We show that the lattices of the normal extensions of four well-known logics—propositional intuitionistic logic \, Grzegorczyk logic \, modalized Heyting calculus \ and \—can be joined in a commutative diagram. One connection of this diagram is an isomorphism between the lattices of the normal extensions of \ and \; we show some preservation properties of this isomorphism. Two other connections are join semilattice epimorphims of the lattice of the normal extensions of \ onto that of \ and of the (...) lattice of the normal extensions of \ onto that of \. The link between \ and \ is a well-known isomorphism established by the Blok–Esakia theorem. (shrink)

We will outline the contributions of A.V. Kuznetsov to modal logic. In his research he focused mainly on semantic, i.e. algebraic, issues and lattices of extensions of particular modal logics, though his proof of the Full Conservativeness Theorem for the proof-intuitionistic logic KM (Theorem 17 below) is a gem of proof-theoretic art.

We deal with monotone structural deductive systems in an unspecified propositional language \ . These systems fall into several overlapping classes, forming a hierarchy. Along with well-known classes of deductive systems such as those of implicative, Fregean and equivalential systems, we consider new classes of unital and weakly implicative systems. The latter class is auxiliary, while the former is central in our discussion. Our analysis of unital systems leads to the concept of Lindenbaum–Tarski algebra which, under some natural conditions, is (...) a free algebra in a variety closely related to the deductive system in focus. (shrink)

Alexander Vladimirovich Kuznetsov, also known to the second generation of Soviet logicians as Sasha Kuznetsov, was born in Moscow on the 28 th of October, 1926. He lived a short yet fruitful life and died of cancer 1 in Chişinău, Moldova, on the 24 th of July, 1984.

On the 28th of October, 2006, Alexander Vladimirovich Kuznetsov, so is his full name, would have turned 80. Although belated, the editorial board of Logic and Logical Philosophy, we, the editors and contributors of the present issue, and other members of the logic community mark this event with the present issue. Most of those who contributed to it knew Kuznetsov in person and/or were influenced by him or by his ideas, which very often resided in somebody else’s papers or became (...) part of a scientific folklore. But, to be sure, there are even more mathematicians and logicians who have been witnesses to his scientific activity and/or have taken advantage of its results. (shrink)

We outline the Gödel-McKinsey-Tarski Theorem on embedding of Intuitionistic Propositional Logic Int into modal logic S4 and further developments which led to the Generalized Embedding Theorem. The latter in turn opened a full-scale comparative exploration of lattices of the (normal) extensions of modal propositional logic S4, provability logic GL, proof-intuitionistic logic KM, and others, including Int. The present paper is a contribution to this part of the research originated from the Gödel-McKinsey-Tarski Theorem. In particular, we show that the lattice ExtInt (...) of intermediate logics is likely to be the only constructing block with which ExtS4, the lattice of the extensions of S4, can be formed. We, however, advise the reader that our exposition is different from the historical lines along which some of the results discussed below came to light. Part 1, presented here, deals mostly with structural issues of extensions of logics, where algebraic semantics, though underlying this approach, is used merely occasionally. Part 2 will be devoted to algebraic analysis of the Embedding Theorem. (shrink)

We seek to trace how the assertion–rejection dichotomy arose, as well as in what forms it was realized in logical discourse. From this viewpoint, we observe the approaches to the concept of rejection by Łukasiewicz, Carnap, and Słupecki. We also explore the controversy between rejection and negation. Our main observation is that for a correct understanding of this dichotomy, it is necessary to distinguish between the object language and metalanguages of different levels.

ABSTRACT This is a continuing attempt in a series of papers [KM 93, Mur 93, Mur 96] to show how computer-represented knowledge can be arranged as elements of an effectively represented semantic (or algebraic) domain in the sense of [GS 90]. We present a direct deductive description of the domain, which was defined semantically in [KM 93], via the Scott's notion of information system. Also, the internal structure of the continuous ampliative operations coordinated with the domain's effective basis is established. (...) Though we always remain in the paradigm of the toleration of contradictory information described in [Bel 75, Bel 76], the approach in question could be extended to include domains for consistency knowledge bases. (shrink)

This paper is devoted to the concepts of consequence and rejection, formulated as operators on a nonempty set of sentences, which may initially be unstructured. One of the issues that we pay attention to is the “cyclicity” of these concepts when they are defined one through the other. In addition, we explore this cyclicity, when the set of all sentences acquires some structure, or we can assume some structure of sentences in the sense that the operation of substitution can be (...) applied to them. (shrink)

We discuss nonmonotonic reasoning in terms of consequence relations and corresponding operators. Based on the matrix consequence that gives the monotonic case, we define a restricted matrix consequence that illustrates the nonmonotonic case. The latter is a generalization of the relation of logical friendliness introduced by D. Makinson. We prove that any restricted single matrix consequence, although it may be nonmonotonic, is always weakly monotonic and, in the case of a finite matrix, the restricted matrix consequence is very strongly finitary. (...) Further, by modifying the definition of logical friendliness relation formulated specifically in a proof-theoretic manner, we show a possibility of obtaining other reflexive nonmonotonic consequence relations, for which a limited result towards finitariness is proved. This leads to numerous questions about nonmonotonic consequence relations in the segment between the monotonic consequence relation based on intuitionistic propositional logic and logical friendliness. (shrink)

We show that no formula of first order logic using linear ordering and the logical relation y = 2x can define the property that the size of a finite model is divisible by 3. This answers a long-standing question which may be of relevance to certain open problems in circuit complexity.

We show that no formula of first order logic using linear ordering and the logical relation $y = 2x$ can define the property that the size of a finite model is divisible by 3. This answers a long-standing question which may be of relevance to certain open problems in circuit complexity.

Interesante y muy bien lograda aproximación al universo teórico construido por Ricardo Guastini, filósofo del derecho italiano.

“The world of life which is comprised of the lithosphere, the hydrosphere and the atmosphere”: this definition of the biosphere is not complete since it does not express the determining influence of living organisms on its composition, on its structure and on the processes of its continuing evolution. The part of living matter in the biosphere is relatively small (about 0.25%), but this part has a considerable influence on its structure.The biosphere should be considered as the universal source of all (...) food products without exception. Mankind's ability to feed itself depends on the productivity of this biosphere in the first place. Moreover, its condition determines not only the quantity but also the quality of nourishment. The problem is a critical one today because of the increasing pollution of the biosphere by products poured into it by various human activities. (shrink)

This article summarizes the recommendations concerning robotics as issued by the Commission for the Ethics of Research in Information Sciences and Technologies (CERNA), the French advisory commission for the ethics of information and communication technology (ICT) research. Robotics has numerous applications in which its role can be overwhelming and may lead to unexpected consequences. In this rapidly evolving technological environment, CERNA does not set novel ethical standards but seeks to make ethical deliberation inseparable from scientific activity. Additionally, it provides tools (...) and guidance for researchers and research institutions. (shrink)

This chapter provides a brief history of Kantianism in Russia since the late eighteenth century and identifies the main themes of Kantianism in Russia. It considers the reasons for the uneven and intermittent spread of Kantianism, the main motives behind the fierce resistance to Kantianism within the framework of certain trends of Orthodox thought, and the ways in which this philosophical polemic was reflected in the Russian literature. The achievements of Russian Kantianism are analyzed with attention to both its undeniable (...) merits and its weaknesses and inconsistencies. In addition, the scope and scale of Russian Kantianism will be compared with Schellingism and Hegelianism in Russia. On the basis of this comparison, I will argue against the stereotype that Russian philosophy is resistant to Kant. (shrink)

Critics attack normative ethical stakeholder theory for failing to recognize the special moral status of shareholders that justifiesthe fiduciary duties owed to them at law by managers. Stakeholder theorists reply that there is nothing morally significant about shareholders that can underwrite those fiduciary duties. I advance an argument that seeks to demonstrate both the special moral status of shareholders in a firm and the concomitant moral inadequacy of stakeholder theory. I argue that (i) if some relations morally requirefiduciary duties, and (...) (ii) the shareholder-manager relation possesses the features that make fiduciary duties morally necessary to thoserelations, then (iii) stakeholder theory is morally lacking. (shrink)

La Base de français médiéval (BFM) fait partie des corpus de français médiéval (9e-15e s.) les plus anciens et les plus utilisés par les linguistes diachroniciens et plus largement par tous ceux qui s’intéressent à l’histoire du français. Elle est le fruit d’une collaboration entre linguistes-philologues et spécialistes de la méthode textométrique implémentée dans la plateforme TXM. L’article présente un état des lieux du corpus BFM2022 focalisé sur la représentativité et l’interopérabilité des données. Il illustre l’apport des outils numériques pour (...) l’équilibrage des données et présente la stratégie de standardisation multi-niveau (structure textuelle, références, métadonnées, annotations) ayant permis à la Base de s’intégrer à des corpus diachroniques plus étendus pour des recherches en diachronie longue. (shrink)

To believe that every single scientist ought to be individually engaged in ethical thinking in order for science to be responsible at a collective level may be too demanding, if not plainly unrealistic. In fact, ethical labor is typically distributed across different kinds of scientists within the scientific community. Based on the empirical data collected within the Horizon 2020 ‘RRI-Practice’ project, we propose a classification of the members of the scientific community depending on their engagement in this collective activity. Our (...) classification offers, on the one hand, a model of how the ethical aspects of science are taken into consideration by scientists and, on the other, some indications on how to institutionalize ethics in science. (shrink)

Introduction. The problems of state and local governance in sparsely populated and rural areas is relevant for the Russian Federation due to the presence of depressed areas, depopulation of the countryside, small towns, monotowns, migration of the rural population to large cities, regional capitals, other regions and abroad. These processes are typical for many other modern states. Solving the problems of rural and sparsely populated areas includes providing socially significant services, protecting the health and safety of residents, developing education, creating (...) and maintaining social infrastructure, and creating jobs. The purpose of the article is to identify the most important management problems in rural and sparsely populated areas and reveal possible solutions to these problems using the example of Great Britain. Methods. The research is based on a systematic approach to management in rural and sparsely populated areas. Analysis of factual data, legal sources, published survey results, foreign Internet sources. Comparative analysis of problems and measures of state policy in different states. Scientific novelty of the research. The author highlights the current measures taken in the UK at the central, local levels in order to overcome the problems of rural and sparsely populated areas. These activities as a basis for developing practical recommendations may be important for solving similar problems in Russian regions, including in the context of the COVID-19 epidemic and economic problems in the near future. Results. As a result the author identifies problems in the field of management in rural and sparsely populated and hard-to-reach areas, as well as possible directions of state policy in the UK and Russia to overcome these problems. Conclusions. The most important direction of state policy for solving the problems highlighted in the study is the development of local interests of the community, the integration of state support measures and local events. As measures aimed at solving social and infrastructural problems of sparsely populated areas in the UK, one can single out government programs implemented at the national and regional levels with the participation of industrial enterprises and businesses, a grant mechanism for the implementation of financial support, combined with the empowerment of local communities. There is no such policy in Russia yet. (shrink)

The article is devoted to the well-known dispute between R. Carnap and W.V.O. Quine on the meaning of statements with names of abstractions, which also revealed their disagreements on the more general question of the nature of the dependence of ontology on the choice of language of knowledge. According to Quine, the choice of language carries with it certain ontological commitments – judgments of existence that must be true for anyone who appropriately uses the language in question. The language of (...) abstractions (using appropriate names and indications) is widely used not only in philosophy and everyday communication, but also in the sciences, including natural sciences. The names of abstractions (or, alternatively, quantification by corresponding entities) cannot be completely excluded from science, as Carnap, in particular, points out. He also considers it wrong to attribute to a scientist with empiricist views the belief in the existence of something that he, as an empiricist, is not ready to consider existing. In his view, the choice of language (framework) does not carry any ontological obligations: it determines what should be the correct answer to the so-called internal questions of the theory but does not affect metaphysical questions. Carnap interprets meaningful statements about abstractions as analytical truths, while Quine believes that most references to abstractions are removable from the language of science, and those that are not removable create additional ontological obligations, which, however, for some reason say nothing about reality itself. But why this is so, if the theory implicating them claims to describe reality, is not clear. This debate about the role of judgments about abstractions in scientific knowledge gave rise to a whole branch of metaphysical and ontological research, best known as metaontology. The main parties in this dispute are realists, who interpret irreducible abstractions as part of reality and denotations of certain names, and anti-realists, who, as a rule, deny the connection of statements with such names with reality, treating them as pseudo-statements or something similar. The solution to the problem, which is proposed in this article, consists in abandoning the belief, widespread both in philosophy and in everyday thought, which can be generally called “The theory of reference” and which consists in the fact that the contribution of names and certain other types of expressions to communication is their denotations. If we assume that names have no denotations at all and their semantic contribution to statements is only their senses or something similar, then the names of abstractions in this respect will be no different from other types of names. In this case, it would be no need to either assume that they designate some “Platonic” entities in order for some statements with them being true, nor interpret these judgments as pseudo-statements or as truths of some special kind that are not related to reality. The interpretation of statements with such names and their evaluation will not pose any special problem for the empiricist with this approach. (shrink)

La Meditación de la técnica contiene las reflexiones de José Ortega y Gasset sobre un fenómeno de invasora presencia en el mundo contemporáneo. Trata, en suma, de inscribir el hecho de la técnica en el marco de una antropología filosófica, fundada en el sistema orteguiano, para así contribuir a la comprensión del momento histórico contemporáneo. El volumen incluye, además del curso ¿Qué es la técnica?, desarrollado en 1933 en la Universidad de Santander, otros textos afines: la conferencia El mito del (...) hombre allende a la técnica pronuncida en Darmstadt y varios ensayos sobre el conocimiento científico, que prueban la permanente atención que Ortega prestó a las novedades de la ciencia contemporánea. En esta nueva edición el texto se ha revisado y corregido conforme a los manuscritos originales o las primeras ediciones. La principal novedad es una Introducción al curso ¿Qué es la técnica?, sólo editada póstumamente. (shrink)

We argue that the Rawlsian social contract argument advanced for stakeholder theory by R. Edward Freeman, writing alone and with William M. Evan, fails in three main ways. First, it is true to Rawls in neither form, nor purpose, nor the level of knowledge (or ignorance) required to motivate the veil of ignorance. Second, it fails to tailor the veil of ignorance to the fairness conditions that are required to solve the moral problem that Freeman and Evan set out to (...) solve (whereas Rawls’s own use of the device surely tailors the veil of ignorance to the problem of designing a just social order). Third, the argument, considered apart from its claimed Rawlsian pedigree, fails to bolster the stakeholder theory because it fails to demonstrate the rationality of adopting the institutional rules that Freeman and Evan favor. (shrink)

ABSTRACT This article contributes to methodological debates in contemporary critical theory regarding the scope and features of immanent critique. I spell out the philosophical commitments presupposed by this approach to criticism and identify its basic features by comparing it with more recognizable argumentative or interpretative strategies. This comparison yields three immanent-critical requirements – for inherence, contradiction, and access – which bring into relief the heuristic and ampliative character of immanent criticism. Yet, these requirements also imply that “immanent critique” is not (...) a method in any strict sense, since they are multiply interpretable and hence generative of distinctive critical comportments. (shrink)

We study when classes can have the disjoint amalgamation property for a proper initial segment of cardinals. Theorem A For every natural number k, there is a class $K_k $ defined by a sentence in $L_{\omega 1.\omega } $ that has no models of cardinality greater than $ \supset _{k - 1} $ , but $K_k $ has the disjoint amalgamation property on models of cardinality less than or equal to $\mathfrak{N}_{k - 3} $ and has models of cardinality $\mathfrak{N}_{k (...) - 1} $ . More strongly, we can have disjoint amalgamation up to $\mathfrak{N}_\alpha $ for α > ω, but have a bound on size of models. Theorem B For every countable ordinal a, there is a class $K_\alpha $ defined by a sentence in $L_{\omega 1.\omega } $ that has no models of cardinality greater than $ \supset _{\omega 1} $ , but K does have the disjoint amalgamation property on models of cardinality less than or equal to $\mathfrak{N}_\alpha $ . Finally we show that we can extend the $\mathfrak{N}_\alpha $ to $ \supset _\alpha $ in the second theorem consistently with ZFC and while having $\mathfrak{N}_i \ll \supset _i $ for 0 > i < α. Similar results hold for arbitrary ordinals α with |α|= K and $L_{k + ,\omega } $. (shrink)

Coming fromI andCl, i.e. from intuitionistic and classical propositional calculi with the substitution rule postulated, and using the sign to add a new connective there have been considered here: Grzegorozyk's logicGrz, the proof logicG and the proof-intuitionistic logicI set up correspondingly by the calculiFor any calculus we denote by the set of all formulae of the calculus and by the lattice of all logics that are the extensions of the logic of the calculus, i.e. sets of formulae containing the axioms (...) of and closed with respect to its rules of inference. In the logiclG the sign is decoded as follows: A = (A & A). The result of placing in the formulaA before each of its subformula is denoted byTrA. The maps are defined (in the definitions of x and the decoding of is meant), by virtue of which the diagram is constructed. (shrink)

Life has semiotic nature; and as life forms differ in their complexity, functionality, and adaptability, we assume that forms of semiosis also vary accordingly. Here we propose a criterion to distinguish between the primitive kind of semiosis, which we call “protosemiosis” from the advanced kind of semiosis, or “eusemiosis”. In protosemiosis, agents associate signs directly with actions without considering objects, whereas in eusemiosis, agents associate signs with objects and only then possibly with actions. Protosemiosis started from the origin of life, (...) and eusemiosis started when evolving agents acquired the ability to track and classify objects. Eusemiosis is qualitatively different from protosemiosis because it can not be reduced to a small number of specific signaling pathways. Proto-signs can be classified into proto-icons that signal via single specific interaction, proto-indexes that combine several functions, and proto-symbols that are processed by a universal subagent equipped with a set of heritable adapters. Prefix “proto” is used here to characterize signs at the protosemiotic level. Although objects are not recognized by protosemiotic agents, they can be reliably reconstructed by human observers. In summary, protosemiosis is a primitive kind of semiosis that supports “know-how” without “know-what”. Without studying protosemiosis, the biosemiotics theory would be incomplete. (shrink)

Although the term taxon is one of the most common concepts in biology, a range of its meanings cannot be comprehended by an universal definition. Usually, biologists construe their knowledge of “the same” taxon by substantially different interpretations, so they find themselves in need either to justify this “multiplication of taxon essences”, or to surmount their plurality unifying its interpretations into a single explanation of what a taxon is. In both cases, an ontological status (“reality”) of that taxon is questioned. (...) Therefore, discrepancy between universality of the taxon concept in biology and unavoidable plurality of its interpretations can be regarded as a source of problem of the taxon ontology. The present work aims to clarify the premises of this discrepancy using phenomenological approach. Three ways of the taxon positing (as a class, as a place in the world, and as a individualized body) have been distinguished. Taxon as a class is established by common essence that is shared by a set of living beings. These living beings are regarded as speculative objects beyond an idea of the world, i.e. as objects of the experimental science. A question about ontology of taxon as a class refers to the scholastic problem of universalia; its status can be defined within the scope of the nominalism/realism opposition. Taxon as a place of common appearance of the specimens is regarded in the context of the etiological relations unifying various entities into the entire world. Taxon as a place refers to a certain position in the Natural System that is construed as an etiological map of the world. In this case a specimen of a living being is known as a curiosity, i.e. representant of its relationships as well as of the place of its origin. Ontological status of a taxon as a place is to be clarified within the framework of the natural/artificial opposition. The positing of a taxon as a collective body marked off by limits of joint survival of living beings is characteristic for biology in the strict sense which arose in the very beginning of the 19 century. A taxon as a body established by the techniques of disciplinary power sensu M. Foucault extended from the human bodies to bodies of other living beings. The ontological status of a taxon as a collective body can be defined within the scope of the wild/domesticated opposition. Therefore, the discrepancy between the universality of the taxon concept and the plurality of its interpretations is underlayed by interpenetration of three distinct modi of taxon establishing. Distinguishing between these three modi can clarify sources of ontological problems concerned with the term taxon in each case when they arise. (shrink)

This essay offers a comparative analysis of the notion of trust in Hegel and Confucius. It shows that Hegel’s two senses of trust depend upon his theory of recognition and recognitive struggle. The competitive thrust of Hegel’s account of trust, it argues, introduces a series of problems that cannot be adequately resolved within his theory, since it presupposes the kinds of trusting relations—self-, intersubjective- and world-trust—that it purports to explain. This essay then turns to the Confucian notions of xin 心 (...) and li 理 to address the problems in the Hegelian account. It concludes by outlining the Confucian account’s salience for critical social theory. (shrink)

We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct D-extensions of rank α. This is surprising, because the proof of the statement in the first-order case depends heavily on compactness. We also show that types over (D,ℵ₀)-homogeneous models have multiplicity (Morley degree) 1.

The dominant research consensus in the history and philosophy of mathematics appears to be that the history of mathematics has little to do with the philosophy of mathematics, and that the philosophy of mathematics has little to do with the history of mathematics. The philosopher of mathematics works on a specialized set of problems with perhaps only an antiquarian regard to the history of mathematics, while the historian works on the historical transmission of mathematical texts and artifacts with perhaps only (...) a passing interest in the philosophical underpinnings of those developments. (shrink)

Entombed Epigraphy and Commemorative Culture in Early Medieval China: A History of Early Muzhiming. By Timothy M. Davis. Studies in the History of Chinese Texts, vol. 6. Leiden: Brill, 2015. Pp. xiv + 414. €125, $162.

To explore the mechanism of sensation correlations between EP component amplitude and signal detection indices were studied. The time of sensation coincided with the peak latency of those EP components that showed a correlation with both indices. The components presumably reflected information synthesis in projection cortical neurons. A mechanism providing the synthesis process is proposed.

Numerous results about capturing complexity classes of queries by means of logical languages work for ordered structures only, and deal with non-generic, or order-dependent, queries. Recent attempts to improve the situation by characterizing wide classes of finite models where linear order is definable by certain simple means have not been very promising, as certain commonly believed conjectures were recently refuted (Dawar's Conjecture). We take on another approach that has to do with normalization of a given order (rather than with defining (...) a linear order from scratch). To this end, we show that normalizability of linear order is a strictly weaker condition than definability (say, in the least fixpoint logic), and still allows for extending Immerman-Vardi-style results to generic queries. It seems to be the weakest such condition. We then conjecture that linear order is normalizable in the least fixpoint logic for any finitely axiomatizable class of rigid structures. Truth of this conjecture, which is a strengthened version of Stolboushkin's conjecture, would have the same practical implications as Dawar's Conjecture. Finally, we suggest a series of reductions of the two conjectures to specialized classes of graphs, which we believe should simplify further work. (shrink)