In treatises or advanced textbooks on theoretical physics, it is apparent that the way mathematics is used is very different from what is to be found in books of mathematics. There is, for example, no close connection between books on analysis, on the one hand, and any classical textbook in quantum mechanics, for example, Schiff, , or quite recent books, for example Ryder, , on quantum field theory. The differences run a good deal deeper than the fact that the books (...) on theoretical physics are not written in the definition-theorem-proof style characteristic of pure mathematics. Although a good many propositions are proved in the books on physics, there are almost with exception no existential proofs, and consequently there is no really serious systematic use of quantifiers. Another important characteristic is the free use of infinitesimals. In fact, most results would not lose anything, from a physicist's point of view, by leaving them in approximate form, i.e., instead of strict equalities or inequalities, using equalities or inequalities only up to an infinitesimal.The discrepancy between the way mathematics is ordinarily done in theoretical physics and the way it is built up from a foundational standpoint in any of the standard modern views raises the question of whether it might be possible to construct quite directly a rigorous foundation that reflects a significant part of this standard practice in theoretical physics. Other parts of standard practice in physics, for example, the use of physically intuitive but nonrigorous arguments, are not present in our system. (shrink)
uando Augusto consolidaba el Imperio romano, en su centro cultural, Alejandría, nace Filón. Filósofo, exégeta y maestro en su comunidad judía, Filón es testigo de la convivencia del judaísmo de lengua griega con una sociedad helenizada que en Egipto parecía acercarse al ideal de la pax romana. Pero también es el principal informante sobre el primer pogrom contra su comunidad en el año 38. Sus escritos constituyen la más importante expresión del judaísmo de lengua griega que encontró su ocaso en (...) la época de la destrucción del Templo de Jerusalén. Este volumen primero de las Obras completas de Filón de Alejandría se abre con una introducción general a la edición y traduce dos de los tratados más significativos de la obra filoniana: De opificio mundi y Legum allegoriae 1-3. La creación del mundo es el tratado fundamental de Filón, donde interpreta la doble narración de la producción del mundo según el Génesis, desde perspectivas eclécticas basadas en el Timeo y en tradiciones pitagóricas, aristotélicas y estoicas. Moisés se convierte en el verdadero filósofo para todos los hombres inteligentes de la ecúmene alejandrina, el que enseña la creación y la discriminación de un mundo inteligible y otro sensible. Alegorías de las Leyes es el inicio del Comentario Alegórico, donde los elementos narrativos de la producción artesanal de Adán y de la derivada producción de Eva por la costilla, considerados de forma mítica, dan paso a una interpretación —digna de Dios— de la producción del Intelecto y de la Sensibilidad, primero arquetípicos, después histórico-mundanos. (shrink)
There are several conceptions of truth, such as the classical correspondence conception, the coherence conception and the pragmatic conception. The classical correspondence conception, or Aristotelian conception, received a mathematical treatment in the hands of Tarski (cf. Tarski  and ), which was the starting point of a great progress in logic and in mathematics. In effect, Tarski's semantic ideas, especially his semantic characterization of truth, have exerted a major influence on various disciplines, besides logic and mathematics; for instance, linguistics, the (...) philosophy of science, and the theory of knowledge. The importance of the Tarskian investigations derives, among other things, from the fact that they constitute a mathematical, formal mark to serve as a reference for the philosophical (informal) conceptions of truth. Today the philosopher knows that the classical conception can be developed and that it is free from paradoxes and other difficulties, if certain precautions are taken. We believe that is not an exaggeration if we assert that Tarski's theory should be considered as one of the greatest accomplishments of logic and mathematics of our time, an accomplishment which is also of extraordinary relevance to philosophy, as we have already remarked. In this paper we show that the pragmatic conception of truth, at least in one of its possible interpretations, has also a mathematical formulation, similar in spirit to that given by Tarski to the classical correspondence conception. (shrink)
RolandoChuaqui y yo, nos encontramos una ´ unica vez, en Bah´ıa Blanca en agosto 1992, en el Simposio Latino- Americano de L´ ogica Matem´ atica. Lamentablemente, Chuaqui muri´ o antes de mi pr´ oxima visita a Am´ erica del Sur, igual que otro gran l´ ogico latinoamericano, Carlos Alchourr´ on. Chuaqui estuvo en Bah´ıa Blanca juntos con varios alumnos que hablaron sobre aspectos de la l´.
Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis with a PRA consistency proof, proposed around 1995 by Patrick Suppes and Richard Sommer. It is built on a previous system by RolandoChuaqui and Patrick Suppes, which was recently reconsidered by Michal Rössler and Emil Jeřábek. A $\Pi _1 $ -transfer principle has already been added to ERNA and the consistency of the resulting theory proved in PRA. Here, we equip ERNA with Σ₂-transfer (...) and a saturation principle, while keeping the consistency proof inside PRA. We show that the extended theory allows for generalized transfer, a basic tool of nonstandard analysis, and interprets several strong theories, like BΣ₂ and IΣ₂. (shrink)
Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis with a PRA consistency proof, proposed in around 1995 by Patrick Suppes and Richard Sommer. It is based on an earlier system developed by RolandoChuaqui and Patrick Suppes. Here, we discuss the inherent problems and limitations of the classical nonstandard framework and propose a much-needed refinement of ERNA, called , in the spirit of Karel Hrbacek’s stratified set theory. We study the metamathematics of (...) and its extensions. In particular, we consider several transfer principles, both classical and ‘stratified’, which turn out to be related. Finally, we show that the resulting theory allows for a truly general, elegant and elementary treatment of basic analysis. (shrink)
Elementary Recursive Nonstandard Analysis, in short ERNA, is a constructive system of nonstandard analysis proposed around 1995 by Patrick Suppes and Richard Sommer, who also proved its consistency inside PRA. It is based on an earlier system developed by RolandoChuaqui and Patrick Suppes, of which Michal Rössler and Emil Jeřábek have recently proposed a weakened version. We add a Π₁-transfer principle to ERNA and prove the consistency of the extended theory inside PRA. In this extension of ERNA (...) a σ₁-supremum principle 'up-to-infinitesimals', and some well-known calculus results for sequences are deduced. Finally, we prove that transfer is 'too strong' for finitism by reconsidering Rössler and Jeřábek's conclusions. (shrink)
This article addresses the critique of the modern conception of history and time through a reading of Hannah Arendt. Arendt’s work provides an alternative to the thought with universal pretensions that has dominated the panorama of modernity. She thinks the historical through contradiction and gives a place to human experience next to facts. In thinking the event Arendt shows the insufficiency of the modern chronological appropriation of the past and the limits of using theory as a given framework of interpretation. (...) Understanding the historical event is to challenge the chronology assumed in our forms of understanding and representing the real. Her work blurs the tacit boundary that lurks in modern forms of representation between a ‘dynamic’ present and a ‘congealed’ past. Arendt’s thinking provides a critique of the modern notions of time and history as of the use of theory as a fixed framework of interpretation. (shrink)
This volume studies a fundamental element of Montesquieu’s argumentative architecture that is most apparent in his De l’Esprit des Lois: the problem of giving order to, and establishing a network of consistent explanations of political, social and cultural diversity. Following a thorough and careful analysis of his writings, the volume approaches this subject by observing the use of the information sources available to Montesquieu, the relationships between them, and the judgments he expresses. The book examines some of Montesquieu’s essential theoretical (...) contributions, such as the idea of despotism, and the connection between politics, society and religion, on the basis of his reflections on the variety of mainly non-European societies and cultures. It demonstrates a number of possible inconsistencies and unresolved questions in Montesquieu’s argumentation. One of the main subjects of the book is the consideration of geographical context as an essential element for elaborating uniform criteria of political analysis. The book collects contributions concerning Montesquieu’s reflections on China, Tartary, Japan, India, America, Russia, and the Islamic world, and, building on this earlier research, it shows the importance of Montesquieu’s thought and explains the reason for his longstanding influence. (shrink)
Artículos ¿Por qué democracia? Referencia a los derechos humanos y a la ciudadanía. Why democracy? Reference to human rights and citizenship. Bozo de Carmona, Ana Julia Libertad de expresión y "libertad cómica". Free speech and "comical liberty".Calvo González, José La justicia según J. Finnis. Justice according to John Finnis. Hocevar G., Mayda G. El lenguaje sagrado y su escritura. The sacred language and its writing. Lizaola, Julieta Del carácter coactivo de la μετηνεστασζ en Tucídides. On cornening to compelling nature of (...) Thucydides' μετηνεστασζ. Meabe, Joaquín E. Apuntes para una filosofía crítica de la historia regional. Notes for a critical philosophy concern to the regional history. Mora García, José Pascual Competencia política partidista en los textos de Simón Bolívar . The defender political competition in the Simon Bolivar’s writings . Ortiz Palanques, Marco Fundamentación socio-jurídica de los procesos normativos. Social and juridical reasoning about the normatives changes. Pavó Acosta, Rolando Filosofía y psicopatología en Karl Jaspers: los entramados de la existencia. Philosophy and psychopathology in Karl Jaspers: the studworks of the existence. Portuondo Pajón, Gladys L. La doctrina platónica del alma en la «república». The platonic doctrine of the soul in the «republic» dialogue. Suzzarini, Andrés Una aproximación a la concepción romana del derecho. An estimate study to the roman concept of law. Terán Pimentel, Milagros Interdisciplinares Lo dionisíaco y lo apolíneo en Don Juan Tenorio. The dionysiac and the apolline in Don Juan Tenorio. Pérez Lo Presti, Alirio. (shrink)
In tracing historically the development of Filipino philosophy as traditionally conceived, the author discovered that the early Filipino philosophers were Enlightenment thinkers. This was the direct consequence of the Filipino colonial experience and the explanation why the trajectory of Filipino philosophy is basically Western in orientation.