle of voluntarism is predominant and implies that responsible business activities are discretionary and reach beyond the rule of law. This principle fails to explain that governments have a great interest in CSR and exercise influence on firms’ CSR activities. Therefore, we argue in favour of a contingency approach on voluntarism in CSR. To this end, we analyse the academic literature to demonstrate how governments are part of the CSR debate. We selected 703 (...) papers where the impact of governments is mentioned from five journals in our field in the period 1982–2011. We studied the titles and abstracts of these papers and provide an overview of: the geographical orientation of the reviewed studies; the variety of government levels involved; and the various subjects where governments appear to be involved. In addition, an in-depth reading of a subsample of 39 articles offers more details on the role of governments in the CSR literature. Hence, we offer a structured overview on the discussion of CSR and governments while stimulating a contingent understanding of the voluntarism concept in CSR. (shrink)

In the corporate social responsibility (CSR) literature, the principle of voluntarism is predominant and implies that responsible business activities are discretionary and reach beyond the rule of law. This principle fails to explain that governments have a great interest in CSR and exercise influence on firms’ CSR activities. Therefore, we argue in favour of a contingency approach on voluntarism in CSR. To this end, we analyse the academic literature to demonstrate how governments are part of the CSR debate. We selected (...) 703 papers where the impact of governments is mentioned from five journals in our field (BEER, BEQ, BSE, BAS, JBE) in the period 1982–2011. We studied the titles and abstracts of these papers and provide an overview of: (i) the geographical orientation of the reviewed studies; (ii) the variety of government levels involved; and (iii) the various subjects where governments appear to be involved. In addition, an in‐depth reading of a subsample of 39 articles offers more details on the role of governments in the CSR literature. Hence, we offer a structured overview on the discussion of CSR and governments while stimulating a contingent understanding of the voluntarism concept in CSR. (shrink)

Having the ambition to contribute to the practical value of the theory on corporate social performance (CSP), this paper approaches the question whether CSP can contribute to the competitive advantage of firms. We adopted an explorative case-study methodology to explore the variety of positive and negative effects of CSP on the competitiveness of organizations. As this study aimed at identifying as great variety of these effects as possible, we selected a diversified group of respondents. Data was thus collected through embedded (...) units of analysis in a petrochemical company, and triangulated with the opinions of experts on CSP. Overall, we found various positive and negative effects of CSP on the competitiveness of organizations. CSP is therefore not an innocent adventure for executives, but rather a strategy for achieving corporate objectives. If not carefully implemented, the CSP strategy may harm the competitive advantage of the firm, as our results have suggested. (shrink)

This paper investigates the role that universities play in supporting social entrepreneurs (SEs) across their ecosystem. Adopting the resource-based view (RBV) approach, we argue that universities attract, mobilize, and deploy multiple resources that benefit SEs through four main mechanisms (i.e., teaching, research, outreach, and the development of partnerships). We use a qualitative approach of 62 semi-structured interviews and 8 focus groups in Ecuador, Bolivia, and Colombia. Our contribution shows that employing different resources and engaging in supportive activities of universities towards (...) SEs facilitate the development of university capabilities, such as an increased reputation, development of leadership skills for students and staff, and wider access to ecosystem resources that support other university activities related to teaching, research, and community outreach. The role that partnerships play in the development of these capabilities is fundamental, thanks to the different strategic alliances and mobilization of resources between universities and other actors while supporting SEs. This study contributes to our understanding of the role universities can play to intensify the nature of supportive ecosystems for SEs. This contribution is relevant not only to academics but also to practitioners, as this will shed light on the building, development, and scaling of a supportive ecosystem for SEs. (shrink)

Social innovations (SIs) offer creative solutions to complex social problems and often require the exchange of necessary resources, knowledge, and expertise among various actors. These actors form an ecosystem that can support the development of successful SIs. In this special topic forum introduction, we first discuss the literature related to the support function of ecosystems. We use the theoretical lens of prosocial behavior to explain the various types of support in an ecosystem. We argue that there are three archetypes of (...) support in ecosystems, namely, altruistic, communitarian, and commercial support. Subsequently, we present the three papers accepted for publication in the special topic forum. One paper refers to the three support archetypes, although indirectly, while the other two refer to one specific archetype of ecosystem support for SIs. This introductory paper concludes with discussion on the opportunities for future research. Without a clear understanding of the different archetypes of support, it would be difficult for both scholars and practitioners to design vibrant ecosystems in assistance to SI. (shrink)

The problem of opportunity discovery is at the heart of entrepreneurial activity. Cognitive limitations determine the search for and the analysis of information and, as a consequence, constrain the identification of opportunities. Moreover, typical personal characteristics – locus of control, need for independence and need for achievement – suggest that entrepreneurs will tend to take a central position in their stakeholder environments and thus fail to adapt to the complexity of stakeholder relationships in their entrepreneurial activity. We approach this problem (...) by adopting a network perspective on stakeholder management. We propose a heuristic approach of stakeholder analysis, which requires two mappings of the entrepreneurial constituents. The first mapping focuses on current interactions between the entrepreneur and their stakeholders, while the second focuses on a specific issue and the stakeholders that constitute it. In effect, such a stakeholder analysis requires entrepreneurs to use the complexity of stakeholder relationships in order to go beyond their cognitive limitations and thus facilitate the discovery of new opportunities. As we will argue, this has clear implications for the ethics and activities of entrepreneurs. (shrink)

As corporate social responsibility involves a voluntary business endeavour to address social and environmental issues beyond legal compliance, governments cannot fall back on hierarchical command-and-control policies to support it. As such, it is complementary with the increasing popularity of public policies known as New Governance policies, where the government is engaged in a horizontal inter-organizational network of societal actors and where public policy is both formed and executed by the interacting and voluntary efforts from a multitude of stakeholders. However, such (...) policies are known to generate substantive uncertainty about the content of CSR and its related issues, strategic uncertainty regarding the behavior of the actors involved and institutional uncertainty related to the interaction process involved in the institutional change. We explore New Governance policy instruments to address these uncertainties in the context CSR and discuss the experiences with these methods in the European Union. (shrink)

We study the algorithmic complexity of embeddings between bi-embeddable equivalence structures. We define the notions of computable bi-embeddable categoricity, \ bi-embeddable categoricity, and degrees of bi-embeddable categoricity. These notions mirror the classical notions used to study the complexity of isomorphisms between structures. We show that the notions of \ bi-embeddable categoricity and relative \ bi-embeddable categoricity coincide for equivalence structures for \. We also prove that computable equivalence structures have degree of bi-embeddable categoricity \, or \. We furthermore obtain results (...) on the index set complexity of computable equivalence structure with respect to bi-embeddability. (shrink)

The role of governments in business and society research remains underexplored. The generally accepted principle of voluntarism, which frames responsible business conduct as an unregulated subject under managerial discretion, accounts for this gap. Paradoxically, there are sufficient acknowledgments in academia and practice on different roles of governments. The present article identifies three broad topics for research, addressing the paradox between the principle of voluntarism and the role of governments in B&S, the boundaries of governments and business in their contribution to (...) B&S issues, and the mechanisms of government intervention that affect corporate social performance. The authors approach the first topic with a literature review of 703 articles marked with the term “government” from five journals in the field between 1982 and 2011. This study indicates that the principle of voluntarism remains, despite the broad variety of research related to the role of government in B&S. In addition, the identified content provides deeper insight into the mechanisms of government intervention and on the boundaries of governments in the B&S discourse. This article then provides a summary of the other three research articles included in this special research forum, with a contribution oriented toward the latter two research avenues posited. (shrink)

The early literature on base of the pyramid strategies argued that multinational enterprises can contribute significantly to poverty alleviation of the poorest population in the world. An emergent perspective suggests that the solution to poverty lies within the BOP itself. Here, entrepreneurship within the BOP population is seen as the more credible solution to poverty. In this Special Issue introduction, we briefly present how the literature has further shifted the discussion of BOP strategies toward issues such as innovation, networks, business (...) models, and sustainability at the BOP. This analysis signals a gap in our knowledge related to the success factors in business models of BOP entrepreneurs, with attention to economic, social, and environmental impacts. We present the five articles accepted for publication in this Special Issue, of which three contribute to our knowledge of BOP business models and two to our knowledge of sustainability at the BOP. In conclusion, we propose several avenues for future research. (shrink)

We study the algorithmic complexity of isomorphic embeddings between computable structures.

At the present stage, it is becoming more and more important for large companies to maintain their own impeccable reputation. Western companies have been introducing and developing compliance systems for quite a long time, and now Russian companies are also concerned about the development of such systems. Compliance strengthens the company’s reputation, which gives it another competitive advantage in the market. The purpose of the article is to study trends and prospects for the development of compliance in Russia, the problems (...) of its implementation in Russian companies. The paper provides a theoretical analysis of the concept and essence of compliance in the activities of companies, the features and components of compliance systems. Compliance systems and the work of compliance services were studied on the example of 50 large companies that were surveyed in March 2020. It was determined that less than half of the companies have such services; the full independence of such services is not always fully ensured; the capabilities of these services to perform compliance functions are not fully used and the most popular area of compliance is anti-corruption compliance. Prospects for further research are related to the study of the development of compliance in Russia, including the introduction of advanced foreign experience in Russian companies. The applied value of the material lies in the systematisation of information on the trends in the development of compliance in Russia at the present stage. (shrink)

“Tell me," Wittgenstein once asked a friend, "why do people always say, it was natural for man to assume that the sun went round the earth rather than that the earth was rotating?" His friend replied, "Well, obviously because it just looks as though the Sun is going round the Earth." Wittgenstein replied, "Well, what would it have looked like if it had looked as though the Earth was rotating?” What would it have looked like if we looked at all (...) sciences from the viewpoint of Wittgenstein’s philosophy? Wittgenstein is undoubtedly one of the most influential philosophers of the twentieth century. His complex body of work has been analysed by numerous scholars, from mathematicians and physicists, to philosophers, linguists, and beyond. This volume brings together some of his central perspectives as applied to the modern sciences and studies the influence they may have on the thought processes underlying science and on the world view it engenders. The contributions stem from leading scholars in philosophy, mathematics, physics, economics, psychology and human sciences; all of them have written in an accessible style that demands little specialist knowledge, whilst clearly portraying and discussing the deep issues at hand. (shrink)

By analyzing the Dirac equation with static electric and magnetic fields it is shown that Dirac’s theory is nothing but a generalized one-particle quantum theory compatible with the special theory of relativity. This equation describes a quantum dynamics of a single relativistic fermion, and its solution is reduced to solution of the generalized Pauli equation for two quasiparticles which move in the Euclidean space with their effective masses holding information about the Lorentzian symmetry of the four-dimensional space-time. We reveal the (...) correspondence between the Dirac bispinor and Pauli spinor , and show that all four components of the Dirac bispinor correspond to a fermion . Mixing the particle and antiparticle states is prohibited. On this basis we discuss the paradoxical phenomena of Zitterbewegung and the Klein tunneling. (shrink)

The purpose of the study is an institutional view of the state and modern Russia, as opposed to the civilizational and formational worldview. It allows you to switch public and scientific consciousness from a statocentric to a sociocentric worldview, in its own way reveals the correlation of the categories of people, society and the state in the political universe. As a result, the history of political society appears to be a socio-dialectical sequence of public legal structures built by historically changeable (...) political norms. The analysis of institutional transitions and political norms allows us to assert that modern society, including the Russian one, is rationally moving towards a libertarian institution, i.e. to co-governance of citizens equal in law. (shrink)

We present a system of relational syllogistic, based on classical propositional logic, having primitives of the following form: $$\begin{array}{ll}\mathbf{Some}\, a \,{\rm are} \,R-{\rm related}\, {\rm to}\, \mathbf{some} \,b;\\ \mathbf{Some}\, a \,{\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{some}\, b;\\ \mathbf{All}\, a\, {\rm are}\,R-{\rm related}\, {\rm to}\, \mathbf{all} \,b.\end{array}$$ Such primitives formalize sentences from natural language like ‘ All students read some textbooks’. Here a, b denote arbitrary sets (of objects), and R denotes an (...) arbitrary binary relation between objects. The language of the logic contains only variables denoting sets, determining the class of set terms, and variables denoting binary relations between objects, determining the class of relational terms. Both classes of terms are closed under the standard Boolean operations. The set of relational terms is also closed under taking the converse of a relation. The results of the paper are the completeness theorem with respect to the intended semantics and the computational complexity of the satisfiability problem. (shrink)

This article pursues two distinct yet interrelated levels of analysis. Theoretically, the article seeks to destabilize Western narratives of a transition from humanism to anti- and post-humanism in radical scholarship by foregrounding two traditions from Eastern Europe and the Caribbean where the language of the human persisted long after its declared obsolescence in the West. The argument made here is that these divergent narratives of the human were neither wholly contingent nor just a matter of distinct intellectual traditions, but were (...) deeply interwoven with both the history of the Cold War and the legacies of colonialism. On a praxical-political level, the article also engages in a close reading of arguably the major tradition of Marxist humanism in Eastern Europe, that of the Praxis circle in former Yugoslavia. While examining the specific political and theoretical reasons for the persistence of humanism in the writings of Praxis, the article argues that, in the end, their radica.. (shrink)

The article examines the problem of correlation between the “knowledge society” and “knowledge practice,” based on analysis of the phenomenon of security expertise as a part of political expertise. In the article, we consider the relationship between politics and security and demonstrate under what circumstances security becomes politics. It is noted that at present the concept of security has become very multifaceted and includes various spheres, from military-political to informational and humanitarian. We defines security expertise, list its key parameters, origin, (...) its institutionalization and practices. Special attention is paid to the characteristics of the main schools in the study of security expertise problems. Their general ideology and inherent problems are analyzed, including the correspondence of the quality of the expertise to recognized standards of scientific knowledge. We explain why security issues appeal to experts and result in numerous studies. We raise an issue of causes that may lead to possible deprofessionalization of security expertise. We identify a number of institutions with an expert status in the field of security and explain the global growth of analytical centers specializing in security expertise. A brief description of such analytical centers and their main features is given. We look into examples of practical impact of expertise on political decision-making, and possible mechanisms of expert support. It is concluded that expert analysis can exercise direct impact on political processes, and the experts become influential shadow participants. On the one hand, this may contribute to adopting more balanced decisions, but, on the other hand, it may result in deprofessionalization of experts who will try to adjust to the demands of politicians. Thus, in the sphere of security expertise, one of the results of the formation of a “knowledge society” is a decrease in the autonomy of the scientific sphere, which has a side effect in the form of deprofessionalization of knowledge. (shrink)

Many philosophers affiliated with the analytic school contend that the history of philosophy is not relevant to their work. The present study challenges this claim by introducing a strong variant of the philosophical history of philosophy termed the “logical–contextual history of philosophy.” Its objective is to map the “logical geography” of the concepts and theories of past philosophical masters, concepts and theories that are not only genealogically, but also logically related. Such history of philosophy cannot be set in opposition to (...) the traditional “systematic philosophy.” Rather, the logical–contextual history of philosophy is, like the traditional school philosophies, systematic, although it develops along different lines. (shrink)

The present review takes into consideration the existing literature on Professor Dr. Miglena Nikolchina's new monograph, “God with a Machine: Extracting the Human”, with a particular focus on the science-fictional aspects of the book, tracking their culmination in the debates about the future and the inquiries that construct the very notion of humanity.

A brief essay of Nikolay Raynov against war.

This paper advances an assessment of Kant’s Critique of Pure Reason made from a bird’s eye view. Seen from this perspective, the task of Kant’s work was to ground the spontaneity of human reason, preserving at the same time the strict methods of science and mathematics. Kant accomplished this objective by reviving an old philosophical discipline: the peirastic dialectic of Plato and Aristotle. What is more, he managed to combine it with logic. From this blend, Kant’s transcendental idealism appeared as (...) a new logic that paralleled Aristotle’s syllogistic logic. The first result of this move was that philosophy became a formal study that treats even such subjects as ethics with rigour. Another outcome was that it established philosophy as a professional – school – discipline. In the twentieth century academy, this development was echoed by the emergence of analytic philosophy, in which Kant’s new logic evolved into a philosophical logic. (shrink)