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)

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 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)

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.

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)

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)

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)

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)

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)

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

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)

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)

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)

This paper raises the question whether the Economic Nobel Prize is ideologically biased. Based on a review of a significant number of the Prize Committee’s award justifications, the article concludes at a persistent bias against private property and the free market and in favour of collectivism and state interventionism. From a methodological point of view, the Prize has contributed to the widespread use by professional economists of formal mathematics within the positivistic approach. With respect to research findings, the Prize has (...) favoured the doctrine that market processes are faulty, while government policies are an appropriate fix. Additionally, the paper casts doubts on the scientific integrity of the Prize, given the Committee’s acknowledged lack of concern for fundamental revisionism and outright dismissal of possible criticisms. (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)

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)

The article is devoted to the analysis of the existing leading methodologies for building enterprise architecture. The purpose of the study is to develop a more accurate understanding of what methodologies exist for building an enterprise architecture. Knowledge is important for analyzing the company's activities, building its architecture for effective work, as well as for using ready-made solutions in conducting business. Scientific novelty lies in the structuring of data within a single study. As a result, leading methodologies were analyzed, described (...) structurally, and for top management the main stages of planning are given. (shrink)

The purpose of the study is to study the theoretical foundations of the business activity of the enterprise and develop measures to improve it on this basis. The article discusses the theoretical aspects of transformation, regulation and increase of business activity of economic entities. The analysis of the business activity of the enterprise reflects a systematic assessment of the efficiency of the use by the business entity of its resources, which ensures the achievement of positive results and the creation of (...) a favorable investment climate, maintaining a stable financial condition and constant expansion and growth of production and sales volumes. The scientific novelty lies in the development and refinement of theoretical provisions and the definition of directions for increasing the business activity of small businesses. As a result, the main directions of increasing business activity have been identified. (shrink)

Drawing upon in-depth analyses of Lev Vygotsky’s theories of early childhood and investigating the ways in which his ideas are reflected in contemporary educational settings, this book brings into sharp relief the numerous opportunities for preschool learning and development afforded by Vygotskian approaches. Discussion of recent developments in the understanding and implementation of Vygotsky’s ideas in Western and Russian contexts facilitates comparison, and provides readers with fresh impetus to integrate elements into their own practice. Chapters are clearly structured and address (...) the multitude of aspects touched upon by Vygotsky, including cognitive development, communication and interaction, play, literacy and the quality of preschool settings. Providing a comprehensive exploration of current stances on Vygotsky's ideas in diverse cultural-historical contexts, Vygotsky's Theory in Early Childhood Education and Research will be of interest to researchers, practitioners, educators and politicians involved in early years education. (shrink)

The paper suggests an explanation of the failure of liberal reforms in Russia in 1990th using a specific concept of social space. A society can be interpreted as ‘rings in the water’ system with an individual as the center and more distant social groups as ‘rings’. The key factor in such system would be an individual’s ability to translate his/her will through the ‘rings’. Russian social space is characterized by a sharp discrepancy between high standards for personal spiritual and moral (...) growth and low ethical standards of real social life. What is strictly forbidden inside the personal social circle (the ‘ring’ of relatives and close friends) is easilycondoned outside of it. External ‘rings’ of social space are more like ‘dangerous and irrational wild nature’ than cultural territory. This discrepancy (constant for Russian history for at least last 500-600 years) puts all kinds of barriers for active social interaction. The failure of liberal reforms in Russia shouldn’t be interpreted as the failure of liberal ideas, but as the failure of an attempt to apply them to the territory mentally and socially absolutely alien to them. (shrink)

The present paper considers using Social Networking Sites (SNS) as the primary means of communication . Current situations of communication are often associated with the active use of various SNS - convenient tool for information exchange, as new media, and one of the most widespread ways of self-presentation. The author comes to the conclusion that a SNS (like Facebook) gives no effective means to discern the real face - ego-, personal or actual social identity. However, modern Internet technologies provide us (...) with useful instruments, applied to the social network analysis and semiotic approach, to define the virtual social (or personal) identity that can (or cannot) be the same as the real one. (shrink)

Karl Popper has often been cast as one of the most solitary figures of twentieth-century philosophy. The received image is of a thinker who developed his scientific philosophy virtually alone and in opposition to a crowd of brilliant members of the Vienna Circle. This paper challenges the received view and undertakes to correctly situate on the map of the history of philosophy Popper’s contribution, in particular, his renowned fallibilist theory of knowledge. The motive for doing so is the conviction that (...) the mainstream perspective on Popper’s philosophy makes him more difficult to understand than might otherwise be the case. The thinker who figures most significantly in the account of Popper developed in these pages is Leonard Nelson. Both a neo-Friesian and neo-Kantian, this philosopher deeply influenced Popper through his student Julius Kraft, who met with Popper on numerous occasions in the mid 1920s. It is in the light of this influence that we understand Popper’s recollection that when he criticized the Vienna Circle in the early 1930s, he looked upon himself “as an unorthodox Kantian”. (shrink)

This paper outlines the intellectual biography of Walter Dubislav. Besides being a leading member of the Berlin Group headed by Hans Reichenbach, Dubislav played a defining role as well in the Society for Empirical/Scientific Philosophy in Berlin. A student of David Hilbert, Dubislav applied the method of axiomatic to produce original work in logic and formalist philosophy of mathematics. He also introduced the elements of a formalist philosophy of science and addressed more general problems concerning the substantiation of human knowledge. (...) What set Dubislav apart from the other logical empiricists was his expertise in the history of logic and exact philosophy which enabled him to elucidate and advance the thinking in both disciplines. In the realm of logic proper, Dubislav is best known for his pioneering work in theory of definitions. What is more, he did original work on the so called ‘quasi truth-tables’ which aided Reichenbach in developing his logic of probability. Dubislav also elaborated an influe.. (shrink)

From 1901 till, at least, 1919, Russell persistently maintained that there are two kinds of logic, between which he sharply discriminated: mathematical logic and philosophical logic. In this paper, we discuss the concept of philosophical logic, as used by Russell. This was only a tentative program that Russell did not clarify in detail, so our task will be to make it explicit. We shall show that there are three (-and-a-half) kinds of Russellian philosophical logic: (i) “pure logic”; (ii) philosophical logic (...) investigating the logical forms of propositions; (iii) philosophical logic exploring the logical forms of facts: in epistemology; and in the external world. In particular, Russell’s program or philosophical logic of the facts of the external world remained less than sketchily outlined. We shall discuss it in some detail in the hope that it can start a new life. (shrink)

This text offers a discussion of the concept and experience of alienation, as it has been theorized in two very different traditions. Accordingly, I juxtapose a recent discussion by Italian Autonomist Marxist Franko “Bifo” Berardi to that of Argentine philosopher and scholar of indigenous cosmologies Rodolfo Kusch. Unlike Berardi’s anti-capitalist critique, Kusch identifies Western Modernity (and not just capitalism) as the source of alienation, and proposes a “de-linking” from its categories and epistemic practices. I caution that even a progressive meta-theory (...) such as Marxism can engage in conceptual violence, when it claims universal validity. (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)

Between April and November 1912, Bertrand Russell and Ludwig Wittgenstein were engaged in a joint philosophical program. Wittgenstein‘s meeting with Gottlob Frege in December 1912 led, however, to its dissolution – the joint program was abandoned. Section 2 of this paper outlines the key points of that program, identifying what Russell and Wittgenstein each contributed to it. The third section determines precisely those features of their collaborative work that Frege criticized. Finally, building upon the evidence developed in the preceding two (...) sections, section 4 recasts along previously undeveloped lines Wittgenstein‘s logical–philosophical discoveries in the two years following his encounter with Frege in 1912. The paper concludes, in section 5, with an overview of the dramatic consequences the Frege-Wittgenstein critique had for Russell‘s philosophical development. (shrink)

In the cytoplasm of practically all living cells, potassium is the major cation while sodium dominates in the media (seawater, extracellular fluids). Both prokaryotes and eukaryotes have elaborate mechanisms and spend significant energy to maintain this asymmetric K+/Na+ distribution. This essay proposes an original line of evidence to explain how bacteria selected potassium at the very beginning of the evolutionary process and why it remains essential for eukaryotes.

A brief essay of Nikolay Raynov against war.