In this paper, we propose to study the problem of universals in Thomas Aquinas with ‘’analytic glasses’’ (according to the famous phrase of Jonathan Barnes). Starting with the semantic criteria of Peirce used by Armstrong, we propose to present a new reading of the position of Thomas, especially of the De ente et essentia . We introduce the thesis of Thomas Aquinas in contemporary discussions highlighting the difficulty of classifying Thomas Aquinas as a realist or as a universalist. Our (...) main goal is thus to present a new reading of the position of Aquinas, while showing how and why his thesis might be a promising solution in the discussion of the problem of universals. (shrink)

En este trabajo se discute acerca de la posibilidad de llevar a cabo afirmaciones epistémicamente objetivas respecto del arte a partir de la filosofía de la sociedad de John Searle y de la epistemología del desacuerdo. Para ello se considerarán las distinciones ontológicamente objetivo/subjetivo y epistémicamente objetivo/subjetivo en relación con el arte como fenómeno relativo a la intencionalidad, señalándolo como ontológicamente subjetivo y epistémicamente objetivo. Luego se discutirá acerca del desacuerdo en torno a obras polémicas de arte y de la (...) disolución de tales desacuerdos al considerar la oposición entre creencia y aceptación según la propuesta de Jonathan Cohen. Finalmente, mostrando la posibilidad de generar acuerdos en torno al juicio de gustos, se señala el rol de las instituciones relativas al arte en nuestra comprensión del estatuto artístico de las obras polémicas. De esta manera, se pretende señalar que la apreciación de una obra como ‘arte’ es una cuestión objetiva dependiente de las instituciones que operan en nuestra sociedad. (shrink)

El objetivo de este artículo es presentar dos tópicos de Lógica matemática y sus fundamentos: El primer tópico es una actualización de la demostración de Alonzo Church del Teorema de completitud de Gödel para la Lógica de primer orden, la cual aparece en su texto "Introduction to Mathematical Logic" (1956) y usa el procedimientos efectivos de Forma normal prenexa y Forma normal de Skolem; y el segundo tópico es una demostración de que la propiedad de partición (tipo Ramsey) del espacio (...) topológico de Baire llamada "Propiedad de partición polarizada" es falsa en el Modelo Básico de Cohen. (shrink)

Drawing on behavioral economics, nudges (policy interventions based on choice architecture) have the capacity to strategically shape policymaking, subtly guiding individual behavior by adjusting their decision environment. Applied to enhance vaccinations, boost retirement savings, or promote healthy habits, these interventions align with consensus-defined well-being. As governments adopt nudges, scholars have explored their role in fostering virtues. This paper argues that nudges have the potential to efficiently contribute to virtuous development by instilling and sustaining habits, respecting individual choice, and ensuring deliberation. (...) It introduces the concept of virtue nudges, emphasizing the alignment of habits with virtues for targeted behavioral change and the formation of morally virtuous habits. (shrink)

Applied behavior analysis (ABA) has featured an increasing concern for understanding and considering the cultural diversity of the populations behavior analysts serve in recent years. As an expression of that concern, the new BACB’s Ethics Code for Behavior Analysts is more explicit and comprehensive in its inclusion of ethical obligations concerning cultural diversity. The purpose of this paper is to offer a discussion on the limitations of both our capacity and willingness to know and overcome our ignorance about our own (...) and other cultures. We examine different ways in which our ignorance of other cultures plays out even in willful compliance with the BACB ethics code. We suggest part of the problem is that the BACB ethics code seems to operate under the assumption that practitioners are always aware or can be aware of what they do not know and their biases. In contrast, we offer a reflection on a more complex picture of our understanding of ourselves and other cultures where we cannot assume people are aware of what they ignore and of their biases. Ethically, we find that in some cases these blindspots are accounted for by the BACB ethics code and should be foreseen and addressed by the behavior analyst (BA). But in other cases, when a person is not aware of what they ignore, understanding the connection between cultural diversity ignorance and professional behavior requires a different approach. Our analysis suggests an attitude of being thoughtfully diligent and humble while learning about cultural diversity issues and examining the areas where we might be ignorant and not aware of our ignorance. We argue that BAs’ obligations to respect the dignity of clients and their families and to provide effective treatment call for this attitude of diligence and humility that goes beyond mere compliance. (shrink)

Es conocido que el método de forcing es una de las técnicas de construcción de modelos más importantes de la Teoría de conjuntos en la actualidad, siendo el mismo muy útil para investigar problemas de matemática y/o de fundamentos de la matemática. El destacado matemático Joan Bagaria afirma lo siguiente sobre el método de forcing en su artículo "Paul Cohen y la técnica del forcing" (Gaceta de la Real Sociedad Matemática Española, Vol. 2, Nº 3, 1999, págs 543-553) : "Aunque (...) Cohen recibió la medalla Fields por su demostración de la independencia de la hipótesis del continuo y del axioma de elección, su contribución va mucho más allá de estos problemas. Su nuevo método, el forcing, no sólo ha permitido resolver un sinfín de problemas importantes en prácticamente todas las áreas de las matemáticas, si no que ha cambiado para siempre nuestra concepción de la matemática como ciencia". El objetivo principal del siguiente trabajo es estudiar el método de forcing describiendo algunas de sus aplicaciones (forcing de Cohen, forcing aleatorio, forcing de Mathias, forcing de Sacks, forcing de Silver, etc.), y ofreciendo una aproximación a sus fundamentos metamatemáticos. Se aspira que estas notas sirvan de apoyo para aprender dicho método. (shrink)

Este artículo presenta y defiende una concepción expresiva del mundo perceptual que depende de la intersubjetividad. En un primer momento se muestra el desarrollo del concepto de expresión en Husserl y en Merleau-Ponty. El punto central de este desarrollo es que, en contraste con la concepción tradicional del concepto de expresión que es lingüística y consiste en el manifestarse exteriormente de algo interno, se propone ahora una idea de expresión que ya no separa radicalmente lo expresado de la expresión, no (...) se concibe como traducción, y se aplica a la relación entre subjetividad y corporalidad. Para ajustar la aplicación de la expresión a la percepción, se argumenta que las apariencias perceptuales requieren de una cualificación en términos de la posición o perspectiva del sujeto que percibe. Esta “posición” o perspectiva no es únicamente espacio-temporal, sino que también es pragmática. Finalmente, se introduce la intersubjetividad, entendida pragmáticamente, a través de la idea de que hay maneras de explorar el mundo con los sentidos que son constituidas socialmente por los diferentes grupos sociales de los que hacemos parte. Se argumenta que esta concepción pragmatista, diferente a la ruta predominante en fenomenología basada en el significado como un asunto de conciencia de la experiencia, también es defendible en el terreno fenomenológico, particularmente a través de la noción husserliana de toma de posición (Stellungnahme) y la idea merleau-pontiana de las maneras de interrogar el mundo perceptualmente. -/- This article presents and defends an expressive and intersubjectively dependent conception of the perceptual world. The first section deals with the phenomenological development of the concept of expression in Husserl and Merleau-Ponty. In this development, and in contrast with the traditional conception of expression –a linguistic conception based on the external manifesting of something inner–, a new conception appears: one that doesn’t keep a hard separation between the expression and what is expressed, is not modeled after translation, and can be applied to the relationship between subjectivity and corporeality. To further precise the way expression and perception fit together, I argue that perceptual appearances require being qualified in terms of the position or perspective of the perceiving subject. This “position” or perspective is not only spatiotemporal but also pragmatic. Lastly, a pragmatically understood intersubjectivity is brought into play. I look at the fact that there are different ways of exploring the world with our senses that are socially constituted. This constitution takes places in and through the different social groups to which we belong. I argue that this pragmatist conception, while different from the dominant phenomenological understanding that takes meaning to be about the consciousness of experiences, is also defensible on phenomenological grounds. This alternative understanding finds support in Husserl’s idea of position-taking (Stellungnahme) and Merleau-Ponty’s claim that there exist different ways of interrogating the world perceptually. (shrink)

Resumen: En la actualidad uno de los libros más usados para dar lógica elemental es el de Irving Copi y Carl Cohen (Introducción a la lógica, 2001), allí se presentan unas reglas para decidir la validez de los silogismos categóricos de forma estándar. Pero en tal texto ni en ninguno que nosotros conozcamos se ofrece una fundamentación de las mismas. Es decir, una demostración de que ellas son realmente una condición necesaria y suficiente de la validez de un silogismo categórico (...) de forma estándar, lo único que hemos leído es su motivación como condición necesaria. El objetivo de este trabajo es ofrecer una fundamentación de las mismas usando la noción de conjunto (o clase) y la técnica de diagramas de Venn, un concepto y una técnica que están expuestos en los principales textos de lógica elemental, incluyendo el referido anteriormente. -/- Abstract: Currently, one of the most widely used textbooks in elementary logic is the one by Irving Copi and Carl Cohen (Introduction to Logic, 2001). They offer rules for deciding the validity of standard categorical syllogisms. But neither that textbook, nor any other we know of, provides the foundations of these rules; that is to say, the demonstration that they are a necessary and sufficient condition for the validity of a standard categorical syllogism. We have only found motivations for the necessary condition. The main goal of this work is to provide a foundation of these rules using the notion of set as well as Venn diagrams, a concept and a technique exposed in the main textbooks of logic, including the aforementioned. (shrink)

En el ámbito de la lógica matemática existe un problema sobre la relación lógica entre dos versiones débiles del Axioma de elección (AE) que no se ha podido resolver desde el año 2000 (aproximadamente). Tales versiones están relacionadas con ultrafiltros no principales y con Propiedades Ramsey (Bernstein, Polarizada, Subretículo, Ramsey, Ordinales flotantes, etc). La primera versión débil del AE es la siguiente (A): “Existen ultrafiltros no principales sobre el conjunto de los números naturales (ℕ)”. Y la segunda versión débil del (...) AE es la siguiente (B): “Existen ultraflitros sobre ℕ”. Se sabe que A implica B, pero se desconoce si B implica A. Di Prisco y Henle conjeturan en los artículos ([1], [2]) que esto no ocurre, es decir, conjeturan que B no implica A, en otras palabras, conjeturan que A es más fuerte estrictamente que B, que A es independiente de B, pero esto no se ha podido demostrar todavía aunque se ha intentado hacer desde hace aproximadamente 21 años. Una descripción detallada de este problema abierto puede encontrarse en esta ponencia (dictada en el marco del Día Mundial de la Lógica 14-01-2022) y en el artículo [3]. [1] C. Di Prisco y H. Henle. “Doughnuts, Floating Ordinals, Square Brackets, and Ultraflitters”. Journal of Symbolic Logic 65 (2000) 462-473. [2] C. Di Prisco y H. Henle. “Partitions of the reals and choice”. En “Models, algebras and proofs”. X. Caicedo y C.M. Montenegro. Eds. Lecture Notes in Pure and Appl. Math, 203, Marcel Dekker, 1999. [3] F. Galindo. “Tópicos de ultrafiltros”. Divulgaciones Matemáticas. Vol. 21, No 1-2, 2020. (shrink)

Teacher quality, its effect on students’ outcomes, and the association of these with economic growth, is the core of recent discussions in Latin America given the region’s weak results in international learning assessments. This paper investigates whether there is an effect of philosophy on the outcomes of critical reading for students in B.Ed. programs in Colombia. Relying on exact matching combined with propensity score matching with regression adjustment, we use national data from Colombia to show that students in B.Ed. in (...) philosophy outperformed students in other B.Ed. in critical reading test (0.401–0.124 SD), and, importantly, with higher effects observed for students with lower prior academic achievement (0.44 SD). This suggests that philosophy can help to narrow educational outcomes of students whose socioeconomic conditions are disadvantageous, contributing to social justice in education. (shrink)

A modified visual search task demonstrates that humans are very good at resuming a search after it has been momentarily interrupted. This is shown by exceptionally rapid response time to a display that reappears after a brief interruption, even when an entirely different visual display is seen during the interruption and two different visual searches are performed simultaneously. This rapid resumption depends on the stability of the visual scene and is not due to display or response anticipations. These results are (...) consistent with the existence of an iterative hypothesis-testing mechanism that compares information stored in short-term memory (the perceptual hypothesis) with information about the display (the sensory pattern). In this view, rapid resumption occurs because a hypothesis based on a previous glance of the scene can be tested very rapidly in a subsequent glance, given that the initial hypothesis-generation step has already been performed. (shrink)

In this paper I examine a recent incarnation of common objection to evidentialism. According to this common objection, evidentialism gives the wrong verdicts in cases where the subject has been irresponsible in inquiry. Sandy Goldberg (2021) has argued that a particularly vivid instance of this problem occurs when an individual violates normative expectations that have been placed on them in their inquiry. Having laid out Goldberg’s case, I argue that the desirable verdicts can be better attained by endorsing evidentialism and (...) supplementing it with an account of robust justification that I have defended elsewhere. (shrink)

This introduction to this collection of essays presents diverse perspectives on social identities, inviting readers to reconsider established notions and explore new approaches to understanding these complex social phenomena. The contributions challenge traditional philosophical boundaries, intersecting ontological, epistemological, ethical, and political considerations. // The authors situate different views on the ontology of social identities within some extant options. Thus, they contrast their "social identity affordance view" with two alternative approaches: the Cambridge Social Ontology group's positioning theory and Weichold & Thonhauser's (...) broad conception of social identities. Their view understands social identities as realities that structure social life and shape individuals' self-conceptions, emphasizing the importance of historical contingency and social context. // The introduction then proceeds to review the contributions to the volume. The volume comprises three sections: "Experiences of Social Identities," exploring how specific identities are understood and experienced; "Horizons of Social Identities," examining how identities develop and change over time; and "Some Frameworks of Social Identities," presenting alternative frameworks for conceptualizing social identities. (shrink)

Using two decades worth of experimental philosophy (aka x-phi), Edouard Machery argues in Philosophy within its Proper Bounds (OUP, 2017) that philosophers’ use of the “method of cases” is unreliable because it has a strong tendency to elicit different intuitive responses from non-philosophers. And because, as Machery argues, appealing to such cases is usually the only way for philosophers to acquire the kind of knowledge they seek, an extensive philosophical skepticism follows. I argue that Machery’s “Unreliability” argument fails because, once (...) its premises are percisified, they are either self-defeating or without justification. This is a significant result because Machery’s arguments are the most widely cited and discussed x-phi arguments for philosophical skepticism and many hold that Machery provides the most empirically informed, convincing, and thus best case for this kind of skepticism. So, if my arguments are sound, then the best x-phi argument for philosophical skepticism fails. I further argue that this result provides strong reason to believe the more general conclusion that “negative” x-phi is likely doomed: x-phi likely can never support a substantive philosophical skepticism. Ultimately, I argue for the broad conclusion that all empirically minded arguments for philosophical skepticism are likely to fail for the same reasons that Machery’s does, i.e. they are (likely) self-defeating. (shrink)

This paper critically explores the ethical dimensions of Behavioral Public Policy (BPP), a domain grounded in the understanding that human rationality is bounded and that this limitation often leads to behaviors deemed irrational. By applying the behavioral lens, which posits that people operate under bounded rationality, BPP aims to craft interventions that safeguard individuals against their biases. However, this approach raises significant ethical concerns, both in the scientific underpinnings of BPP and its application through policy interventions. Accordingly, this paper examines (...) two distinct ethical dimensions of BPP, both as a scientific discipline and through its intervention methodologies. The analysis of the first dimension argues that, viewing bounded rationality as only instrumental in decision-making processes, risks oversimplifying ethical complexities. Such simplification may ignore the moral and value-based rationalities underlying decisions, potentially misattributing instances of immorality and akrasia (the failure to act according to one's judgment) to mere deficiencies in rational thinking. Secondly, the paper examines the impact of BPP on moral behavior and character development, addressing ethical concerns like the evidentiary basis of BPP research, the bounded rationality of choice architects themselves, and the morality of behavior changes induced by policy. Overall, this article provides a much-needed examination of the moral considerations associated with behavioral strategies in public policy and its epistemological foundations, contributing to a more comprehensive understanding of their ethical implications . (shrink)

El objetivo de este artículo es presentar una demostración de un teorema clásico sobre álgebras booleanas y ordenes parciales de relevancia actual en teoría de conjuntos, como por ejemplo, para aplicaciones del método de construcción de modelos llamado “forcing” (con álgebras booleanas completas o con órdenes parciales). El teorema que se prueba es el siguiente: “Todo orden parcial se puede extender a una única álgebra booleana completa (salvo isomorfismo)”. Donde extender significa “sumergir densamente”. Tal demostración se realiza utilizando cortaduras de (...) Dedekind siguiendo el texto “Set Theory” de Jech, y otras ideas propias del autor de este artículo. Adicionalmente, se formulan algunas versiones débiles del axioma de elección relacionadas con las álgebras booleanas, las cuales son también de gran importancia para la investigación en teoría de conjuntos y teoría de modelos, pues estas son poderosas técnicas de construcción de modelos, como por ejemplo, el teorema de compacidad (permite construir modelos no estándar, etc) y el teorema del ultrafiltro, que permite construir ultraproductos (pueden ser usados para investigar problemas de cardinales grandes, etc). Se presentan algunas referencias de problemas abiertos sobre el tema. -/- The objective of this paper is to present a demonstration of a classical theorem on boolean algebras and partial orders of current relevance in set theory, as for example, for applications of model construction method called forcing" (with boolean algebras complete or with partial orders). The theorem to be proved is as follows: Any partial order can be extended to a single complete boolean algebra (up to isomorphism)". Where to extend means embed densely". Such a demonstration is done using Dedekind's cuts following the text Set Theory" of Jech, and other ideas of the author of this article. In addition, some weak versions of the axiom of choice related to boolean algebras are formulated, which are also of great importance for the research in set theory and model theory, since this are powerful model construction techniques, such as the compactness theorem (allows the construction of non-standard models, etc.) and the ultralter theorem, which allows the construction of ultraproducts (can be used to investigate problems of large cardinals, etc). Some references of open problems on the subject are presented. (shrink)

El objetivo principal de este artículo es presentar la demostración directa del Teorema de compacidad de la Lógica de primer orden (Gama tiene un modelo si y sólo si cada subconjunto finito de Gama tiene un modelo) que se realiza utilizando el Método de construcción de modelos llamado "Ultraproductos" que, a su vez, usa "Ultrafiltros". Actualmente es más común demostrar el Teorema de compacidad como un corolario del Teorema de completitud de Gödel y usar el método de reducción al absurdo (...) para probarlo. Sin embargo, vale la pena estudiar también esta prueba directa que usa Ultraproductos porque dicha técnica tiene importantes aplicaciones en investigaciones contemporáneas de matemáticas, por ejemplo en la Teoría de conjuntos y en el Análisis. Al final del artículo se realiza un breve comentario sobre Compacidad, Ultraproductos, Cardinales grandes y Modelos no estándar. (shrink)

In this essay I revise, based on the notion of the ‘enlightened ruler’ or mingzhu and his critique of the literati of his time, the common belief that Han Fei was an amoralist and an advocate of tyranny. Instead, I will argue that his writings are dedicated to advising those who ought to rule in order to achieve the goal of a peaceful and stable society framed by laws in accordance with the dao.

The purpose of this essay is to articulate a specific desideratum for any theory of Latinidad, namely, that there is no adequate conception of Latinx without an attendant conception of Afro-Latinx. In order to be reflective of those whom it purports to describe in the U.S. and elsewhere in the hemisphere, the term Latinx must be plastic enough to encompass the many internal differences, and even antagonisms, between its different constituent parts. Within it, we argue here in particular, it must (...) include its Afro-descended history, which includes not just African-descended people but also a denial of the influences of African-descended culture writ large. Our central claim here, then, is that a certain African-descendedness is constitutive of Latinidad in multiple registers, including history, cultural practices, and social identificatory processes despite Latinidad’s pernicious exclusionary history. (shrink)

I argue that Husserl’s concept of position-taking, Stellungnahme, is adequate to understand the idea of second nature as an issue of philosophical anthropology. I claim that the methodological focus must be the living subject that acts and lives among others, and that the notion of second nature must respond to precisely this fundamental active character of subjectivity. The appropriate concept should satisfy two additional desiderata. First, it should be able to develop alongside the biological, psychological, and social individual development. Second, (...) it should be able to underlie the vast diversity of human beings within and across communities. As possible candidates, I contrast position-taking with two types of habit-like concepts: instinct and habitus, on the one hand, and customary habits, on the other. I argue that position-taking represents the active aspect of the subject while the habit-like concepts are passive. A subject’s position-takings and ensuing comportments are tied together by motivations, which evince a certain consistency, and for this reason are expression of the subject’s identity. I conclude by nuancing the relation between Stellungnahme and passivity. Passivity is deemed necessary to action but subservient to it; position-taking is thought to be prior to passivity. (shrink)

This paper presents an impact evaluation of the policies for teacher education programs within the framework of the National Development Plan 2014-2018. The programs were compelled to obtain high-quality accreditation, increase the credits in school practices, and the English level, among other requirements. Relying on multivariable regression, it shows that, for the year 2021, there is no association between high-quality accreditation in most modules of the Saber Pro tests, or it is negative in the global score and quantitative reasoning. In (...) a second step, using Differences–in–Differences, it evidences how the changes made by the programs had positive effects on the performance of students compared to other professional programs. The results show significant improvement in most modules of the Saber Pro test, except for the English module. The effects were homogeneous by characteristics of the students and institutions, but heterogeneous by area of knowledge, indicating that the effect is mainly due to the curricular changes of the programs. (shrink)

Epistemic Utility Theory is often identified with the project of *axiology-first epistemology*—the project of vindicating norms of epistemic rationality purely in terms of epistemic value. One of the central goals of axiology-first epistemology is to provide a justification of the central norm of Bayesian epistemology, Probabilism. The first part of this paper presents a new challenge to axiology first epistemology: I argue that in order to justify Probabilism in purely axiological terms, proponents of axiology first epistemology need to justify a (...) claim about epistemic value—what I label ‘Downwards Propriety’—much stronger than any they have offered justification. The second part of this paper offers an argument that this challenge cannot be met: that there is no hope for providing a purely axiological justification of Downwards Propriety, at least given widely accepted assumptions about epistemic value. (shrink)

Since the concept of “nudge” was introduced in 2008 by Thaler and Sunstein, proposing that small interventions based on changes in choice architectures can alter people’s behavior and make it easier for them to achieve their desired goals, the application in public policy of behavioral economics has gained significant attention. This has led to the emergence of different types of policies based on behavioral insights, which have been used in a variety of areas, including health or finance, with the goal (...) of promoting well-being and addressing social and economic issues. After providing a basic theoretical background as a frame of reference to understand gender violence, this study explores the use of tools from the field of behavioral economics as it is applied in public policy. Regulatory (paternalistic) and non-regulatory (libertarian) interventions based on behavioral insights will be considered: nudges, boosts, shoves, budges, or sludge audits, are examined as potential interventions to use in matters related to this type of violence. After evaluating these behavioral policy instruments and their potential effectiveness, the limitations of the behavioral perspective are recognized, and the need for a multifaceted approach to combating gender violence is acknowledged. The article concludes by arguing that public policies addressing gender violence should not only utilize behavioral tools but should also incorporate strategies related to education, legislation, and social norms. (shrink)

Ultrafilters are very important mathematical objects in mathematical research [6, 22, 23]. There are a wide variety of classical theorems in various branches of mathematics where ultrafilters are applied in their proof, and other classical theorems that deal directly with ultrafilters. The objective of this article is to contribute (in a divulgative way) to ultrafilter research by describing the demonstrations of some such theorems related (uniquely or in combination) to topology, Measure Theory, algebra, combinatorial infinite, set theory and first-order logic, (...) also formulating some updated open problems of set theory that refer to non-principal ultrafilters on N, the Mathias’s model and the Solovay’s model. -/- Resumen: Los ultrafiltros son objetos matemáticos muy importantes en la investigación matemática [6, 22, 23]. Existen una gran variedad de teoremas clásicos en diversas ramas de la matemática donde se aplican ultrafiltros en su demostración, y otros teoremas clásicos que tratan directamente sobre ultrafiltros. El objetivo de este artículo es contribuir (de una manera divulgativa) con la investigación sobre ultrafiltros describiendo las demostraciones de algunos de tales teoremas relacionados (de manera única o combinada) con topología, teoría de la medida, álgebra, combinatoria infinita, teoría de conjuntos y lógica de primer orden, formulando además algunos problemas abiertos actuales de la teoría de conjuntos que se refieren a ultrafiltros no principales sobre N, al Modelo de Mathias y al Modelo de Solovay. (shrink)

En el presente texto se defenderá la idea según la cual, la filosofía y el filosofar están intrínsecamente ligados. Se partirá de un caso paradigmático, el caso de la filosofía analítica. A partir de su definición,se pretenderá mostrar que las características más sobresalientes de dicha corriente están fundamentalmente ligadas al acto de filosofar.Por medio de dicho ejemplo, se desea mostrar que enseñar la filosofía consiste en enseñar a filosofar, y que por lo tanto una no puede ser separada de la (...) otra. Aprender a filosofar es entonces, aprender a ver un problema detrás de cada página de un texto filosófico, una argumentación detrás de cada problema y finalmente, una verdad detrás de cada argumentación. El precio a pagar por dicha separación es bastante alto, se podría hablar de épocas de decadencia intelectual. (shrink)

Para matemáticos interesados en problemas de fundamentos, lógico-matemáticos y filósofos de la matemática, el axioma de elección es centro obligado de reflexión, pues ha sido considerado esencial en el debate dentro de las posiciones consideradas clásicas en filosofía de la matemática (intuicionismo, formalismo, logicismo, platonismo), pero también ha tenido una presencia fundamental para el desarrollo de la matemática y metamatemática contemporánea. Desde una posición que privilegia el quehacer matemático, nos proponemos mostrar los aportes que ha tenido el axioma en varias (...) áreas fundamentales de la matemática, su aplicación en la lógica de primer orden, así como una breve descripción de las pruebas de consistencia relativa debidas a Gödel y Cohen, las cuales establecieron su independencia del sistema axiomático Zermelo-Fraenkel (ZF). Con todo lo anterior mostraremos cómo el quehacer matemático contemporáneo se adscribe al platonismo matemático en los términos de Bernays y Ferreirós. Revisaremos también los argumentos de Zermelo y Cantor para permitir el uso de asunciones en la matemática, los cuales se acercan a los planteamientos de la investigación científica y esbozan relaciones con la filosofía de la práctica matemática. Finalmente, justificamos el uso del axioma de elección en la contemporaneidad, abogando por unas relaciones de equidad entre la matemática y la filosofía, presentando además su plena vigencia, a través de la referencia a algunos problemas abiertos en la actualidad que vinculan el axioma de elección con la teoría de Ramsey. (shrink)

El estudio de los "cardinales grandes" es uno de los principales temas de investigación de la teoría de conjuntos y de la teoría de modelos que ha contribuido con el desarrollo de dichas disciplinas. Existe una gran variedad de tales cardinales, por ejemplo cardinales inaccesibles, débilmente compactos, Ramsey, medibles, supercompactos, etc. Tres valiosos teoremas clásicos sobre cardinales medibles son los siguientes: (i) compacidad débil, (ii) Si κ es un cardinal medible, entonces κ es un cardinal inaccesible y existen κ cardinales (...) inaccesibles menores que κ , y (iii) Si existe un cardinal medible, entonces el axioma de constructibilidad (V=L) es falso. El objetivo de este artículo es presentar una demostración de cada uno de estos tres teoremas en el contexto de la teoría de modelos usando ideas del texto de Chang y Keisler (Model Theory). Tales demostraciones tienen en común el uso del método de construcción de modelos llamado ultraproductos, de lógicas infinitarias o fragmentos de la lógica de segundo orden, y del axioma de elección. Cardinales grandes y/o ultraproductos son importantes en teoría de conjuntos, teoría de modelos, análisis matemático, teoría de la medida, probabilidades, topología, análisis funcional, física, teoría de números, finanzas, etc. (shrink)

The objective of this document is to present three introductory notes on set theory: The first note presents an overview of this discipline from its origins to the present, in the second note some considerations are made about the evaluation of reasoning applying the first-order Logic and Löwenheim's theorems, Church Indecidibility, Completeness and Incompleteness of Gödel, it is known that the axiomatic theories of most commonly used sets are written in a specific first-order language, that is, they are developed within (...) the framework of first-order logic, so this note is relevant; and the third note refers to the presence of mathematical platonism in the axioms of ZFC and in the axioms of "complete ordered field", it is known that the last axioms mentioned characterize (except isomorphism) the real number system and are currently used to develop the real Analysis in the context of set theory. It is hoped that this article will be of pedagogical utility for students interested in set theory and in the philosophy of mathematics (that are beginning in the subject). (shrink)

En este artículo se presentan dos demostraciones del teorema de interpolación: Una para la lógica proposicional y otra para la lógica de primer orden. Ambas se realizan en el contexto de la teoría de modelos. El teorema de interpolación afirma que si A y B son fórmulas, donde A no es una contradicción, B no es válida, y B es una consecuencia lógica de A, entonces existe una fórmula C que esta escrita en el lenguaje común al de A y (...) de B, tal que C es una consecuencia lógica de A y B es una consecuencia lógica de C. El teorema de interpolación fue demostrado por primera vez para la lógica de primer orden por William Craig en 1957, y desde entonces se ha investigado la posibilidad de generalizarlo o aplicarlo. Dicho teorema tiene generalizaciones o aplicaciones en teoría de la demostración, teoría de modelos abstracta, ciencias de la computación, lógica modal, lógica intuicionista, etc. Se presentan ejemplos de aplicaciones o generalizaciones de la propiedad de interpolación relacionados con lógicas infinitarias, cuantificadores generalizados, segundo orden, no clásicas, abstractas, etc. También se ofrecen referencias de problemas abiertos sobre interpolación en el contexto de la teoría de modelos abstracta. (shrink)

En este artículo realizamos una reconstrucción del Programa original de Hilbert antes del surgimiento de los teoremas limitativos de la tercera década del siglo pasado. Para tal reconstrucción empezaremos por mostrar lo que Torretti llama los primeros titubeos formales de Hilbert, es decir, la defensa por el método axiomático como enfoque fundamentante. Seguidamente, mostraremos como estos titubeos formales se establecen como un verdadero programa de investigación lógico-matemático y como dentro de dicho programa la inquietud por la decidibilidad de los problemas (...) matemáticos y en específico la decidibilidad de la Lógica de primer orden cobra peso. Luego pasamos a analizar como la inquietud por la decibilidad toma lugar dentro del pensamiento filosófico-matemático de Hilbert presentándose como uno de los grandes problemas a los cuales la metamatemática debe encontrar una solución, esto lo hacemos mostrando un contraste con autores, como John von Neumann y Roberto Torretti, quienes de alguna u otra manera no interpretan el problema de la decidibilidad de la Lógica de primer orden como un problema de peso dentro del programa original de Hilbert. Finalmente argumentamos que el resultado meta-teórico de Church puede entenderse como una refutación del optimismo intelectual que permea a todo el programa original de Hilbert. (shrink)

Many think that expressivists have a special problem with negation. I disagree. For if there is a problem with negation, I argue, it is a problem shared by those who accept some plausible claims about the nature of intentionality. Whether there is any special problem for expressivists turns, I will argue, on whether facts about what truth-conditions beliefs have can explain facts about basic inferential relations among those beliefs. And I will suggest that the answer to this last question is, (...) on most plausible attempts at solving the problem of intentionality, ‘no’. (shrink)

We study several perfect set properties of the Baire space which follow from the Ramsey property ω→(ω) ω . In particular we present some independence results which complete the picture of how these perfect set properties relate to each other.

This paper provides an interpretation of Aristotle’s criticism to the solution to Meno’s Paradox suggested by Plato. According to Aristotle, when Plato says that reminiscence (anámnēsis) is achieved, what is actually achieved is induction (epagōgê). Our interpretation is based on two aspects: (1) semantic criticism, since Plato’s use of the term anámnēsis is unusual; and (2) the theory is not able to give an adequate explanation of the effective discovery.

¿Qué ha pasado con el problema del cardinal del continuo después de Gödel (1938) y Cohen (1964)? Intentos de responder esta pregunta pueden encontrarse en los artículos de José Alfredo Amor (1946-2011), "El Problema del continuo después de Cohen (1964-2004)", de Carlos Di Prisco , "Are we closer to a solution of the continuum problem", y de Joan Bagaria, "Natural axioms of set and the continuum problem" , que se pueden encontrar en la biblioteca digital de mi blog de Lógica (...) Matemática y Fundamentos de la Matemática (ver). También en la entrada "The Continuum Hypothesis" de la web de Enciclopedia de Filosofía de la Universidad de Stanford existe información importante y actualizada al respecto. En esta breve nota se comenta sobre el tema de una manera divulgativa. (shrink)

El objetivo de este trabajo es presentar en un solo cuerpo tres maneras de relativizar (o generalizar) el concepto de conjunto constructible de Gödel que no suelen aparecer juntas en la literatura especializada y que son importantes en la Teoría de Conjuntos, por ejemplo para resolver problemas de consistencia o independencia. Presentamos algunos modelos resultantes de las diferentes formas de relativizar el concepto de constructibilidad, sus propiedades básicas y algunas formas débiles del Axioma de Elección válidas o no válidas en (...) ellas. (shrink)

From mitochondria to meerkats, the natural world is full of spectacular examples of social behaviour. In the early 1960s W. D. Hamilton changed the way we think about how such behaviour evolves. He introduced three key innovations - now known as Hamilton's rule, kin selection, and inclusive fitness - and his pioneering work kick-started a research program now known as social evolution theory. This is a book about the philosophical foundations and future prospects of that program. [Note: only the Introduction (...) is available to download.]. (shrink)

The objective of this article is to present an original proof of the following theorem: Thereis a generic extension of the Solovay’s model L(R) where there is a linear order of P(N)/fin that extends to the partial order (P(N)/f in), ≤*). Linear orders of P(N)/fin are important because, among other reasons, they allow constructing non-measurable sets, moreover they are applied in Ramsey's Theory .

Proponents of enactivism should be interested in exploring what notion of action best captures the type of action-perception link that the view proposes, such that it covers all the aspects in which our doings constitute and are constituted by our perceiving. This article proposes and defends the thesis that the notion of sensorimotor dependencies is insufficient to account for the reality of human perception, and that the central enactive notion should be that of perceptual practices. Sensorimotor enactivism is insufficient because (...) it has no traction on socially dependent perceptions, which are essential to the role and significance of perception in our lives. Since the social dimension is a central desideratum in a theory of human perception, enactivism needs a notion that accounts for such an aspect. This article sketches the main features of the Wittgenstein-inspired notion of perceptual practices as the central notion to understand perception. Perception, I claim, is properly understood as woven into a type of social practices that includes food, dance, dress, music, etc. More specifically, perceptual practices are the enactment of culturally structured, normatively rich techniques of commerce of meaningful multi- and inter-modal perceptible material. I argue that perceptual practices explain three central features of socially dependent perception: attentional focus, aspects’ saliency, and modal-specific harmony-like relations. (shrink)

On a view implicitly endorsed by many, a concept is epistemically better than another if and because it does a better job at ‘carving at the joints', or if the property corresponding to it is ‘more natural' than the one corresponding to another. This chapter offers an argument against this seemingly plausible thought, starting from three key observations about the way we use and evaluate concepts from en epistemic perspective: that we look for concepts that play a role in explanations (...) of things that cry out for explanation; that we evaluate not only ‘empirical' concepts, but also mathematical and perhaps moral concepts from an epistemic perspective; and that there is much more complexity to the concept/property relation than the natural thought seems to presuppose. These observations, it is argued, rule out giving a theory of conceptual evaluation that is a corollary of a metaphysical ranking of the relevant properties. -/- conceptual ethics, explanation, naturalness, epistemic value, concept/property, semantic internalism. (shrink)

Qu’est-ce que la théologie analytique ? Que veut la théologie analytique et que pouvons-nous attendre d’elle ? Ces questions semblent constituer le défi d’aujourd’hui pour la théologie analytique. Nous répondrons à ces questions, en proposant de la distinguer des autres disciplines avec lesquelles elle semble se confondre. Cette recherche nous conduira d’abord à proposer une nouvelle définition de la théologie analytique fondée sur trois critères et par la suite à distinguer deux manières de faire la théologie analytique: (i) une théologie (...) analytique de bas en haut et (ii) une théologie analytique de haut en bas. Selon notre thèse, seule une théologie analytique confessante de haut en bas peut être considérée comme une théologie analytique à part entière. (shrink)

Deliberative democracy is increasingly criticised as out of touch with the realities of partisan politics. This paper considers the rise of fake and hyperpartisan news as one source of this scepticism. While popular accounts often blame such content on citizens’ political biases and motivated reasoning, I survey the empirical evidence and argue that it does not support strong claims about the inability of citizens to live up to deliberative ideals. Instead, much of this research is shown to support the deliberative (...) capacities of citizens and points to their potential in helping to reduce the spread of false and misleading content. (shrink)

Desde que en 2008 se introdujera el concepto de nudge en el libro Nudge, que argumentaba que las pequeñas intervenciones basadas en cambios en la arquitectura de elección pueden alterar el comportamiento de las personas y facilitarles el logro de sus objetivos deseados, el uso de la economía del comportamiento en políticas públicas ha crecido significativamente, lo que ha llevado a la aparición de diferentes intervenciones basadas en conocimientos conductuales. Estas intervenciones se han aplicado en distintas áreas de políticas públicas (...) y administrativas, incluyendo salud, finanzas, o medio ambiente, con el objetivo de promover el bienestar y abordar problemas sociales y económicos. El uso de estas aplicaciones en cuestiones relacionadas con la violencia de género ha sido con frecuencia ignorado. De este modo, el objetivo de este estudio es analizar el uso de herramientas de la economía del comportamiento en políticas públicas, como nudges, boosts o auditoría de sludges y su aplicación a asuntos relacionados con este tipo de violencia. Al mismo tiempo que se señalan los posibles beneficios de su uso, también se reconocen las limitaciones del enfoque conductual, apuntando a la necesidad de una aproximación multifacética para combatir dicha violencia. Así, las políticas públicas que traten con violencia de género debe. (shrink)

Endocrinologists apply the idea of feedback loops to explain how hormones regulate certain bodily functions such as glucose metabolism. In particular, feedback loops focus on the maintenance of the plasma concentrations of glucose within a narrow range. Here, we put forward a different, organicist perspective on the endocrine regulation of glycaemia, by relying on the pivotal concept of closure of constraints. From this perspective, biological systems are understood as organized ones, which means that they are constituted of a set of (...) mutually dependent functional structures acting as constraints, whose maintenance depends on their reciprocal interactions. Closure refers specifically to the mutual dependence among functional constraints in an organism. We show that, when compared to feedback loops, organizational closure can generate much richer descriptions of the processes and constraints at play in the metabolism and regulation of glycaemia, by making explicit the different hierarchical orders involved. We expect that the proposed theoretical framework will open the way to the construction of original mathematical models, which would provide a better understanding of endocrine regulation from an organicist perspective. (shrink)

This paper distinguishes three concepts of "race": bio-genomic cluster/race, biological race, and social race. We map out realism, antirealism, and conventionalism about each of these, in three important historical episodes: Frank Livingstone and Theodosius Dobzhansky in 1962, A.W.F. Edwards' 2003 response to Lewontin (1972), and contemporary discourse. Semantics is especially crucial to the first episode, while normativity is central to the second. Upon inspection, each episode also reveals a variety of commitments to the metaphysics of race. We conclude by interrogating (...) the relevance of these scientific discussions for political positions and a post-racial future. (shrink)

There are two central kinds of epistemological mistakes: believing things you shouldn’t, and failing to believe things that you should. The knowledge-first program offers a canonical explanation for the former: if you believe something without knowing it, you violate the norm to believe only that which you know. But the explanation does not extend in any plausible way to a story about what’s wrong with suspending judgment when one ought to believe. In this paper I explore prospects for a knowledge-centering (...) account of positive epistemic norms that describe epistemic duties to believe. (shrink)

En los escritos de Aristóteles está frecuentemente relacionada la investigación (zethesis) con la deliberación (boulé). En el presente texto se hará una revisión de dicha relación, y se tratará de rechazar una relación meramente analógica entre investigar y deliberar, que, como se intentará mostrar, se basa fundamentalmente en una fuerte distinción entre razón teórica y razón práctica. Se tratará de probar una relación mucho más fuerte entre investigación y deliberación, mostrando que no es ni su objeto ni las habilidades racionales (...) y cognitivas lo que distingue la una de la otra, sino simplemente su finalidad: investigar es el género de la deliberación, y, por tanto, es preciso distinguir entre investigación teórica e investigación práctica o deliberación, cuyo fin, a diferencia de la investigación teórica, es hallar la manera de alcanzar un estado de cosas determinado, lo cual no depende tanto del objeto mismo, como es el caso de la teoría, sino del agente. (shrink)

En este trabajo matemático-filosófico se estudian cuatro tópicos de la Lógica matemática: El método de construcción de modelos llamado Ultraproductos, la Propiedad de Interpolación de Craig, las Álgebras booleanas y los Órdenes parciales separativos. El objetivo principal del mismo es analizar la importancia que tienen dichos tópicos para el estudio de los fundamentos de la matemática, desde el punto de vista del platonismo matemático. Para cumplir con tal objetivo se trabajará en el ámbito de la Matemática, de la Metamatemática y (...) de la Filosofía de la matemática. El desarrollo de la investigación arrojó como resultado que tales tópicos son muy importantes para el estudio de los fundamentos de la matemática, desde el punto de vista del platonismo matemático, y en el trabajo se explica detalladamente con abundantes ejemplos el porqué (al final de cada sección y al final del mismo). (shrink)