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)

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.

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)

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)

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)

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 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)

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 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)

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)

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)

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 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 study the algorithmic complexity of isomorphic embeddings between computable structures.

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)

The Berlin Group was an equal partner with the Vienna Circle as a school of scientific philosophy, albeit one that pursued an itinerary of its own. But while the latter presented its defining projects in readily discernible terms and became immediately popular, the Berlin Group, whose project was at least as sig-nificant as that of its Austrian counterpart, remained largely unrecognized. The task of this chapter is to distinguish the Berliners’ work from that of the Vienna Circle and to bring (...) to light its impact in the history of scientific philosophy. (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)

Dieser Versuch einer philosophischen Autobiographie ist hauptsächlich der Geschichte meiner Ideen und Anregungen im Bereich der Philosophie gewidmet. In dieser Zusammenfassung werden vor allem meine philosophischen Begegnungen und Veröffentlichungen besprochen. Es ist weniger die Geschichte meines privaten Lebens, da bei mir privates und berufliches Leben zum großen Teil zusammenfallen.

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)

The article is devoted to the philosophy of industrial design as the most important area of aesthetic and engineering activity of people, shaping the appearance of modern society. The object of the study is industrial design, and its subject is the philosophical foundations of industrial design. The goal of the study is to identify the philosophical essence of industrial design in epistemological, ontological and anthropological dimensions. Attention is paid to the historical aspects of industrial design, which allows us to more (...) accurately understand the essence of this phenomenon. The author’ also considered modern industrial design, which in its philosophy is characterized by a strong anti-globalist orientation. It is noted that the philosophical understanding of industrial design contributes to the understanding of the features of its historical development. The main conclusion of the study is that industrial design has a certain philosophical content associated not only with the aesthetic side of reality, but also with its axiological and ethical structure. The epistemological problems of industrial design are important: products act as carriers of certain knowledge and concepts and accumulate the cultural experience of mankind. Anthropological problems of design are associated with the model of a human creator and a human recipient of activity. The scientific novelty of the research lies in the understanding of industrial design, which is a systemic object, developing in space and time. In its existence, this object combines presence and “service”, independent givenness and significance for a person. (shrink)

This article examines how Gregory of Nazianzus (Gregory the Theologian, ca. 330-390) constructs an image of the priest using political metaphor and vocabulary from previous traditions. The author chooses a specific text from ancient political thought that was close to his own understanding of Christian tradition (Plato’s Republic). In turn, the biblical material he uses comprises fragments that are highly political in nature (for example, criticism of the rulers of Israel by the prophets). Combining these texts first of all leads (...) to their transformation, and secondly allows him to piece together an image of the priest as ruler of the Church. The combination of these two traditions makes it possible to describe both the historical and contemporary legitimization of this image – one novel for Late Antiquity – and to define the main characteristics of its ethos. (shrink)

In the late 1920s and early 1930s, the philosopher Hans Reichenbach led a group of like-minded colleagues in Berlin that must count as an independent point of origin of the movement of logical empiricism. Like the Vienna Circle with whom they cooperated on numerous occasions, their concern was to develop a philosophy of science adequate to the latest advances in science itself. Differences of philosophical background and interests, however, resulted in putting different accents by justifying scientific knowledge.

Unsere These lautet, dass die Geschichte des logischen Empirismus bisher nicht in ihrer ganzen Komplexität dargestellt wurde. Es herrscht das Bild vor, dass vor allem der Wiener Kreis die wissenschaftliche Philosophie seiner Zeit dominiert habe. In Wirklichkeit waren Hans Reichenbach und die Philosophen und Wissenschaftler in seiner Gruppe mehr als nur geistige Verwandte der Wiener logischen Empiristen. Die Berliner Gruppe war ein gleichberechtigter Partner bei der Verbreitung wissenschaftlicher Philosophie im deutschsprachigen Raum um 1930 und schlug dabei durchaus einen individuellen Weg (...) ein. Reichenbach hat daher auch ausdrücklich die Eigenständigkeit der Berliner Gruppe innerhalb des logischen Empirismus verteidigt (Hoffmann 1994, 26). Dabei kämpfte er nicht einfach für Gleichberechtigung mit dem Wiener Kreis. Reichenbach beanspruchte sogar die Priorität der Initiative. (shrink)

Husserl’s theory of manifolds was developed for the first time in a very short form in the Prolegomena to his Logical Investigations, §§ 69–70 (pp. 248–53), then repeatedly discussed in Ideas I, §§ 71–2 (pp. 148–53), in Formal and Transcendental Logic, §§ 51–4 (pp. 142–54), and finally in the Crisis, § 9 (pp. 20–60). Husserl never lost sight of it: it was his idée fixe. He discussed this theme over forty years, expressing the same, in principle, ideas on it in (...) different terms and versions. His discussions of it, however, were always cut short and inconclusive, so that he never developed his theory of manifolds in detail. Main claim in this essay is that Husserl’s theory of manifolds is twofold. It is (1) a theory of theories, advanced in the good German tradition of Wissenschaftslehre, launched first by Bernard Bolzano. The latter, in turn, is an offspring of the ancient tradition of mathesis universalis, explored in the modernity by Descartes and Leibniz. Further, (2) the theory of manifolds is also a formal theory of everything. Its objective is to provide a systematic account of how the things in the world (its parts) hang together in wholes of quite different kind. It is to be noted that Husserl explicitly speaks about (1) and only implicitly about (2). In this paper we shall also show that the theory of everything is intrinsically connected with the theory of theories. (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)

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)

Die Psychologie hat sich im zweiten Viertel des 19. Jahrhunderts langsam zu einer autonomen Disziplin entwickelt. Im Unterschied zu den anderen Figuren in dieser Entwicklung, Johann Friedrich Herbart, Ernst Heinrich Weber und Gustav Theodor Fechner, hat Lotze in seiner Medicinische Psychologie (1852) von Anfang an die neue Disziplin, die Psychologie, konsequent in enger Verbindung mit der Philosophie entwickelt. Damit hat er die Hoffnung gebremst, die Psychologie völlig experimentellen Untersuchungen zu überlassen, die um diese Zeit schon viele gepflegt haben. Lotze scheute (...) sich jedoch, diese Disziplin „philosophische Psychologie“ zu benennen. Sie war für ihn nur physiologische Psychologie, herausarbeitet mit Hilfe der Philosophie. Sie stellt nur Tatsachen fest, untersucht wie Körper und Seele sich zueinander verhalten und dies nicht nur empirisch, sondern auch „metaphysisch“. (shrink)

Many authors believe that the manuscripts Frege wrote in 1924–1925 are not theoretically of interest. They are rather a product of his emotional despair and theoretical dead-end which he reached in the last years of his life. Such is also the judgement of Michael Dummett delivered in his seminal book Frege: Philosophy of Language. According to Dummett, “the few fragmentary writings of Frege’s final period—1919–1925—are not of high quality: they are interesting chiefly as showing that Frege did, at least at (...) the very end of his life, acknowledge the failure of the logicist programme” (Dummett 1981, p. 664). In this paper we will try to show that the widely accepted negative assessment of Frege’s latest writings is due to a lack of understanding of their true idea. In fact, the change in Fre-ge’s mind in the last two or three years of his life was result of long deliberations on a severe tension in his founding intuitions. The change itself made his logico-philosophical project more coherent and, thus, is of utmost theoretical importance. (shrink)

The received view has it that Hans Reichenbach and his friends of the Berlin Group worked close together with the more prominent Vienna Circle. In the wake of this view, Reichenbach was often treated as a logical positivist – despite the fact that he decisively opposed it. In this chapter we follow another thread. We shall show the “third man”– besides Reichenbach and Walter Dubislav – of the Berlin Group, Kurt Grelling, as a man who could grasp the academic trends (...) of the time faster than anybody else, who was better informed about logic and philosophy of nature than his two prominent colleagues and thus, could better delineate, although tentatively, central threads of research of the Berlin Group. Grelling did this on several occasions, but most ostensibly in the last years of his life when he was focused on problems of formal ontology. On the basis of this analysis, we shall see that in the early 1920s, Reichenbach too was led by a project in ontology of science that he elaborated together with the psychologist Kurt Lewin. Moreover, Reichenbach’s later philosophy of nature was also shaped by this project. We present this direction of philosophy of science as a “road less travelled” which, however, if revived, can point to a new direction that will more closely connect philosophy and science. (shrink)

It is generally acknowledged that Kant’s new “transcendental” philosophy produced a “Copernican revolution” in this discipline. Instead to philosophically explore the world, Kant investigated the possibility of cognizing the world through human reason. Unfortunately, it is not thus clear which exactly method helped Kant to produce it. The claim of the present paper is that Kant’s new approach in philosophy went together with a change of the style followed in this discipline. Instead of doing philosophical “meditations” (like Descartes) or composing (...) philosophical “essays” (like Locke and Hume), Kant introduced, what we call here, a diachronic encyclopedic approach of doing philosophy, which was brought about in the context of the highly influential in his years Encyclopédie of D’Alembert and Diderot. In contrast to the latter, however, Kant’s project prompted a logical unification of all substantial ideas introduced in philosophy so far. (shrink)

This is a review of the book Mozg - kultura - socium. Kantianskaya programma v cognitivnykh issledovaniyakh by Bazhanov V.A. The author`s main aim is a reconsideration of some fundamental principles of epistemology and philosophy of science in the light of state-of-the-art advancements of neurosciences. According to the author of the book, social and cultural revolution in neurosciences has been crucially modifying the initial Kantian program of consciousness research and the modes of linguistic representation of its results. In particular, in (...) epistemology the universal concept of transcendental subject has been altered with regard to neurobiological and social data, which concern some preconditions of cognitive activity. In philosophy of science such a shift of research perspective allows to implement a naturalistic interpretation of natural sciences, clarifies the problem of empirical foundations of mathematics and sheds a new light on the problem of apriori elements of mathematical thought. The analysis of evolutionary and neurobiological preconditions of logical thought leads to the sort of revival of psychologism program in logic, which enables author to put forward an original interpretation of the problem of plurality of logical systems. Finally, some topics of social sciences as well as problems of genesis of art, ethical and religious systems, can acquire new interpretation with respect to modern investigations in cognitive science. (shrink)

By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering (...) and double slit diffraction we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the presented by Khrennikov (Found. Phys. 35(10):1655, 2005) concept of real contexts (complexes of physical conditions) to determine uniquely the properties of quantum ensembles. Namely we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows a correct statistical interpretation and becomes compatible with classical physics. (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)