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)

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)

The literary genesis of Einbahnstraße by Walter Benjamin represents a very special case of the use of the procedures of surrealism in the philosophical-literary production of the author. The process of evolution of thinking that ended up in the writing of this piece is unveiled throughout the present analysis. This is a sign of both waiver and restart; the opening for a new productive dimension in the career of one of the most important —and misunderstood— philosophers of the 20th century. (...) More than enlightening a small master piece of philosophy from a literary perspective, or analyzing a small master piece of literature from the philosophy, what is being problematized here is the division, cultivated or figured throughout the years, between both disciplines. This work is intended to recover what is insoluble from the philosophical-literary labor of Walter Benjamin, besides tracing a possible reconfiguration for an interdisciplinary field of work to come up and contribute in the understanding of the problem called The Retreat of Metaphor by Jacques Derrida. (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)

What is the epistemic function of imagination? Traditionally, philosophers have claimed that the epistemic function of imagination is exhausted by its ability to provide justification for modal beliefs, or that it is epistemically irrelevant. However, in recent years a number of philosophers have broken with the tradition by arguing that imagination can generate justification or knowledge about contingent empirical facts. This paper argues against this view by developing a new dilemma. The upshot of the argument is that although imagination does (...) have an important epistemic function that has evaded the traditional view, it cannot give rise to new empirical justification or knowledge. (shrink)

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)

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)

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)

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)

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)

In this paper, I explain a challenge to the Equal Weight View coming from the psychology of group inquiry, and evaluate its merits. I argue that while the evidence from the psychology of group inquiry does not give us a reason to reject the Equal Weight View, it does require making some clarifications regarding what the view does and does not entail, as well as a revisiting the ethics of belief.

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)

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)

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)

A number of philosophers have recently suggested that the role of intuitions in the epistemology of armchair philosophy has been exaggerated. This suggestion is rehearsed and endorsed. What bearing does the rejection of the centrality of intuition in armchair philosophy have on experimentalist critiques of the latter? I distinguish two very different kinds of experimentalist critique: one critique requires the centrality of intuition; the other does not.

What would happen if one morning you wake up clumsy, as if your sense of touch were unreliable, arbitrarily on and off? And what would this clumsiness look like if we could transfer it to the moral sense? The article expounds an interesting analogy between the sense of touch, loosely construed, and the moral sense: just as a sort of consistency is necessary for the sense of touch to do its job, so it is for the moral sense to play (...) its part. Touch enables us to navigate the everyday world of coffee pots and staircases; our moral sensibility comes into play when we act or when we judge our actions and those of others, and plays a directive role in what we feel, how we feel it, and how we react to it. Taking the analogy further, I will suggest that inconsistency causes, in both cases, a certain clumsiness, and that clumsiness is linked to arbitrariness – like the person that helps others in dire need, but only does so on some rainy days. (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)

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)

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)

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)

Epistemic Courage is a timely and thought-provoking exploration of the ethics of belief, which shows why epistemology is no mere academic abstraction - the question of what to believe couldn't be more urgent. Jonathan Ichikawa argues that a skeptical, negative bias about belief is connected to a conservative bias that reinforces the status quo.

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.

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)

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)

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)

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)

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)

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)

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)

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.

The most pressing difficulty coherentism faces is, I believe, the problem of justified inconsistent beliefs. In a nutshell, there are cases in which our beliefs appear to be both fully rational and justified, and yet the contents of the beliefs are inconsistent, often knowingly so. This fact contradicts the seemingly obvious idea that a minimal requirement for coherence is logical consistency. Here, I present a solution to one version of this problem.

¿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)

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 .

In “Against Arguments from Reference” (Mallon et al., 2009), Ron Mallon, Edouard Machery, Shaun Nichols, and Stephen Stich (hereafter, MMNS) argue that recent experiments concerning reference undermine various philosophical arguments that presuppose the correctness of the causal-historical theory of reference. We will argue three things in reply. First, the experiments in question—concerning Kripke’s Gödel/Schmidt example—don’t really speak to the dispute between descriptivism and the causal-historical theory; though the two theories are empirically testable, we need to look at quite different data (...) than MMNS do to decide between them. Second, the Gödel/Schmidt example plays a different, and much smaller, role in Kripke’s argument for the causal-historical theory than MMNS assume. Finally, and relatedly, even if Kripke is wrong about the Gödel/Schmidt example—indeed, even if the causal-historical theory is not the correct theory of names for some human languages—that does not, contrary to MMNS’s claim, undermine uses of the causalhistorical theory in philosophical research projects. (shrink)

El objetivo principal de este trabajo es presentar el sistema lógico que resulta de extender, de una manera natural, a la Silogística con la Lógica proposicional, y demostrar que tal extensión se puede caracterizar como un sistema axiomático. Los axiomas que se utilizan son los de Jan Łukasiewicz , y la completitud de tal sistema de axiomas se prueba utilizando un método análogo al método del conjunto maximal consistente con testigos de Henkin, siguiendo algunas ideas que utiliza John Corcoran para (...) probar que su sistema de reglas de inferencia para la Silogística es completo. (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)

This work articulates two thesis: one Socratic and one Platonic; and displays how the first one is heir of the second. The Socratic one is called the principle of priority of definition; the Platonic one is the Recollection theory. The articulation between both theses is possible due to the Meno’s paradox, which makes a criticism on the first thesis, but it is solved with the second one. The consequence of this articulation is a new interpretation of the Recollection theory, as (...) a theory of knowledge acquisition that depends, mainly, on a distinction between knowledge and true opinion. To conclude, a new interpretation of the knowledge/true opinion distinction is displayed –not in the traditional fashion, evaluating the propositions one by one, and in an atomic way–, but as big blocks or chains of propositions shaping knowledge through explanatory reasoning (aitías logismós). (shrink)

In this paper, I propose to analyse two objections raised by Turner Jr in his paper “On Two Reasons Christian Theologians Should Reject The Intermediate State” in order to show that the intermediate state is an incoherent theory. As we shall see, the two untoward consequences that he mentions do not imply a metaphysical or logical contradiction. Consequently, I shall defend an Intermediate State and I shall propose briefly one metaphysical conception of the human being able to reply to Turner (...) Jr’s objections. (shrink)

A minimal essentialism (‘intrinsic biological essentialism’) about natural kinds is required to explain the projectability of human science terms. Human classifications that yield robust and ampliative projectable inferences refer to biological kinds. I articulate this argument with reference to an intrinsic essentialist account of HPC kinds. This account implies that human sciences (e.g., medicine, psychiatry) that aim to formulate predictive kind categories should classify biological kinds. Issues concerning psychiatric classification and pluralism are examined.

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)

Suppose that Ann says, “Keith knows that the bank will be open tomorrow.” Her audience may well agree. Her knowledge ascription may seem true. But now suppose that Ben—in a different context—also says “Keith knows that the bank will be open tomorrow.” His audience may well disagree. His knowledge ascription may seem false. Indeed, a number of philosophers have claimed that people’s intuitions about knowledge ascriptions are context sensitive, in the sense that the very same knowledge ascription can seem true (...) in one conversational context but false in another. This purported fact about people’s intuitions serves as one of the main pieces of evidence for epistemic contextualism. (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)

If states are permitted to create and maintain a military force, by what means are they permitted to do so? This paper argues that a theory of just recruitment should incorporate a concern for moral risk. Since the military is a morally risky profession for its members, recruitment policies should be evaluated in terms of how they distribute moral risk within a community. We show how common military recruitment practices exacerbate and concentrate moral risk exposure, using the UK as a (...) case study. We argue that the British state wrongs its citizens by subjecting them to excessively morally risky recruitment practices. Since, we argue, this risk exposure cannot be justified by appealing to the benefits of a military career for recruits, our argument calls for reform of existing practices. Our method of evaluation is generalizable and thus can be used to assess other states’ practices. (shrink)

How ought we to go about forming and revising our beliefs, arguing and debating our reasons, and investigating our world? If those questions constitute normative epistemology, then I am interested here in normative metaepistemology: the investigation into how we ought to go about forming and revising our beliefs about how we ought to go about forming and revising our beliefs -- how we ought to argue about how we ought to argue. Such investigations have become urgent of late, for the (...) methodology of epistemology has reached something of a crisis. For analytic epistemology of the last half-century has relied overwhelmingly on intuitions,1 and a growing set of arguments and data has begun to call this reliance on intuition seriously into question (e.g., Weinberg, Nichols, and Stich 2001; Nichols, Stich, and Weinberg 2003; Cummins 1998). Although that method has not been entirely without defenders (BonJour 1998; Bealer 1996; Jackson 1998; Sosa forthcoming; Weatherson 2003), these defenses have not generally risen to the specific challenges leveled by the anti-intuitionist critics. In particular, the critics have attacked specific ways of deploying intuitions, and the defenders have overwhelmingly responded with in-principle defenses of the cogency of appealing to intuition. An analogy here would be someone’s responding to arguments alleging systematic.. (shrink)

Michael WiIliams maintains that skepticism about the extemal worId is vitiated by a commitment to foundationalism and epistemological realism. (The latter is, approximately, the view that there is such a thing as knowledge of the extemal world in general, which the skeptic can take as a target). I argue that skepticism is not encumbered in the ways Williams supposes. What matters, first of all, is that we can’t perceive the difference between being in an ordinary environment and being in the (...) sort of situation the skeptic describes (e.g. having one’s brain manipulated by deceitful experimenters). This point can be upheld without embracing any substantial foundationalist tenet, such as the existence of basic beliefs, the availabiIity of something “given,” or the epistemic priority of experience. As to “epistemological realism,” I find that Williams has offered no principled way to distinguish between ordinary chaIIenges to knowledge and skeptical challenges which, supposedly, have no cIaim on our concem. (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)

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)

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)