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, [11], or quite recent books, for example Ryder, [10], 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)

This unique book presents a new interpretation of probability, rooted in the traditional interpretation that was current in the 17th and 18th centuries.

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)

Rolando Chuaqui 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 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 Rolando Chuaqui 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)

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 Rolando Chuaqui 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 with a PRA consistency proof, proposed around 1995 by Patrick Suppes and Richard Sommer. It is built on a previous system by Rolando Chuaqui 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)

Despite the growing popularity of machine learning models in the cyber-security applications ), most of these models are perceived as a black-box. The eXplainable Artificial Intelligence has become increasingly important to interpret the machine learning models to enhance trust management by allowing human experts to understand the underlying data evidence and causal reasoning. According to IDS, the critical role of trust management is to understand the impact of the malicious data to detect any intrusion in the system. The previous studies (...) focused more on the accuracy of the various classification algorithms for trust in IDS. They do not often provide insights into their behavior and reasoning provided by the sophisticated algorithm. Therefore, in this paper, we have addressed XAI concept to enhance trust management by exploring the decision tree model in the area of IDS. We use simple decision tree algorithms that can be easily read and even resemble a human approach to decision-making by splitting the choice into many small subchoices for IDS. We experimented with this approach by extracting rules in a widely used KDD benchmark dataset. We also compared the accuracy of the decision tree approach with the other state-of-the-art algorithms. (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)

To design and develop AI-based cybersecurity systems ), users can justifiably trust, one needs to evaluate the impact of trust using machine learning and deep learning technologies. To guide the design and implementation of trusted AI-based systems in IDS, this paper provides a comparison among machine learning and deep learning models to investigate the trust impact based on the accuracy of the trusted AI-based systems regarding the malicious data in IDs. The four machine learning techniques are decision tree, K nearest (...) neighbour, random forest, and naïve Bayes. The four deep learning techniques are LSTM and GRU. Two datasets are used to classify the IDS attack type, including wireless sensor network detection system and KDD Cup network intrusion dataset. A detailed comparison of the eight techniques’ performance using all features and selected features is made by measuring the accuracy, precision, recall, and F1-score. Considering the findings related to the data, methodology, and expert accountability, interpretability for AI-based solutions also becomes demanded to enhance trust in the IDS. (shrink)

Against the background of the 2022 national elections in the Philippines, in which the Church failed in the moral fight against the return of the Marcoses and the continuation of the Duterte regime in power, this article makes a social discernment as to why the Church has not succeeded in its social mission in shaping the social consciousness of the Filipino people. Why has the Catholic social tradition not taken root in the Philippine soil and in the Filipino soul? The (...) author argues that the Church has located itself in the center rather than grounding itself in the margins. The author proposes a reappropriation of the Catholic social tradition from the margins to more dynamically transform Philippine society. (shrink)

At the peak of this heated confrontation between Nero and Seneca, in which the latter exhorts the emperor to seek the people's love and trust rather than their hatred, Nero retorts that it is meet for the people to fear their prince . This is unsurprising and represents Nero as merely the latest in a long line of tragic tyrants . In the exchange that follows, however, is the slightly puzzling : ‘metuant necesse est’:: ‘quicquid exprimitur graue est’. It is (...) not only that Nero simply reiterates a concept already asserted in the line before which had prompted Seneca's ‘at plus diligi’. More than that, Seneca's exprimitur is a non sequitur after ‘metuant necesse est’. exprimere is to ‘squeeze out’, ‘to extort’, ‘to elicit’, but in Latin metus is hardly ever ‘extorted’, exprimere, on the other hand, is commonly said of sincere or pretended assent, applause, jubilation, or forced admission. The verb occurs again at 494 ‘humiles … uoces exprimit nostri metus’; 581 ‘exprimere ius est, ferre quod nequeunt preces?’; elsewhere in Sen. Oed. 529 ‘ulline poena uocis expressae fuit’; Clem. 1.1.7 ‘omnibus … nunc ciuibus tuis … haec confessio exprimitur esse felices’; Plin. Pan. 2.2 ‘uoces illas quas metus exprimebat’. (shrink)

En el siguiente trabajo se aborda la confrontación de Eugen Fink con Martin Heidegger de cara al concepto de mundo. En este sentido se analiza el contraste entre un concepto existencial de mundo, del modo como el Heidegger de la ontología existencial lo desarrolla, y un concepto cosmológico de mundo, que Fink propone a partir de su interpretación del giro (Kehre) heideggeriano y que lo conduce hacia el despliegue de una ontología cosmológica del juego, cuyo camino filosófico-metódico queda abierto por (...) una fenomenología especulativa en contraposición o como superación de la fenomenología hermenéutica heideggeriana. (shrink)

This article is a reflection on chance as a scientific object, starting from a materialistic point of view. I analyze the relationship between motion and complexity by introducing the notion of an open system and the categories that result from it: state of nature and observable, to review the debate on chance and certainty.

En este artículo se analizan las posiciones de José Imbelloni y Alfred Métraux respecto a la cultura de la Isla de Pascua. Abordar esta cuestión los llevaba a discutir sobre las relaciones que habían existido, o no, entre Oceanía y América. El debate que aquí desarrollamos se centra en dos elementos de la cultura material de la isla: los moais y las tabletas parlantes. El punto central, y en el que oscilarán ambos antropólogos, es entre la cuestión de la originalidad, (...) y autonomía, de los rasgos culturales de los pascuenses, o el préstamo, y origen foráneo, de esos rasgos. Se discute así cuánto hay de creativo y cuánto de copia en una cultura. (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.

The contribution offers an interpretation of the last phase of Nietzsche’s production, based on the influence of some economic concepts. In 1887, Nietzsche encountered the work of the proto-marginalist economist Emmanuel Herrmann and his book “Cultur und Natur: Studien im Gebiete der Wirthschaft”. At the time, Nietzsche was working on the attempt – later abandoned – to offer a comprehensive interpretation of Western metaphysics and history. aimed at a “transvaluation of all values” and based on the idea of will to (...) power. Herrmann’s economic theory played a significant role in this project, offering a model capable of articulating all social and natural processes – and particularly life – in terms of purely immanent relations. By linking the ideas of transvaluation and will-to-power to the logic of capitalistic accumulation and of market society, we can gain an understanding of the influence of economical concepts on Nietzsche’s project, which should in turn allow a better evaluation of its historical relevance. (shrink)

Even in mathematical logic the proposition as an arbitrary technical device can be eliminated and replaced by the constative. The items of experience of the external world—objects, properties, relationships, and the like— are processed in consciousness on the basis of a situational demand that defines the situational context which in turn elicits a particular constatival attitude. The output of this mental processing is the appropriate pragmatic constatival response that generally is publicly communicated.

This paper traces the development of “cultural philosophy,” distinguishes it from the “philosophy of culture,” discusses African and Filipino philosophical dimensions, and then makes the concluding remarks. This paper argues that while cultural philosophy is a significant development in the history of ideas, any given culture must opt to develop its own philosophical tradition.

Every ASEAN member envisions itself to become economically and politically efficient and stable—of becoming a First World country. No doubt there are many ways of approaching this vision and making it a reality. But I will argue in this paper that education can play a major role in transforming the region into a First World technopole or economic power through what Alvin Toffler calls the philosophy of “educational futurism.” Educational futurism states that we tailor our present educational plans on our (...) future dreams or visions. (shrink)

It is not only important for a Filipino teacher or scholar of philosophy to transform oneself into a Filipino philosopher by innovating within one's favorite philosopher , by rejecting a philosophical position and formulating one's own , or by examining old philosophical questions and offering one's own novel perspectival solutions. It is more important to transform oneself into a world-class philosopher.