We show that the variety of Heyting algebras has finitary unification type. We also show that the subvariety obtained by adding it De Morgan law is the biggest variety of Heyting algebras having unitary unification type. Proofs make essential use of suitable characterizations (both from the semantic and the syntactic side) of finitely presented projective algebras.

We show that some common varieties of modal K4-algebras have finitary unification type, thus providing effective best solutions for equations in free algebras. Applications to admissible inference rules are immediate.

By means of models in toposes of C-sets (where C is a small category), necessary conditions are found for the minimum quantified extension of a propositional (intermediate, modal) logic to be complete with respect to Kripke semantics; in particular, many well-known systems turn out to be incomplete.

The logicD-J of the weak exluded middle with constant domains is proved to be incomplete with respect to Kripke semantics, by introducing models in presheaves on an arbitrary category. Additional incompleteness results are obtained for the modal systems with nested domains extendingQ-S4.1.

We show that (contrary to the parallel case of intuitionistic logic, see [7], [4]) there does not exist a translation fromS42 (the propositional modal systemS4 enriched with propositional quantifiers) intoS4 that preserves provability and reduces to identity for Boolean connectives and.

Sufficient syntactic conditions for canonicity in intermediate and intuitionistic modal logics are given. We present a new technique which does not require semantic first-order reduction and which is constructive in the sense that it works in an intuitionistic metatheory through a model without points which is classically isomorphic to the usual canonical model.

In this paper we present a general theory of normal forms, based on a categorial result for the free monoid construction. We shall use the theory mainly for proposictional modal logic, although it seems to have a wider range of applications. We shall formally represent normal forms as combinatorial objects, basically labelled trees and forests. This geometric conceptualization is implicit in and our approach will extend it to other cases and make it more direct: operations of a purely geometric and (...) combinatorial nature will be introduced in order to give a mathematical description of the basic logical/algebraic constructions .We begin by recalling the above-mentioned categorial construction: we need a careful inspection of it because in the various examples considered later we plan to deduce from it in a uniform way the normal forms and the description of finitely generated free algebras. This method always works whenever we can describe the category of algebras corresponding to the logic under consideration as a T-objects category. When this simple description seems not to be available, still the general theory might be of some interest, because a description of the category of algebras as a T-objects category plus equation is possible .The central part of the paper is more advanced and specific: we show how the general approach presented here can provide some insights even in the basic case of the modal system K. Section 4 contains a contribution to the theory of normal forms, namely the description of the uniform substitution. This result will enable us to give a duality theorem for the category of finitely generated free modal algebras and in Section 5 to provide a characterization of the collections of normal forms which happen to be normal forms for a logic, thus giving a description of the lattice of modal logics.Section 6 deals with some applications: we shall show how to use normal forms in order to prove for the modal system K the definability of higher-order propositional quantifiers and of the tense operator F .As to the prerequisites, the paper is almost self-contained. The reader is only assumed to have familiarity with standard techniques in algebraic logic ). Knowledge of the basic facts about adjoint functors is required too, see e.g. McLane or the appendix. (shrink)

We investigate finitarity of unification types in locally finite varieties of Heyting algebras, giving both positive and negative results. We make essential use of finite dualities within a conceptualization for E-unification theory 733–752) relying on the algebraic notion of a projective object.

Recent studies reported the development of psychological distress symptoms in patients who recovered from COVID-19. However, evidence is still scarce and new data are needed to define the exact risk and protective factors that can explain the variability in symptoms manifestation. In this study, we enrolled 257 patients who recovered from COVID-19 and we evaluated the levels of psychological distress through the Symptoms Checklist-90-R scale. Data concerning illness-related variables were collected from medical records, while the presence of subjective cognitive difficulties, (...) both before and after the illness, as well as the level of the cognitive reserve, were assessed over a clinical interview. Results revealed that being female and reporting the presence of subjective cognitive difficulties after COVID-19 were associated with higher levels of psychological distress. At the same time, being admitted to the hospital and having a high CR were protective factors. Adding new information to this emerging research field, our results highlight the importance of a complete psychological and cognitive assessment in patients with COVID-19. (shrink)

A. M. Pitts in [Pi] proved that HA op fp is a bi-Heyting category satisfying the Lawrence condition. We show that the embedding $\Phi: HA^\mathrm{op}_\mathrm{fp} \longrightarrow Sh(\mathbf{P_0,J_0})$ into the topos of sheaves, (P 0 is the category of finite rooted posets and open maps, J 0 the canonical topology on P 0 ) given by $H \longmapsto HA(H,\mathscr{D}(-)): \mathbf{P_0} \longrightarrow \text{Set}$ preserves the structure mentioned above, finite coproducts, and subobject classifier, it is also conservative. This whole structure on HA op (...) fp can be derived from that of Sh(P 0 ,J 0 ) via the embedding Φ. We also show that the equivalence relations in HA op fp are not effective in general. On the way to these results we establish a new kind of duality between HA op fp and a category of sheaves equipped with certain structure defined in terms of Ehrenfeucht games. Our methods are model-theoretic and combinatorial as opposed to proof-theoretic as in [Pi]. (shrink)

We characterize (both from a syntactic and an algebraic point of view) the normal K4-logics for which unification is filtering. We also give a sufficient semantic criterion for existence of most general unifiers, covering natural extensions of K4.2⁺ (i.e., of the modal system obtained from K4 by adding to it, as a further axiom schemata, the modal translation of the weak excluded middle principle).

This text through the direct use to Foucault’s work and using the concepts of ‘care of the self’ and biopolitics is questioning and analyzing resistance and practices of freedom. Mainly, from the Foucault’s courses at the College de France and the methodological tools found there, here I present a discussion about Gilles Deleuze’s contributions to Foucault’s thought and I develop a dialog where I try to explain the concepts of domination, power, ethics, esthetics and the relationship of the self with (...) himself. (shrink)

Abstract.Formal topologies are today an established topic in the development of constructive mathematics. One of the main tools in formal topology is inductive generation since it allows to introduce inductive methods in topology. The problem of inductively generating formal topologies with a cover relation and a unary positivity predicate has been solved in [CSSV]. However, to deal both with open and closed subsets, a binary positivity predicate has to be considered. In this paper we will show how to adapt to (...) this framework the method used to generate inductively formal topologies with a unary positivity predicate; the main problem that one has to face in such a new setting is that, as a consequence of the lack of a complete formalization, both the cover relation and the positivity predicate can have proper axioms. (shrink)

The role played by continuous morphisms in propositional modal logic is investigated: it turns out that they are strictly related to filtrations and to suitable variants of the notion of a free algebra. We also employ continuous morphisms in incremental constructions of (standard) finitely generated free ????4-algebras.

This article suggests developing the concept of spiritual ecology into that of balanced spiritual ecosystems. Philosophies, theologies, education systems, political parties, and gender-based and ethnic identity politics need to be critiqued both from within and without so that they can finally contribute to the creation, maintenance and flourishing of balanced spiritual ecosystems.Contribution: Spiritual ecology is a concept on which converge different worldviews. This article recommends using balanced spiritual ecosystems, instead. The new concept could provoke further reflection on how our -ontologies (...) and communities co-exist and whether they do it organically and spiritually. This article befits HTS’s interest in ‘theology and nature’. (shrink)

Heideggers Kritik am Nationalsozialismus ist vor allem ab 1963 greifbar in Vorträgen, Vorlesungen (zu Nietzsche) und den "Beiträgen zur Philosophie". Entgegen Thesen der jüngsten Heidegger-Kontroverse hat sich Heidegger nach einer Phase der falschen politischen Besetzung seiner Philosophie im Jahre 1933 vor allem ab 1936 von der Bewegung des Nationalsozialismus gelöst. Er begreift den Nationalsozialismus zunehmend klar als eine Erscheinungsform des Nihilismus, der "Seinsverlassenheit" und des Herrschaftsdenkens des reinen "Willens zur Macht". Dabei geht Heideggers subtile philosophische Kritik des Nationalsozialismus über in (...) eine Kritik der neuzeitlichen Technologie als einer sich fortsetzenden Form planetarischen Herrschaftsdenkens und der Ausbeutung der Erde durch den Menschen. (shrink)

By using some classical reasoning we show that any countably presented formal topology, namely, a formal topology with a countable axiom set, is spatial.

Under some assumptions on an equational theory S , we give a necessary and sufficient condition so that S admits a model completion. These assumptions are often met by the equational theories arising from logic. They say that the dual of the category of finitely presented S-algebras has some categorical stucture. The results of this paper combined with those of [7] show that all the 8 theories of amalgamable varieties of Heyting algebras [12] admit a model completion. Further applications to (...) varieties of modal algebras are given in [8]. (shrink)

Die Entwicklung der Rationalität ist eine Erfolgsgeschichte. Denn die Rationalität war und ist der Motor der abendländischen Kultur und der Grund dafür, dass sie in der Neuzeit allen anderen Weltkulturen machtpolitisch überlegen ist. Zwischen dem 8. und 6. Jahrhundert v. Chr. formierte sich das logische Denken gleich auf mehreren Feldern: Durch die Erfindung der philosophischen Wissenschaft, die Geometrisierung des Raumes und der Schlachtordnung, die Berechnung der Zeit, durch die Geldwirtschaft und die neuen Organisationsformen des Politischen wurde Rationalität zum Synonym für (...) Fortschritt. Auch die Begriffe Freiheit und Demokratie gehören in diesen Zusammenhang. Silvio Vietta zeichnet diese Erfolgsgeschichte nach, beschreibt aber auch ihre Gefahren und Kurzschlüsse. In der Konsequenz entwickelt er eine : ndere9 aisthetisch rückgebundene und reflexive Rationalität, die uns aus den gegenwärtigen Krisen herausführen könnte. (shrink)

The pandemic period has placed the organizations in a state of great tension. It has generated a situation of confusion, lack of rules, and production-related criticalities that have called into question the very existence of many productive realities. This article aims to highlight the dimensions of care and ethics put in place by HR managers in COVID-19. The objective that animated the authors have focused on the HRM level of medium and large companies in Italy to highlight the protective actions (...) toward people and the organization in the period COVID 19, highlighting what were the ethical values and actions of care put in place. In this article, we wanted to give voice to managers who had management tasks in their organizations by asking them to tell us how they dealt with the challenges imposed by the emergency. In the research, we start from a way of understanding workplaces understood as a “process of ongoing social relationship” within which the HR function is dedicated to the care of the quality of relationships. HR managers have to manage a complex role of mediating between the interests of people and employers by trying to find good mediations. (shrink)

We prove a generalization of the hyper-game theorem by using an abstract version of inductively generated formal topology. As applications we show proofs for Cantor theorem, uncountability of the set of functions from N to N and Gödel theorem which use no diagonal argument.

Das Buch stellt Nietzsches und Levinas' Destruktionen des griechisch-europäauml;ischen Denkens und der in ihm eingeschlossenen Moral einander gegenüuuml;ber. Dabei werden Anlässe ihrer Kritik und ihre Ausnahmestellung im philosophischen Diskurs herausgearbeitet. Im Anschluss werden Nietzsches und Levinas' Alternativen zu den allgemeinen moralischen Werten verglichen und ihre Vereinbarkeit und Unvereinbarkeit geklärt. Beide Alternativen führen auf eine prinzipiell unbegrenzte Verantwortung des Einzelnen hinaus, die mit Textbeispielen Dostojewskijs unterlegt wird.

The quantified extension of a canonical prepositional intermediate logic is complete with respect to the generalization of Kripke semantics taking into consideration set-valued functors defined on a category.

Este artigo descreve e comenta a criação, por parte de Allan Kardec, de um complexo arcabouço de divulgação de sua produção no novo campo de estudos a que denominou “Espiritismo”, ou “ciência espírita”. Embora não fazendo parte do mundo acadêmico, no sentido institucional do termo, o pesquisador francês efetivamente se aproximou, no desenvolvimento dessa interface com o público, daquilo que à época começava a se tornar padrão nas áreas mais maduras da ciência. Criou uma sociedade de estudos, a Sociedade Parisiense (...) de Estudos Espíritas, em que fatos, hipóteses e métodos eram apresentados e discutidos, antes de eventualmente serem incorporados em textos e divulgados mais amplamente. Para essa divulgação, conjugou a publicação de livros temáticos a uma revista de assuntos espíritas gerais, a Revista Espírita, para veicular ensaios e resultados preliminares, servindo também de via de mão dupla para a interação com assinantes e correspondentes, interessados em contribuir com a elaboração da teoria espírita. Dado, porém, que o Espiritismo não era, nem pretendia ser, uma disciplina científica inserida no meio acadêmico oficial, existem diversas diferenças entre essas duas instituições espíritas e suas análogas na academia. Estas diferenças são aqui apontadas, explicadas e justificadas, como aspectos típicos do programa kardequiano. (shrink)

Formal topology is today an established topic in the development of constructive mathematics and constructive proofs for many classical results of general topology have been obtained by using this approach. Here we analyze one of the main concepts in formal topology, namely, the notion of formal point. We will contrast two classically equivalent definitions of formal points and we will see that from a constructive point of view they are completely different. Indeed, according to the first definition the formal points (...) of the formal topology of the real numbers can be indexed by a set whereas this is not possible according to the second one. (shrink)

Resumo: Este artigo interroga a consolidação da pesquisa em ensino de Filosofia no Brasil nas últimas décadas, em torno da perspectiva de se tomar o ensino de Filosofia como problema filosófico. Contextualiza o campo de disputas e debates sobre o ensino de Filosofia na educação básica como pano de fundo para estas pesquisas. A partir das reflexões de Michel Foucault sobre a disciplina e seu poder de seleção e organização dos saberes, introduz a noção de “campo disciplinar” para defender que (...) houve um bom desenvolvimento das pesquisas no país, na interface da Filosofia com a Educação, que possibilitou a emergência e certa consolidação de um campo disciplinar, que tem produzido saberes em torno do ensinar Filosofia nos diversos níveis escolares e acadêmicos. Palavras-chave: Disciplina; Campo Disciplinar; Pesquisa; Filosofia; Foucault Research in Philosophy teaching: a disciplinary field? Abstract: This article questions the consolidation of research in Philosophy teaching in Brazil in recent decades, around the perspective of taking the teaching of Philosophy as a philosophical problem. It contextualizes the field of disputes and debates about the teaching of Philosophy in basic education as a background for this research. Based on Michel Foucault’s reflections on discipline and its power to select and organize knowledge, it introduces the notion of “disciplinary field” to argue that there was a good development of research in the country, in the interface between Philosophy and Education, which enabled the emergence and some consolidation of a disciplinary field, which has produced knowledge about teaching philosophy at different school and academic levels. Keywords: Discipline; Disciplinary Field; Research; Philosophy; Foucault Investigación en enseñanza de la Filosofía: ¿un campo disciplinar? Resumo: Este artículo cuestiona la consolidación de la investigación en la enseñanza de la Filosofía en Brasil en las últimas décadas, en torno a la perspectiva de tomar la enseñanza de la Filosofía como un problema filosófico. Contextualiza el campo de disputas y debates sobre la enseñanza de la Filosofía en la educación básica como trasfondo de estas investigaciones. A partir de las reflexiones de Michel Foucault sobre la disciplina y su poder para seleccionar y organizar el conocimiento, introduce la noción de “campo disciplinar” para argumentar que hubo un buen desarrollo de la investigación en el país, en la interfaz entre Filosofía y Educación, lo que posibilitó el surgimiento y cierta consolidación de un campo disciplinar, que ha producido conocimientos sobre la enseñanza de la filosofía en diferentes niveles escolares y académicos. Palabras clave: Disciplina; Campo Disciplinar; Investigación; Filosofía; Foucault Data de registro: 20/01/2023 Data de aceite: 21/02/2024. (shrink)

El artículo pretende analizar el concepto de utopía como central en la teoría crítica de Herbert Marcuse (1898-1979). En primer lugar, abordaremos el debate que el autor desarrolla con Max Horkheimer. En el ensayo fundamental «Teoría tradicional y teoría crítica», Horkheimer subraya la importancia de la utopía para construir una imagen del futuro, pero desconfía de las potencias utópicas y de sus vínculos idealistas. En «Filosofía y teoría crítica» (1937), Marcuse responde a esta postura: la teoría crítica no debe temer (...) a la utopía. En lugar de dejarla para un futuro incierto, Marcuse señala que las promesas utópicas ya se ofrecen en el presente y que el pensamiento crítico también debe tomar nota de ello. Años más tarde (1967), Marcuse reconoce el cambio de la perspectiva utópica basada en la sociedad del trabajo. Con la tecnología, las relaciones sociales se transforman. Pero esto no significa que las energías utópicas estén agotadas, como afirma Jürgen Habermas. Por el contrario, son muchas las luchas sociales que surgen en este periodo. En fin, con Marcuse, las energías utópicas se renuevan, recuperando un nuevo sentido de libertad y necesidad que surge de estas luchas. 190-206. (shrink)

Die jüngst publizierten "Schwarzen Hefte" Heideggers und auch der Neufund des Heftes von 1945/46 machen deutlich: Heidegger entwickelt hier eine Theorie der Globalisierung. Diese führt er nicht auf eine jüdische Weltverschwörung zurück -- da wäre nur eine "Machenschaft" auf eine andere reduziert -- sondern auf die abendländische Kulturgeschichte selbst. Insbesondere der neuzeitliche Siegeszug des "rechnenden Denkens" habe eine Geschichte des Herrschaftsdenkens und des Expansionismus in Gang gesetzt. Darin sieht Heidegger ab 1934 das Dritte Reich wie auch den Bolschewismus und den (...) Kolonialismus Englands und der USA involviert. Heidegger setzt dem entfesselten Herrschaftsdenken auch nach dem Zweiten Weltkrieg -- ihrer "Vernutzung der Erde" und "Verrechnung der Welt" -- die Lehre vom "andren Anfang" der Geschichte entgegen: eine Kulturpraxis der Schonung und Nachhaltigkeit. (shrink)

Aristotle’s conception of causality and the ones Modern philosophers have bequeathed us have been exhaustively discussed, although the contrast between them has not, in my opinion, been sufficiently highlighted. This paper proposes to fill this gap. I start with Aristotelian causality and his theses that causal explanation requires knowledge of causal laws and that the necessity associated with these laws presupposes the existence of causal powers. I discuss next Locke’s and Leibniz’s attempts to modernize Aristotle’s theses on causality. The third (...) part of the paper presents two paradoxes Hume identified, on the one hand, between Locke’s and Leibniz’s theses about our knowledge of causal laws and, on the other hand, between the Aristotelian thesis that there must be causal powers and the scientific practice of Modernity. Hume’s proposal to eliminate these paradoxes is also discussed. I finish with some critical remarks on the humean model about our knowledge of causal laws as compared with his contribution to the analysis of the concept of causality. (shrink)

Este articulo tiene el objetivo de cuestionar los sentidos del aula de filosofia, sobre todo en la educaciön secundaria. Para eso, parte de la definiciön de filosofia expuesta por Deleuze y Guattari en Qu'est-ce que la philosophie?, donde la senala como una actividad de creaciön de conceptos, hace critica a las concepciones del aula de filosofia como momentos de reflexion, de contemplaciön o incluso de diälogos, una vez que ninguna de estas tareas se hace especfficamente filosöfica. Para garantizar esa especificidad, (...) intenta caracterizar el aula de filosofia como un "taller de conceptos", un espacio donde el maestro y los alumnos se hacen creadores de conceptos, alrededor de problemas vividos, tomando como herramientas los conceptos histöricamente producidos. (shrink)

By using algebraic-categorical tools, we establish four criteria in order to disprove canonicity, strong completeness, w-canonicity and strong w-completeness, respectively, of an intermediate propositional logic. We then apply the second criterion in order to get the following result: all the logics defined by extra-intuitionistic one-variable schemata, except four of them, are not strongly complete. We also apply the fourth criterion in order to prove that the Gabbay-de Jongh logic D1 is not strongly w-complete.

We provide a new and elementary proof of strong normalization for the lambda calculus of intersection types. It uses no strong method, like for instance Tait-Girard reducibility predicates, but just simple induction on type complexity and derivation length and thus it is obviously formalizable within first order arithmetic. To obtain this result, we introduce a new system for intersection types whose rules are directly inspired by the reduction relation. Finally, we show that not only the set of strongly normalizing terms (...) of pure lambda calculus can be characterized in this system, but also that a straightforward modification of its rules allows to characterize the set of weakly normalizing terms. (shrink)

Novalis and Nietzsche: Analogies and Differences Between Two Poetic Thinkers.There are several substantial similarities between Novalis and Nietzsche. Stylistically, they both present their arguments and ideas in the form of short and concise prose (Aphorismus,Fragment), but there is also considerable overlap in terms of the general orientation of their thinking: both exhibit a certain concern for earthly nature and show an interest in the figure of the extraordinary individual, but they also have a common interest in physiology, in the idea (...) of fiction, and in the night as a allowing for greater experiential depth. Moreover, Novalis and Nietzsche both warned of the rise of nationalism in Europe, to some extent anticipating a new form of war that eventually became a reality in the First World War. This essay, thus, seeks to outline a range of connections between early German romanticism and Nietzsche that would require further research. (shrink)

Este texto reflete sobre o memoricídio, consequente à presunção racial branca, como vestígio de operações para o genocídio dos corpos e das mentes negras a partir da Peleja de Inácio da Catingueira contra Romano. Sob o jogo discursivo da humilhação, já se encontrava a vontade brutal de destruição de qualquer traço, perspectiva, visão remanescente de saberes e culturas africanas ou descendentes, fossem de cunho material, simbólico, reflexivo, imagético, expressivo, na língua, no corpo. No embate, Inácio, negro, escravizado, já rebaixado sob (...) a égide do sistema escravocrata, embate-se contra a tentativa presunçosa de aniquilamento perpetrada por seu oponente. (shrink)

Both in the Treatise of Human Nature and in the Enquiry concerning Human Understanding, Hume defends that “there is no chance in the world”, and that “what the vulgar call chance is nothing but a secret and conceal’d cause”. This view plays a crucial role in Hume’s influential analysis of free will and moral responsibility. It functions also as a central presupposition in his discussion of miracles. However, Hume himself argued convincingly that the “maxim of causality”, according to which “whatever (...) begins to exist, must have a cause of existence” cannot be established a priori, by either intuition or demonstration. He concludes, then, that such “opinion must necessarily arise from observation and experience”. In the present article I analyse this latter statement, showing, first, what was Hume detailed proposal for funding the principle of causality on experience. Given the apparent weakness of this proposal, I then speculate on what kind of firmer empirical foundation could, instead, have been given, in Hume’s time, to the principle of causality, namely, the indirect support offered by Newtonian mechanics. Finally, I show how this theoretical link between experience and the principle, and also Hume’s straightforward, inductive argument, were undermined by the inception of quantum physics, at the beginning of the 20th century. (shrink)

O presente artigo tenciona apresentar algumas considerações sobre a atual conjuntura política e social do Brasil, enfatizando uma perspectiva que leva em conta a centralidade das periferias metropolitanas na vida social do país. A presença e influência do cristianismo evangélico - em ascensão demográfica, cultural e política -, bem como de novos padrões de sociabilidade constituídos e irradiados a partir da dinâmica social decorrente dos conflitos violentos entre as forças policiais e militares e facções do crime organizado são considerados vetores (...) explicativos indispensáveis na compreensão da realidade social contemporânea do país e são lidos desde a experiência etnográfica do autor enquanto professor no Complexo do Chapadão, na periferia do Rio de Janeiro. (shrink)