An equivalence between the category of MV-algebras and the category $${{\rm MV^{\bullet}}}$$ MV ∙ is given in Castiglioni et al. :67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations $${a = \neg \neg a, \vee = 1}$$ a = ¬ ¬ a, ∨ = 1 and $${a \odot = a \wedge b}$$ a ⊙ = a ∧ b. An object of $${{\rm MV^{\bullet}}}$$ MV ∙ is a residuated lattice which in (...) particular satisfies some equations which correspond to the previous equations. In this paper we extend the equivalence to the category whose objects are pairs, where A is an MV-algebra and I is an ideal of A. (shrink)

This paper deals about dualities for bounded prelinear Hilbert algebras. In particular, we give an Esakia-style duality between the algebraic category of bounded prelinear Hilbert algebras and a category of H-spaces whose morphisms are certain continuous p-morphisms.

A subresiduated lattice is a pair, where A is a bounded distributive lattice, D is a bounded sublattice of A and for every there exists the maximum of the set, which is denoted by. This pair can be regarded as an algebra of type (2, 2, 2, 0, 0), where. The class of subresiduated lattices is a variety which properly contains the variety of Heyting algebras. In this paper we study the subvariety of subresiduated lattices, denoted by, whose members satisfy (...) the equation. Inspired by the fact that in any subresiduated lattice whose order is total the previous equation and the condition for every are satisfied, we also study the subvariety of generated by the class whose members satisfy that for every. (shrink)

In this paper we shall prove that certain subvarieties of the variety of Salgebras (Heyting algebras with successor) has amalgamation. This result together with an appropriate version of Theorem 1 of [L. L. Maksimova, Craig’s theorem in superintuitionistic logics and amalgamable varieties of pseudo-boolean algebras, Algebra i Logika, 16(6):643-681, 1977] allows us to show interpolation in the calculus IPC S (n), associated with these varieties.We use that every algebra in any of the varieties of S-algebras studied in this work has (...) a canonical extension, to show completeness of the calculus IPC S (n) with respect to appropriate Kripke models. (shrink)

This work extend to residuated lattices the results of [ 7 ]. It also provides a possible generalization to this context of frontal operators in the sense of [ 9 ]. Let L be a residuated lattice, and f : L k → L a function. We give a necessary and sufficient condition for f to be compatible with respect to every congruence on L . We use this characterization of compatible functions in order to prove that the variety of (...) residuated lattices is locally affine complete. We study some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P ( x , y ) and Q ( x , y ) on a residuated lattice L which imply that the function $${x \mapsto min\{y \in L : P(x, y) \leq Q(x, y)\}}$$ when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. (shrink)

Let |$\textbf{A}$| be a |$BCK$|-algebra and |$f:A^{k}\rightarrow A$| a function. The main goal of this article is to give a necessary and sufficient condition for |$f$| to be compatible with respect to every relative congruence of |$\textbf{A}$|⁠. We extend this result in some related algebras, as e.g. in pocrims.

In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [ 10 ]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation $${\tau(a) \leq b \vee (b \rightarrow a)}$$, for all $${a, b \in A}$$. These operators were studied from an algebraic, logical and topological point of view by Leo Esakia (...) in [ 10 ]. We will study frontal operators in weak Heyting algebras and we will consider two examples of them. We will give a Priestley duality for the category of frontal weak Heyting algebras in terms of relational spaces $${\langle X, \leq, T, R \rangle}$$ where $${\langle X, \leq, T \rangle}$$ is a WH -space [ 6 ], and R is an additional binary relation used to interpret the modal operator. We will also study the WH -algebras with successor and the WH -algebras with gamma. For these varieties we will give two topological dualities. The first one is based on the representation given for the frontal weak Heyting algebras. The second one is based on certain particular classes of WH -spaces. (shrink)

In this paper we study the variety \(\textsf{WL}\) of bounded distributive lattices endowed with an implication, called weak Lewis distributive lattices. This variety corresponds to the algebraic semantics of the \(\{\vee,\wedge,\Rightarrow,\bot,\top \}\) -fragment of the arithmetical base preservativity logic \(\mathsf {iP^{-}}\). The variety \(\textsf{WL}\) properly contains the variety of bounded distributive lattices with strict implication, also known as weak Heyting algebras. We introduce the notion of WL-frame and we prove a representation theorem for WL-lattices by means of WL-frames. We extended (...) this representation to a topological duality by means of Priestley spaces endowed with a special neighbourhood relation between points and closed upsets of the space. These results are applied in order to give a representation and a topological duality for the variety of weak Heyting–Lewis algebras, i.e., for the algebraic semantics of the arithmetical base preservativity logic \(\textsf{iP}^{-}\). (shrink)

In this paper we study the variety of order Hilbert algebras, which is the equivalent algebraic semantics of the order implicational calculus of Bull.

This work extend to residuated lattices the results of [7]. It also provides a possible generalization to this context of frontal operators in the sense of [9].Let L be a residuated lattice, and f : Lk → L a function. We give a necessary and sufficient condition for f to be compatible with respect to every congruence on L. We use this characterization of compatible functions in order to prove that the variety of residuated lattices is locally affine complete.We study (...) some compatible functions on residuated lattices which are a generalization of frontal operators. We also give conditions for two operations P(x, y) and Q(x, y) on a residuated lattice L which imply that the function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x \mapsto min\{y \in L : P(x, y) \leq Q(x, y)\}}$$\end{document} when defined, is equational and compatible. Finally we discuss the affine completeness of residuated lattices equipped with some additional operators. (shrink)

Book reviewed in this article: Ethical Issues in Social Research. Edited by Tom L. Beauchamp, Ruth R. Faden, R. Jay Wallace, Jr., and LeRoy Walters. Baltimore: The Johns Hopkins University Press, 1982. xii + 436 pp. $25.00 (hardcover); $8.95 (paper). Ethics of Human Subject Research. Edited by Allan J. Kimmel, Jr. San Francisco: Jossey‐Bass, 1981. 106 pp. $6.95 (paper). Social Research Ethics. Edited by Martin Bulmer. New York: Holmes & Meier, 1982. xiv + 284 pp. $39.50 (hardcover); $14.50 (paper). The (...) Ethics of Social Research: Field‐work, Regulation and Publication. Edited by Joan E. Sieber. New York: Springer‐Verlag, 1982. x + 187 pp. $23.50 (hardcover). The Ethics of Social Research: Surveys and Experiments. Edited by Joan E. Sieber. New York: Springer‐Verlag, 1982. xii + 249 pp. $23.50 (hardcover). (shrink)

El presente trabajo resume y comenta algunas de las aportaciones que nos han parecido más relevantes realizadas en los últimos años en torno a la obra filosófica de J. Ortega y Gasset. Desde la aparición del libro de P. Cerezo Galán La voluntad de aventura en 1983, el interés por el problema de Ortega ha experimentado un auge muy significativo y creciente en España, del que son muestra los estudios de Javier San Martín, Mª Carmen Paredes, Fco J. (...) class='Hi'>Martín, Máximo Martín Serrano y Jaime de Salas. Nuestro trabajo, tras una exposición resumida de estas interpretaciones, intenta una síntesis conciliadora que creemos sugerida por los propios textos del filósofo. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Eucharistic Form of God: Trinity, Incarnation, and Sacrament in the Theology of Hans Urs von Balthasar by Jonathan Martin CirauloNicholas J. HealyThe Eucharistic Form of God: Trinity, Incarnation, and Sacrament in the Theology of Hans Urs von Balthasar. By Jonathan Martin Ciraulo. Notre Dame, Ind.: University of Notre Dame Press, 2022. Pp. xiii + 297. $50.00 (hardcover). ISBN: 978-0-268-20223-1.In Fides et Ratio 93, under the heading “current (...) tasks for theology,” John Paul II writes:The chief purpose of theology is to provide an understanding of Revelation and the content of faith. The very heart of theological enquiry will thus be the contemplation of the mystery of the Triune God. The approach to this mystery begins with reflection upon the mystery of the Incarnation of the Son of God: his coming as man, his going to his Passion and Death.... From this vantage-point, the prime commitment of theology is seen to be the understanding of God’s kenosis, a grand and mysterious truth for the human mind, which finds it inconceivable that suffering and death can express a love which gives itself and seeks nothing in return. In this light, a careful analysis of texts emerges as a basic and urgent need: first the texts of Scripture, and then those which express the Church’s living Tradition. On this score, some problems have emerged in recent times, problems which are only partially new; and a coherent solution to them will not be found without philosophy’s contribution.These words about the mystery of Jesus Christ’s life and death as a revelation of the Triune God—and about the emergence of new difficulties and questions—underscore the importance of a dialogue between St. Thomas Aquinas and the great twentieth-century theologian Hans Urs von Balthasar. As two recent books written from a Thomistic perspective have shown (Aidan Nicholas, Balthasar for Thomists [San Francisco: Ignatius Press, 2020]); [End Page 715] Matthew Levering, The Achievement of Hans Urs von Balthasar [Washington, D.C.: The Catholic University of America Press, 2019]), Balthasar’s profound indebtedness to the metaphysics of Aquinas provides a solid foundation for dialogue. And yet a number of difficulties remain. What is the relationship between the so-called real distinction of esse and essence and the hypostatic union of two natures in the person of the Son? How and in what sense does the paschal mystery of Jesus’s death and Resurrection presuppose and express the mystery of the Father’s eternal generation of the Son? In the words of Joseph Ratzinger, “in the pierced heart of the Crucified, God’s own heart is opened up—here we see who God is and what he is like” (Spirit of the Liturgy [San Francisco: Ignatius Press, 2000], 48). How does the mystery of Christ’s Eucharist reveal the heart of God?This last question about the Eucharist and the nature of God is explored in depth in Jonathan Martin Ciraulo’s monograph, The Eucharistic Form of God: Hans Urs von Balthasar’s Sacramental Theology. Despite the expansive title, the primary aim of this book is fairly straightforward: to present Balthasar’s theology of the Eucharist and to show the significance of his thought for contemporary sacramental theology. Anyone who seeks to offer a systematic account of Balthasar’s theology of the Eucharist is confronted with at least two basic obstacles or challenges. First, his reflections on the Eucharist are scattered throughout (and often hidden within) an immense and complex corpus of writings. Second, the most distinctive feature of Balthasar’s theology of the Eucharist is the inseparability of his sacramental theology from his speculative account of the central mysteries of the Christian faith—Trinity, Incarnation, Cross and Resurrection, Church, and eschaton.The Eucharistic Form of God represents a thoughtful, well-written, and original response to this twofold challenge. Regarding the first point: Ciraulo demonstrates an intimate familiarity with the whole of Balthasar’s corpus. He draws together Balthasar’s early writings on German literature, his monographs on Origen, Gregory of Nyssa, and Maximus the Confessor, his engagement with Karl Barth, his interpretation of twentieth-century French Catholic literature... (shrink)

J’ai rencontré Marie-Jeanne Bérère à Lyon en 1994. C’était une petite femme vive, à la parole claire et précise, avec un bel accent bourguignon. Elle avait accepté une interview, à son domicile lyonnais, le 23 mars 1995. Je souhaitais la revoir pour ce numéro de CLIO, Histoire, Femmes et Sociétés sur les Chrétiennes mais elle est décédée dans l’été 2000, à 73 ans, sans avoir eu le temps de rédiger ses mémoires. Son itinéraire de femme engagée dans l’Église catholique est (...) celui d’une chrétienn... (shrink)

El artículo trata sobre el 'reavivamiento hermeneútico' de Agustín, es decir, acerca de la significación filosófica que tiene el influjo histórico y metodológico de san Agustín sobre la obra de Martin Heidegger "Sein und Zeit", y cómo esto se ha vuelto más evidente con las aportaciones de fenomenólogos y patrólogos, especialmente a partir de 1993.

El presente texto tiene como objetivo exponer el concepto de “cultura básica”, fundamental en la fenomenología de Lester Em-bree. En la primera parte se expondrá el contexto biográfico de ese texto. En la segunda se abordará el primer avance que hace Lester Embree, para en la tercera centrarse en el artículo fundamental sobre el mismo. El núcleo del concepto está en relación con la diferencia que Lester Embree establece entre la experiencia y la posicionalidad de uso, valoración y creencia. Estas (...) son características o determinaciones culturales que constituyen el mundo humano, que por eso es siempre un mundo cultural. Esa cultura básica se da también, al menos, en algunos animales no humanos. Aunque se alude a puntos problemáticos de esa teoría, no se entra de lleno en esos problemas.The present paper aims to expose the concept of "basic culture", fundamental in Lester Embree’s phenomenology. In the first part the biographical context of that text is explained. In the second one, the first advance made by Lester Embree is described, and in the third one the fundamental article about it will be focused on. The core of the concept is in relation to the difference that Lester Embree establishes between experience and the positionality of use, valuation and belief. These are characteristics or cultural determinations that constitute the human world, which therefore is always a cultural world. This basic culture also occurs, at least, in some non-human animals. Although problematic points of that theory are alluded to, these problems are not fully developed. (shrink)

An l-hemi-implicative semilattice is an algebra $$\mathbf {A} = $$ A= such that $$$$ is a semilattice with a greatest element 1 and satisfies: for every $$a,b,c\in A$$ a,b,c∈A, $$a\le b\rightarrow c$$ a≤b→c implies $$a\wedge b \le c$$ a∧b≤c and $$a\rightarrow a = 1$$ a→a=1. An l-hemi-implicative semilattice is commutative if if it satisfies that $$a\rightarrow b = b\rightarrow a$$ a→b=b→a for every $$a,b\in A$$ a,b∈A. It is shown that the class of l-hemi-implicative semilattices is a variety. These algebras provide (...) a general framework for the study of different algebras of interest in algebraic logic. In any l-hemi-implicative semilattice it is possible to define an derived operation by $$a \sim b := \wedge $$ a∼b:=∧. Endowing $$$$ with the binary operation $$\sim $$ ∼ the algebra $$$$ results an l-hemi-implicative semilattice, which also satisfies the identity $$a \sim b = b \sim a$$ a∼b=b∼a. In this article, we characterize the commutative l-hemi-implicative semilattices. We also provide many new examples of l-hemi-implicative semilattice on any semillatice with greatest element. Finally, we characterize congruences on the classes of l-hemi-implicative semilattices introduced earlier and we characterize the principal congruences of l-hemi-implicative semilattices. (shrink)

La obra de Julia V. Iribarne se basa, entre otros, en tres conceptos centrales, intersubjetividad trascendental, ética trascendental y antropología trascendental. En este texto de homenaje a su persona y a su trayectoria intelectual, dado que nuestra autora se basa fundamentalmente en los inéditos de Husserl, aclararé, en primer lugar la posición del legado póstumo [Nachlass] husserliano en la obra de este. A continuación dedicaré un apartado a exponer el desarrollo de cada uno de esos conceptos a lo largo de (...) su trayectoria, desde la intersubjetividad, pasando por la ética, hasta antropología trascendental.Julia V. Iribarne’s lifework rests, among others, on three central concepts, transcendental intersubjectivity, transcendental ethics and transcendental anthropology. In this text in tribute to her person and intellectual trajectory, and because Julia V. Iribarne’s writings are founded basically on Husserl’s Nachlass, I shall first clarify my conception about the relation of this Nachlass to his work. Next I will dedicate a section to explain the development of each of the concepts throughout her career, from intersubjectivity,, to ethics and to transcendental anthropology. (shrink)

En el presente trabajo se trata, por un lado, de presentar la posición de Antropología filosófica en España, empezando, en el primer apartado, por una breve historia de su posición en el siglo pasado hasta 1980. En segundo lugar se explora el carácter de esta materia, primero desde la legitimidad de su diseño por Rousseau y Kant —segundo apartado—, y luego desde una orientación en torno a su contenido —apartado tercero—. En el apartado cuarto se examina la posición de la (...) antropología filosófica en la filosofía como filosofía primera, para terminar en el último apartado exponiendo cuál es la situación de la misma en los estudios contemporáneos de grado de filosofía. (shrink)

Let \({\mathcal {K}}\) be a quasivariety. We say that \({\mathcal {K}}\) is a term quasivariety if there exist an operation of arity zero _e_ and a family of binary terms \(\{t_i\}_{i\in I}\) such that for every \(A \in {\mathcal {K}}\), \(\theta \) a \({\mathcal {K}}\) -congruence of _A_ and \(a,b\in A\) the following condition is satisfied: \((a,b)\in \theta \) if and only if \((t_{i}(a,b),e) \in \theta \) for every \(i\in I\). In this paper we study term quasivarieties. For every \(A\in (...) {\mathcal {K}}\) and \(a,b\in A\) we present a description for the smallest \({\mathcal {K}}\) -congruence containing the pair (_a_, _b_). We apply this result in order to characterize \({\mathcal {K}}\) -compatible functions on _A_ (i.e., functions which preserve all the \({\mathcal {K}}\) -congruences of _A_) and we give two applications of this property: (1) we give necessary conditions on \({\mathcal {K}}\) for which for every \(A \in {\mathcal {K}}\) the \({\mathcal {K}}\) -compatible functions on _A_ coincides with a polynomial over finite subsets of _A_; (2) we give a method to build up \({\mathcal {K}}\) -compatible functions. (shrink)

El ejercicio filosófico de raíz marxista en Chile tiene un capítulo escrito por los intelectuales comunistas de la década del 60 del siglo XX. Uno de ellos, Sergio Vuskovic, se abocó a discutir con las tesis althusserianas que identificaron la teorización de Marx como un antihumanismo teórico. Para oponerse a tal perspectiva, Vuskovic realiza una operación teórica al interior de la obra de Marx con el objetivo de afirmar la categoría de sujeto, así como la interna relación entre ejercicio teórico (...) y praxis socio-histórica. Chilean communist intellectuals of the 1960's wrote a chapter of the history of Marxist philosophy. One of them was Sergio Vuskovic who focused on discussing Marx's theories according to Althusser's thesis of anti-humanism. By affirming the subject category and the internal relationship between "theoretical operation" and socio-historical praxis within Marx's philosophy, Vuskovic opposes Althusser's perspective. (shrink)

El objetivo de este ensayo es primero honrar la memoria de Vicent Martínez Guzmán, destacando sus importantes contribuciones a la filosofía. Dada su relación con el autor, ha parecido lo más oportuno centrarse en la relación de su filosofía con la fenomenología puesto que otros colegas desentrañarán otras facetas. Para cumplir ese cometido el ensayo tiene cuatro partes. En la primera se hace una presentación de las etapas de la filosofía de nuestro autor. En la segunda se expone, con bastante (...) amplitud, por la importancia que tiene, la primera concepción de la fenomenología de Vicent Martínez Guzmán. El apartado tercero expone, aunque sea brevemente, por ser más conocido, el sentido fenomenológico de la filosofía para hacer las paces. Por fin, la cuarta comenta la posición de Vicent Martínez Guzmán respecto al ordoliberalismo de la Escuela de Friburgo, considerando la relación de este con la fenomenología husserliana.The aim of this essay is first of all to honor the memory of Vicent Martínez Guzmán, highlighting his important contributions to philosophy. Given its relationship with the author, it has seemed most appropriate to focus on the relationship of his philosophy with phenomenology since other colleagues will unravel other facets. To fulfill this task, the essay has four parts. In the first one, a presentation is made of the stages of our author's philosophy. In the second, the first conception of the phenomenology of Vicent Martínez Guzmán is exposed, quite widely, because of its importance. The third section exposes, even if briefly, for being better known, the phenomenological sense of “philosophy to make peace”. Finally, the fourth section comments on Vicent Martínez Guzmán’s position regarding the ordoliberalism of the Fribourg School, considering its relation to Husserlian phenomenology. (shrink)

En philosophie, le personnage conceptuel trace une nouvelle image de la pensée. Au cinéma, avec la modernité, le personnage découvre une nouvelle image. Après la crise de I’image-action, les signes ne se reconnaissent pas plus qu ’ils ne se déduisent : ils se voient. Celui qui voit, c’est le personnage. Dans cette vision, il devient I’inventeur de nouvelles façons de percevoir. Il est á la fois producteur et créateur. Le propre du personnage conceptuel réside aussi en la création non pas (...) de percepts, mais de concepts. À partir de ces deux constatations, il nous semble intéressant de commenter le troisième chapitre de Qu’est-ce que la philosophie? qui porte sur le personnage conceptuel et de faire une analyse du voyant, personnage de cinéma, qui apparaît dans le premier chapitre de L’image-temps. Grâce à cette étude croisée nous espérons trouver des recoupements et des liens entre personnage, pensée et perception. (shrink)