An l-hemi-implicative semilattice is an algebra \\) such that \\) is a semilattice with a greatest element 1 and satisfies: for every \, \ implies \ and \. An l-hemi-implicative semilattice is commutative if if it satisfies that \ for every \. 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 \ \wedge \). Endowing \\) with the binary operation \ the algebra \\) results an l-hemi-implicative semilattice, which also satisfies the identity \. 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)

In this paper we introduce and study a variety of algebras that properly includes integral distributive commutative residuated lattices and weak Heyting algebras. Our main goal is to give a characterization of the principal congruences in this variety. We apply this description in order to study compatible functions.

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)

In this paper we introduce and study a variety of algebras that properly includes integral distributive commutative residuated lattices and weak Heyting algebras. Our main goal is to give a characterization of the principal congruences in this variety. We apply this description in order to study compatible functions.

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)

We study some operations that may be defined using the minimum operator in the context of a Heyting algebra. Our motivation comes from the fact that 1) already known compatible operations, such as the successor by Kuznetsov, the minimum dense by Smetanich and the operation G by Gabbay may be defined in this way, though almost never explicitly noted in the literature; 2) defining operations in this way is equivalent, from a logical point of view, to two clauses, one corresponding (...) to an introduction rule and the other to an elimination rule, thus providing a manageable way to deal with these operations. Our main result is negative: all operations that arise turn out to be Heyting terms or the mentioned already known operations or operations interdefinable with them. However, it should be noted that some of the operations that arise may exist even if the known operations do not. We also study the extension of Priestley duality to Heyting algebras enriched with the new operations. (shrink)

Extending the relation between semi-Heyting algebras and semi-Nelson algebras to dually hemimorphic semi-Heyting algebras, we introduce and study the variety of dually hemimorphic semi-Nelson algebras and some of its subvarieties. In particular, we prove that the category of dually hemimorphic semi-Heyting algebras is equivalent to the category of dually hemimorphic centered semi-Nelson algebras. We also study the lattice of congruences of a dually hemimorphic semi-Nelson algebra through some of its deductive systems.

A hemi-implicative lattice is an algebra \((A,\wedge,\vee,\rightarrow,1)\) of type (2, 2, 2, 0) such that \((A,\wedge,\vee,1)\) is a lattice with top and for every \(a,b\in A\), \(a\rightarrow a = 1\) and \(a\wedge (a\rightarrow b) \le b\). A new variety of hemi-implicative lattices, here named sub-Hilbert lattices, containing both the variety generated by the \(\{\wedge,\vee,\rightarrow,1\}\) -reducts of subresiduated lattices and that of Hilbert lattices as proper subvarieties is defined. It is shown that any sub-Hilbert lattice is determined (up to isomorphism) by (...) a triple (_L_, _D_, _S_) which satisfies the following conditions: _L_ is a bounded distributive lattice, _D_ is a sublattice of _L_ containing 0, 1 such that for each \(a, b \in L\) there is an element \(c \in D\) with the property that for all \(d \in D\), \(a \wedge d \le b\) if and only if \(d \le c\) (we write \(a \rightarrow _D b\) for the element _c_), and _S_ is a non void subset of _L_ such that _S_ is closed under \(\rightarrow _D\) and _S_, with its inherited order, is itself a lattice. Finally, the congruences of sub-Hilbert lattices are studied. (shrink)

El siguiente texto intenta exponer algunas de las ideas básicas de la tercera de las tres partes que componen Meditaciones del Quijote: la “Meditación primera. Breve tratado de la novela”. En las no muchas páginas que ocupa el texto de Ortega, se ofrece una visión sobre el inmortal libro de Cervantes que no puede dejar indiferentes a los filósofos.

El presente ensayo es una puesta a punto del anterior artículo del autor, que publicado en español en una revista francesa, apenas tuvo difusión en España. Lo fundamental de este, además de aclarar algunos aspectos de aquel, es sacar las consecuencias morales que de él se derivan. En el primer apartado se insiste en la ruptura fenomenológica de la brecha entre la sensibilidad y el entendimiento en la medida en que este vive de la sensibilidad. En el segundo se aclara (...) mediante el recurso a la trascendentalidad animal la ruptura con todo residuo medieval en la palabra “trascendental”, lo que se llama el “carácter profiláctico” del texto. En el tercero, que incluye el grueso del ensayo, se expone cómo los campos objetivos que se analizan en Ideas II, entre ellos los animales, de ser objetos constituidos se convierten en sujetos co-constituyentes. Por fin en el último apartado se plantea el alcance de esa que Husserl llama articulación intencional (de la animalidad y la humanidad), y que yo llamo “articulación trascendental”, interna y externa, gracias a la cual estamos incluidos en la intersubjetividad total de la vida, por la que se hace patente nuestra responsabilidad ante la vida animal. (shrink)

Los museos han perdido visitantes como consecuencia de la COVID-19 y la ciudadanía sigue creyendo que la ciencia es aburrida. En este contexto de crisis, examinamos, mediante técnicas de análisis de contenido, la presencia de la arqueología en programas de radio y estudiamos los recursos lingüísticos que hacen a la comunicación capaz de emocionar, aumentado las posibilidades de éxito de la divulgación científica. Concluimos que la escasez de equipo humano cualificado en comunicación de la ciencia y experto en recursos para (...) hacerla más atractiva, puede poner en peligro la recuperación de los museos como centros de ocio, cultura y conocimiento. (shrink)

The debate about Ortega’s relation to phenomenology has been continuous since the eighties of the last century. Before this date, Ortega’s manifestations that he had abandoned phenomenology at the same moment he came to know it were understood literally, without scrutinising other manifestations of his that he had made on phenomenology, or that his philosophy is similar to that of Husserl’s final works. Both manifestations seek to question the previous ones. The text clarifies first the meaning and importance of this (...) polemic for Spanish philosophy, deeply influenced by that of Ortega’s, and, secondly, I will set out what are the fundamental phenomenological concepts of Ortega’s philosophy. / El debate sobre la relación de Ortega con la fenomenología ha sido continuo desde los años ochenta del siglo pasado. Antes de esta fecha, las manifestaciones de Ortega de que había abandonado la fenomenología en el mismo momento que la conoció, fueron tomadas al pie de la letra, sin examinar otras manifestaciones que había hecho sobre la fenomenología, o la de que su filosofía es similar a la de los últimos trabajos de Husserl. Ambas manifestaciones buscan cuestionar las anteriores. El texto aclara en primer lugar el significado y la importancia de esta polémica en la filosofía española, profundamente influenciada por la de Ortega, y, en segundo lugar, se expondré cuáles son los conceptos fenomenológicos fundamentales de la filosofía de Ortega. (shrink)

Mi intención en esta ponencia es hacerles una presentación de la fenomenología en España, para lo cual repetiré ideas que he expresado en la introducción al libro de Ortega Schriften zur Phänomenologie 15 y, en segundo lugar, resumiré una parte del contenido de la conferencia que pronuncié en el penúltimo Congreso de la Sociedad Española de Fenomenología. 16.

Mi ponencia trata de contribuir a una fenomenología de la percepción, desde la discusión de las posturas sobre la percepción que aparecen en la reciente obra de Lester Embree sobre el método fenomenológico. Desde el convencimiento y asentimiento a la llamada de Lester Embree, de que debemos volver a las cosas mismas, por tanto, dejamos de la erudición para alumbrar fenomenología de las cosas, no podemos tampoco desentendemos de lo que dicen nuestros maestros, y pretendo, con ellos, ir a las (...) cosas, para ver en qué medida la percepción como acceso al mundo es un “acto” en el que intervienen la experiencia directa sensible animal y la aportación lingüística que clasifica el mundo, sin por ello convertir la percepción en lenguaje. En el primer punto plantearé la importancia que el tema tiene en la fenomenología sobre todo por el planteamiento husserliana en las Ideas I. En el segundo veremos la postura de Lester Embree, para, en el tercero, exponer lo que yo creo que está implícito en la propuesta de Husserl, que explicita la percepción como el acceso ponente a la realidad, por tanto radicalmente vinculada a la creencia, de manera que, fenomenológicamente, percepción, creencia y realidad están vinculadas, siendo está vinculación el marco en el que sitúa el comienzo de la legitimidad racional. (shrink)

In the first part of my paper, we will journey through the general structure of the first volume of Ideas, from which we will be able to deduce the position of Volume II. After carrying out a general analysis of the noesis/noema correlation structure in Section III and having provided, in Section IV, the basics of a phenomenology of reason, the second volume of Ideas should study the general fields in which the objects of transcendental experience appear: the world, the (...) animal being, and the spiritual or cultural being. The third, unwritten volume should have been devoted to the study of the superior products of culture, and science. Thus, the second part of this paper will show the place of Ideas’ second volume. The third part, the decisive one, will inquire into the position of the world and the place of the body and culture. Specifically, it will ask whether the experience of the body is understood to be an objective genitive or whether it is also understood, necessarily, as a subjective genitive. The same question will be asked about culture. An understanding of one as objective or subjective genitive radically alters the meaning of the pure ego. (shrink)

The author deals with philosophical ethos in its practical function. After the First World War Husserl not only considers the structure but also the function of phenomenology. A meditation on this function, with regard to the history of philosophy, is his primal task in the Freiburg years. Thus the possibility of developing a rigorous phenomenology of practical reason becomes the basis of phenomenology. The importance of Husserl’s characterization of life in terms of striving is stressed as a key motive in (...) the turn from static to genetic phenomenology. It is argued that instinctive life is inserted in a cultural development that shapes a theoretical side providing content to our primal tendencies as well as the identity of individuals. A decisive point in genetic phenomenology is the passage from instinctive animality to human life. This development rests on a pretheoretic affectivity that colors life as a sort of subconsciousness underlying all our activities. It is the originary stratum through which we approach the world. The article goes on to high-light the importance of Husserl’s concept of culture and specifically of his practical concept of culture which is made up of life-regulations and without which an ideal and a technical culture are devoid of a ground. Finally, the author considers life-regulations as a key problem to be dealt with by phenomenology first in the emotional and then in the practical level. (shrink)

Meditaciones del Quijote, el primer libro de Ortega y Gasset, es un libro de “encrucijada”, palabra que significa cruce de caminos. El presente texto analiza el concepto de cultura, que por un lado viene de la fenomenología, pero por otro mantiene la matriz neokantiana. Por un lado es el modo de ver y apreciar el mundo, mas por otro se refiere a los modos superiores de la cultura, tal como se entendía en el mundo académico alemán.

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)

A partir de la afirmación en la que Ortega dice que el científico se aloja en el ser humano, el texto pretende, por un lado y desde una perspectiva fenomenológica, abordar el vínculo entre las ciencias naturales y las ciencias humanas y sociales y, por otro lado, analizar las consecuencias de las maneras en las que estos dos grupos de ciencias se han relacionado a fin de imaginar la posición que tanto las ciencias naturales como las humanas y sociales deben (...) ocupar. From a phenomenological perspective and begining with the statement from Ortega saying that a scientist lives inside a human being, this text has a twofold structure. First, the author analyzes the relationship among natural sciences and human and social sciences. Second, the author analyzes the consequences of the different ways in which bothsciences have interrelated, in order to imagine the place that either natural sciences, and social sciences and humanities, should occupy. (shrink)

El presente texto es un extracto de la primera lección del curso impartido en Guanajuato en la primavera del año en curso. Su objetivo es determinar los contenidos que configuraron la interpretación convencional de Husserl, para destacar lo que sería el objetivo del curso: la noción del “nuevo” Husserl. El ensayo consta de cinco apartados. En el primero se presenta el contenido global de la obra pública de Husserl. El segundo se dedica a explicar la noción del “nuevo” Husserl. El (...) apartado tres procura exponer los rasgos del Husserl convencional. El cuatro está dedicado a ver la cadena de autores que nos han transmitido al “nuevo” Husserl. Para terminar, en el apartado quinto se hace referencia a algunos textos de Gaos sintomáticos de la comprensión convencional de Husserl. (shrink)