Argumentos ontológicos

In this paper we propose a deep revisten of the classical ontological arguments of Anselm, Descartes, Leibniz and Spinoza. The introduction c1arifies the concept of ontological argument and point out the important logic distinction between the validity of an argument and its soundness, where besides validity it is required that all premises are actually true. The following sections discuss in turn the arguments of Anselm, Descartes, Spinoza and Leibniz. In all cases we have translated the relevant passages of the original argument and formalized its hypothesis and conclusion. In some cases we reconstructed the whole argument and added as hypothesis all statements that served the authors to prove their thesis. By doing this we detached ourselves from what is traditionally considered the argument (for example, as seen in Logic and Theism [Sobel]) and most of the arguments become formally valid.We are aware of the fact that in this way we made explicit the hidden assumptions that made the argument valid while weakening its strength. The reason why is that the new hypothesis are hard to justify as in many cases they have philosophical import and they even committed the fallacy known as petitio principii. Very often the new hypothesis are existential statements, which c1early allow passing from a definition, which simply establishes a correspondence between properties, to an assumption of consistency, stating that certain sets are not empty. The paper includes the issues relevant to this study: the consideration of existence as a predicate, improper descriptions, existential import of universal statements, modal categories and the eventual modal collapse. We should highlight the effort of formalization for which we have used several logics: classical first order logic, higher order (with a description operator) and modal logic. We conclude by pointing out that the subject of ontological arguments still fascinate logicians and philosophers and received attention in the twentieth and the twenty first century.En este artículo proponemos una revisión a fondo de los argumentos ontológicos clásicos: de Anselmo, Descartes, Spinoza y Leibniz. En la introducción se precisa la noción de argumento ontológico y señalamos la importante distinción que hacemos en lógica entre la validez de un argumento y su solidez, esta última tiene en cuenta no sólo la corrección formal del mismo sino también la verdad de las hipótesis. En las siguientes secciones se analizanpor turno los argumentos de Anselmo, Descartes, Spinoza y Leibniz. En todos los casos hemos traducido los pasajes correspondientes del argumento original y formalizado sushipótesis y conclusión. En algunos casos hemos reconstruido el argumento y destacado como hipótesis todos los enunciados que de hecho se usan en la demostración por parte de los autores en estudio. De esta forma a veces nos separamos de lo que tradicionalmente es considerado el argumento (por ejemplo, tal y como se presentan en Logic and Theism [Sobel]) y la mayor parte de los argumentos deviene en formalmente válidos. Somos conscientes de que de esa manera hemos explicitado las premisas ocultas que validan el argumento pero a la vez disminuyen la solidez del mismo por tratarse de hipótesis de dificil justificación y con carga filosófica en muchos casos, incluso de falacias de petición de principio. Frecuentemente se trata de hipótesis existenciales, que claramente permiten pasar de una definición, que simplemente establece una correspondencia entre propiedades, a una asunción de consistencia, estableciendo que no son vacíos ciertos conjuntos. Se mencionan los temas relevantes a este estudio: el de la consideración de la existencia como un predicado, el de las descripciones impropias, el compromiso o aporte existencial de los enunciados universales, las categorías modales y el eventual colapso modal. Habría que destacar el esfuerzo de formalización para la que hemos empleado varias lógicas: clásica de primer, de orden superior (con descriptores como operadores lógicos) y lógica modal. Finalizamos señalando que el tema de los argumentos ontológicos sigue fascinando a los lógicos y filósofos, recibió mucha atención en el siglo XX y también en el XXI

Identity, Equality, Nameability and Completeness

This article is an extended promenade strolling along the winding roads of identity, equality, nameability and completeness, looking for places where they converge. We have distinguished between identity and equality; the first is a binary relation between objects while the second is a symbolic relation between terms. Owing to the central role the notion of identity plays in logic, you can be interested either in how to define it using other logical concepts or in the opposite scheme. In the first case, one investigates what kind of logic is required. In the second case, one is interested in the definition of the other logical concepts (connectives and quantifiers) in terms of the identity relation, using also abstraction. The present paper investigates whether identity can be introduced by definition arriving to the conclusion that only in full higher-order logic a reliable definition of identity is possible. However, the definition needs the standard semantics and we know that with this semantics completeness is lost. We have also studied the relationship of equality with comprehension and extensionality and pointed out the relevant role played by these two axioms in Henkin’s completeness method. We finish our paper with a section devoted to general semantics, where the role played by the nameable hierarchy of types is the key in Henkin’s completeness method

Identity, equality, nameability and completeness. Part II

This article is a continuation of our promenade along the winding roads of identity, equality, nameability and completeness. We continue looking for a place where all these concepts converge. We assume that identity is a binary relation between objects while equality is a symbolic relation between terms. Identity plays a central role in logic and we have looked at it from two different points of view. In one case, identity is a notion which has to be defined and, in the other case, identity is a notion used to define other logical concepts. In our previous paper, [16], we investigated whether identity can be introduced by definition arriving to the conclusion that only in full higher-order logic with standard semantics a reliable definition of identity is possible. In the present study we have moved to modal logic and realized that here we can distinguish in the formal language between two different equality symbols, the first one shall be interpreted as extensional genuine identity and only applies for objects, the second one applies for non rigid terms and has the characteristic of synonymy. We have also analyzed the hybrid modal logic where we can introduce rigid terms by definition and can express that two worlds are identical by using the nominals and the @ operator. We finish our paper in the kingdom of identity where the only primitives are lambda and equality. Here we show how other logical concepts can be defined in terms of the identity relation. We have found at the end of our walk a possible point of convergence in the logic Equational Hybrid Propositional Type Theory (EHPTT), [14] and [15].This research has been possible thanks to the research projects sustained by Ministerio de Econom´ıa y Competitividad of Spain with references FFI2013-47126-P and FFI2017-82554-

Pedagogy of experience in the reconceptualisation of teacher education

Diversos autores (Crandall, 2000; Darling-Hammond, 2006; Jiménez Raya, 2009, 2011; Korthagen, Loughran y Russell, 2006) mantienen que los modelos tradicionales de formación docente, basados en la transmisión de conocimiento del profesor al alumno, están fracasando en su objetivo de preparar a los futuros docentes para la realidad del aula. La formación del docente no debe sólo basarse en la adquisición de conceptos y principios, sino también en el desarrollo de competencias como la autonomía, el pensamiento crítico, la reflexión, la toma de decisiones o la resolución de problemas. Enseñar es una tarea compleja que requiere el desarrollo de habilidades específicas para la comprensión del proceso de enseñanza-aprendizaje. En un mundo marcado por el cambio permanente, se percibe la necesidad de un nuevo modelo en la formación del profesor dirigido a formar docentes con dominio de saberes científicos, con capacidad crítica y de cambio, de permanente indagación, creatividad y capaces de seguir aprendiendo a lo largo de la vida, con una visión humana y social comprometida con la sociedad. Si los métodos tradicionales fracasan en llevar a cabo este cometido, ¿cómo puede entonces la formación de profesores asegurarse de que los docentes entienden la complejidad de la enseñanza y adquieren la capacidad de revisar y reinventar su práctica en respuesta a las nuevas demandas de la sociedad? Para facilitar esta nueva visión de la formación docente es preciso que se propongan y exploren métodos pedagógicos alternativos. En este sentido, abogamos por un enfoque didáctico centrado en la pedagogía de la experiencia como herramienta que pueda ayudar a superar algunas de las carencias de los modelos tradicionales de formación y contribuir de manera muy significativa al desarrollo profesional de los futuros profesores. Este enfoque tiene como objetivo abandonar el modelo tradicional basado en la transmisión de contenidos a través de la lección magistral dictada por el profesor y sustituirlo por un nuevo modelo de enseñanza centrado en la construción de conocimiento por parte del futuro docente, basándose en la reflexión crítica y la indagación pedagógica. El objetivo de esta presentación es discutir cómo la implementación de una pedagogía de casos puede contribuir a reconceptualizar el modelo actual de formación docente con el objetivo de satisfacer las nuevas necesidades profesionales del profesor.Nowadays, traditional approaches to teacher education and development are under increasing critical scrutiny because of their perceived inability to meet the professional needs of (modern language) teachers (Crandall, 2000; Darling-Hammond, 2006; Jiménez Raya, 2009, 2011; Korthagen, Loughran and Russell, 2006). Teacher education cannot be exclusively focused on the acquisition of concepts and principles because teaching is a highly complex task that requires the development of specific skills that will help the teacher understand the complexity of the teaching-learning process. Furthermore, in a rapidly changing world, there is a pressing need for a new model of teacher education aimed at facilitating the acquisition of scientific knowledge about teaching, fostering the acquisition of critical thinking skills, decision-making and problem-solving skills, systematic inquiry, creativity and the ability to continue learning throughout one’s professional life. If traditional approaches to teacher education fail in accomplishing these goals, how can teacher education guarantee that prospective teachers understand the complexity of teaching and acquire the capacity to revise and reinvent their practice in response to the new demands of our society? From our perspective, there are clear implications for teacher education deriving from this new vision, requiring the exploration of alternative teacher education strategies. In this sense, we advocate the implementation of a pedagogy of experience in the belief that it can help overcome some of the limitations of traditional teacher education programmes and can significantly contribute to the professional development of future teachers. This approach aims to abandon the traditional model of transmission of content through the lecture mode and replace it with a new model of teaching focused on the construction of knowledge by the student teacher, based on critical reflection and pedagogical inquiry on experience. The aim of the presentation is to discuss how the implementation of a pedagogy of experience based on the use of cases can contribute to reconceptualizing current transmissive models of teacher education in order to meet teachers’ new professional needs

Completeness in Equational Hybrid Propositional Type Theory

Equational Hybrid Propositional Type Theory (EHPTT) is a combination of propositional type theory, equational logic and hybrid modal logic. The structures used to interpret the language contain a hierarchy of propositional types, an algebra (a nonempty set with functions) and a Kripke frame. The main result in this paper is the proof of completeness of a calculus specifically defined for this logic. The completeness proof is based on the three proofs Henkin published last century: (i) Completeness in type theory (ii) The completeness of the first-order functional calculus and (iii) Completeness in propositional type theory. More precisely, from (i) and (ii) we take the idea of building the model described by the maximal consistent set; in our case the maximal consistent set has to be named, ♦- saturated and extensionally algebraic-saturated due to the hybrid and equational nature of EHPTT. From (iii), we use the result that any element in the hierarchy has a name. The challenge was to deal with all the heterogeneous components in an integrated system.publishe

Case Pedagogy in Initial Teacher Education: An Analysis of its Contribution to the Development of Professional Competences for Autonomy

Case pedagogy is advocated in teacher education for autonomy as a teacher development strategy which can empower (student) teachers to understand and explore the implementation of pedagogy for autonomy. In an initial teacher education module implemented at the University of Granada (Spain), cases have become a crucial tool for promoting student teachers’ professional development towards teacher and learner autonomy. One of the strategies used in the module engages student teachers in exploring the implementation of pedagogy for autonomy during their internship and writing a case narrative on their pedagogical intervention. The present paper analyses six cases developed by student teachers during their internship to examine the dimensions of professional competence towards teacher and learner autonomy identified by Jiménez Raya et al. (2017) that they developed during case construction. These dimensions include 1) developing a critical view of (language) education, 2) centring teaching on learning, 3) managing local constraints to open up spaces for manoeuvre, and 4) interacting with others in the professional community

Amendment application in a multicontaminated mine soil: Effects on trace element mobility

The final publication is available at Springer via http://dx.doi.org/10.1007/s11270-014-1874-4Several amendments were tested for their effectiveness in aiding plant growth and immobilising contaminants in pots containing soil from an arsenopyrite mine contaminated with arsenic and heavy metals. Trace element solubility in pore water was monitored using Rhizon samplers for five weeks. Results showed that amendments containing ferrous sulphate and ferrous sulphate combined with paper mill limited arsenic mobilisation and increased metal solubility. However, ferrous sulphate in combination with calcium carbonate was effective in reducing arsenic and metal solubilisation. Plant biomass of both the grass species used during the experiment, Arrhenatherum elatius and Festuca curvifolia, was a sensitive indicator of the comparative efficiency of the amendments, although metal(loid)s concentration in pore water did not correlate with plant uptakeThis study was supported by the Spanish Ministry of Science and Innovation, project COMFITES CTM2010-21922-C02-02; and by the Comunidad de Madrid, project EIADES S2009/AMB-147

Modular PEM Fuel Cell SCADA & Simulator System

The paper presents a Supervision, Control, Data Acquisition and Simulation (SCADA & Simulator) system that allows for real-time training in the actual operation of a modular PEM fuel cell system. This SCADA & Simulator system consists of a free software tool that operates in real time and simulates real situations like failures and breakdowns in the system. This developed SCADA & Simulator system allows us to properly operate a fuel cell and helps us to understand how fuel cells operate and what devices are needed to configure and run the fuel cells, from the individual stack up to the whole fuel cell system. The SCADA & Simulator system governs a modular system integrated by three PEM fuel cells achieving power rates higher than tens of kilowatts