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)

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.

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)

El objetivo de este estudio es examinar hasta qué punto es válido incluir el pensamiento de Tomás de Aquino, junto al de Aristóteles y Kant, en la estructura filosófica que Heidegger llama, en Ser y tiempo § 44, “concepto tradicional de la verdad”. Partiendo de la definición de la verdad como adecuación del intelecto y la cosa, se somete a discusión la equivalencia entre el concepto aristotélico de ὁμοίωσις, el tomista de adaequatio y el kantiano de Übereinstimmung. Para ello se (...) examina detenidamente la noción de adaequatio, se la distingue de otras nociones cercanas, y se muestra cómo los diferentes sentidos del movimiento de adecuación dan lugar, a su vez, a distintos sentidos de la verdad. Se concluye que no hay equivalencia entre los conceptos de verdad de Aristóteles, Tomás y Kant, y se profundiza en la noción de verdad ontológica. (shrink)

In this paper, I attemp to clarify the controversial use of pathêmata tîs psuchês, made by Aristotle in De Anima and De Interpretatione, specially when he signifies the act of thinking, thoughts and knowledge in general. I defend the thesis that the term pathos is essential for Aristotle's theory of knowledge. My argument is based upon the distinction, made by Aristotle in De Anima and Metaphysics, betwen two meanings of this term: as movement to the other, and as growth to (...) the same. I interpret the latter in connection with the act, and I state the senses in which it would be proper to predicate the passibility and the impassibility of the faculties of cognition, the things which are known, and knowledge itself as act. (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)

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 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)

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 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)

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 ensayo trata de presentar la fenomenología de los actos racionales, actos que son fundamentales, en todo caso, para la ciencia. En la primera parte se expone la fenomenología de la razón tal como aparece en la cuarta sección del libro de Husserl Ideas I. En la segunda parte, teniendo a la vista El origen de la geometría, se expone esa fenomenología de la razón aplicada a la explicación de la ciencia histórica, superando el relativismo en que se ve envuelta, (...) superación que también vale para la antropología cultural. Si en la primera parte se desvela la razón como legitimidad de lo que se da en sí mismo, en la segunda se expone la importante elucidación del apriori de la historia con el que cuenta el historiador y frente al cual nada puede el relativismo. Como conclusión se explica de qué manera incide la fenomenología de la razón de la primera parte en las ciencias humanas.The essay tries to present the phenomenology of rational acts, acts that are fundamental, in any case, for science. In the first part the phenomenology of reason is exposed as it appears in the fourth section of Husserl's book Ideas I. In the second part, considering The Origin of Geometry, this phenomenology of reason applied to explanation of historical science, overcoming the relativism in which it is involved, an overcoming that also applies to cultural anthropology. If in the first part reason is revealed as the legitimacy of what is given in itself, in the second part the important elucidation of the apriori of history is exposed with which the historian must count and against which relativism can do nothing. As a conclusion, it is explained how the phenomenology of reason of the first part affects the human sciences. (shrink)

Prsentación del libro El zigzag husserliano, por Ana Lucas, Editorial Endymion, Madrid, 1991. Libro sobre la filosofía del filósofo burgalés Luis Martín Santos.

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)

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)