Transdisciplinary research knits together knowledge from diverse epistemic communities in addressing social-environmental challenges, such as biodiversity loss, climate crises, food insecurity, and public health. This paper reflects on the roles of philosophy of science in transdisciplinary research while focusing on Indigenous and other subaltern forms of knowledge. We offer a critical assessment of demarcationist approaches in philosophy of science and outline a constructive alternative of transdisciplinary philosophy of science. While a demarcationist focus obscures the complex relations between epistemic communities, transdisciplinary (...) philosophy of science provides resources for meeting epistemic and political challenges of collaborative knowledge production. (shrink)

Review of David Ludwig, Inkeri Koskinen, Zinhle Mncube, Luana Poliseli, and Luis Reyes-Galindo, eds. Global Epistemologies and Philosophies of Science. Routledge, 2021, pp.i-xviii+319.

Citizen Satisfaction Index System (CSIS) was used to assess the delivery of support to education initiatives in the municipality of Banga, Aklan, Philippines. The samples were determined using multiple application of stratified random sampling approach. In accordance with the Philippine Statistical Authority's Data on Census Population and Housing for 2015, barangays having a bigger share of the population contributed more respondents to the 150 targeted participants. Following the inclusion criteria, the probability respondents were chosen using the Kish Grid. Pre-numbered questionnaires (...) were distributed, with odd numbers targeting male responders and even numbers targeting females. The following criteria were used to evaluate the respondents' assessments: awareness, availment of the program/service, satisfaction, and need for action. Furthermore, interviews were conducted to better understand and investigate the respondents' thoughts, behavior, and perspectives. The reasons for their reaction were also obtained. The data was provided in percentage as well as frequency distributions. The study inferred that awareness on alternative learning system and/or special education program should be improved since it is the only program that attained low rating for awareness. Most of the residents were not able to avail education programs because they have no household member who attends school. Majority of the respondents who availed the services were satisfied. However, scholarship and other assistance programs to students may be enhanced to improve service delivery. It is highly recommended by the citizens to improve accessibility to scholarship programs and other forms of financial assistance to students. (shrink)

Hume presenta su teoría estética en el ensayo Sobre el criterio del gusto [On the Standard of Taste], en el que propone la existencia de un criterio [standard] capaz de zanjar discusiones de gusto. Ese criterio se basa en la existencia de ciertas formas y cualidades que complacen naturalmente a todo ser humano. Hume asevera que tal criterio corresponde a la opinión del crítico: un hombre que ha desplegado particularmente sus facultades cognoscitivas, lo cual le permite percibir esas finas cualidades (...) que suscitan naturalmente el placer de lo bello en el ser humano. Con respecto a en qué consisten esas formas y cualidades universalmente placenteras, Hume guarda silencio. Pretendo mostrar cómo la teoría de la emoción en la música desarrollada por Leonard Meyer en su texto Emoción y significado en la música (Emotion and Meaning in Music) puede aportar inmensidades en ese aspecto. (shrink)

Speech Acts, Criteria and Intentions What makes a speech act a speech act? Which are its necessary and sufficient conditions? I claim in this paper that we cannot find an answer to those questions in Austin's doctrine of the infelicities, since some infelicities take place in fully committing speech acts, whereas others prevent the utterance from being considered as a speech act at all. With this qualification in mind, I argue against the idea that intentions—considered as mental states accomplishing a (...) causal role in the performance of the act—should be considered among the necessary conditions of speech acts. I would thus like to deny a merely ‘symptomatic’ account of intentions, according to which we could never make anything but fallible hypotheses about the effective occurrence of any speech act. I propose an alternative ‘criterial’ account of the role of intentions in speech acts theory, and analyse Austin's and Searle's approaches in the light of this Wittgensteinian concept. Whether we consider, with Austin, that speech acts ‘imply’ mental states or, with Searle, that they ‘express’ them, we could only make sense of this idea if we considered utterances as criteria for intentions, and not as alleged behavioural effects of hidden mental causes. (shrink)

El presente estudio busca describir fenomenológicamente la forma que exhibe la pena en el cuerpo, después de la pérdida de un ser querido. Para esto, se consideran las hipótesis de movimiento centrı́peto orientado a la autoafección, y movimiento centrı́fugo aludido a la ruptura de la intercorpereidad. Ambos movimientos, hacen referencia a la sensación ambigua que el cuerpo vive en la pena asociados a la presencia y ausencia del otro que ya no está, ya que el dolor provee un estado de (...) desincronización temporal que vuelve simultáneos el presente-pasado y presente-futuro. Esto trae como consecuencias, la contracción y extensión del cuerpo a partir de la maleabilidad de sus propios lı́mites. (shrink)

El paper realiza una exposición sobre el concepto y contenido de la nulidad y el restablecimiento del derecho como medio de control a la luz de la Ley 1437 de 2011; enfocándola en asuntos ambientales a través del estudio de la licencia ambiental.

In spite of being ubiquitous in life sciences, the concept of information is harshly criticized. Uses of the concept other than those derived from Shannon's theory are denounced as pernicious metaphors. We perform a computational experiment to explore whether Shannon's information is adequate to describe the uses of said concept in commonplace scientific practice. Our results show that semantic sequences do not have unique complexity values different from the value of meaningless sequences. This result suggests that quantitative theoretical frameworks do (...) not account fully for the complex phenomenon that the term “information” refers to. We propose a restructuring of the concept into two related, but independent notions, and conclude that a complete theory of biological information must account completely not only for both notions, but also for the relationship between them. (shrink)

This paper investigates the differences between ancient Greek and modern ethical naturalism, through the account of the whole classical tradition provided by Cicero in De finibus bonorum et malorum. Ever since Hume’s remarks on the topic, it is usually held that derivations of normative claims from factual claims require some kind of proper justification. It ́s a the presence of such justifications in the Epicurean, Stoic, and Academic-Peripatetic ethical theories (as portrayed in De finibus), and, after a negative conclusion, I (...) argue that we should conceive of this issue within a social-historical perspective: The radical difference between ancient and modern naturalistic ethics is due (in Weber’s terms) to the rationalization processes that generated the modern outlook on nature. (shrink)

Foundational ontologies, central constructs in ontological investigations and engineering alike, are based on ontological categories. Firstly proposed by Aristotle as the very ur- elements from which the whole of reality can be derived, they are not easy to identify, let alone partition and/or hierarchize; in particular, the question of their number poses serious challenges. The late medieval philosopher Dietrich of Freiberg wrote around 1286 a tutorial that can help us today with this exceedingly difficult task. In this paper, I discuss (...) ontological categories and their importance for foundational ontologies from both the contemporary perspective and the original Aristotelian viewpoint, I provide the translation from the Latin into English of Dietrich's De origine II with an introductory elaboration, and I extract a foundational ontology–that is in fact a single-category one–from this text rooted in Dietrich's specification of types of subjecthood and his conception of intentionality as causal operation. (shrink)

Ontologies are some of the most central constructs in today's large plethora of knowledge technologies, namely in the context of the semantic web. As their coinage indicates, they are direct heirs to the ontological investigations in the long Western philosophical tradition, but it is not easy to make bridges between them. Contemporary ontological commitments often take causality as a central aspect for the ur-segregation of entities, especially in scientific upper ontologies; theories of causality and philosophical ontological investigations often go hand-in-hand, (...) and were essentially inseparable in medieval thought. This constitutes the foundation for a bridge, and this article analyzes the causality-based ontology of the late medieval philosopher Dietrich of Freiberg from the viewpoint of today's upper-ontology engineering. In this bridging attempt, it offers a translation into English of the first part of Dietrich's De origine (abbreviated title) that is a compromise between traditional scholarly translations of medieval Latin philosophical texts and contemporary ontology. (shrink)

The van Wijngaarden grammars are two-level grammars that present many interesting properties. In the present article I elaborate on six of these properties, to wit, (i) their being constituted by two grammars, (ii) their ability to generate (possibly infinitely many) strict languages and their own metalanguage, (iii) their context-sensitivity, (iv) their high descriptive power, (v) their productivity, or the ability to generate an infinite number of production rules, and (vi) their equivalence with the unrestricted, or Type-0, Chomsky grammars.

El presente estudio aborda el nacimiento como problema filosófico desde una perspectiva intersubjetiva y corporeizada derivada del análisis del Cuerpo y el Otro presente en la Fenomenología de la Percepción de Merleau-Ponty. A partir de lo anterior, se discuten las limitaciones que tendría la coexistencia (Mitdasein) de Heidegger y la Otredad de Lévinas enmarcada en la relación del rostro en su intento de aproximarse a una filosofía del nacimiento desde una perspectiva de mundo compartido (madre-padre-hijo). Además, se plantea la necesidad (...) de incorporar al problema filosófico sobre el nacimiento tres etapas: embarazo-nacimiento-puerperio, ya que estas son fundamentales para ilustrar de manera profunda la dimensión relacional y corporeizada de este proceso que exhibe temporalidad e historicidad. (shrink)

3rd ed, 2021. A circumscription of the classical theory of computation building up from the Chomsky hierarchy. With the usual topics in formal language and automata theory.

For millennia, knowledge has eluded a precise definition. The industrialization of knowledge (IoK) and the associated proliferation of the so-called knowledge communities in the last few decades caused this state of affairs to deteriorate, namely by creating a trio composed of data, knowledge, and information (DIK) that is not unlike the aporia of the trinity in philosophy. This calls for a general theory of knowledge (ToK) that can work as a foundation for a science of knowledge (SoK) and additionally distinguishes (...) knowledge from both data and information. In this paper, I attempt to sketch this generality via the establishing of both knowledge structures and knowledge systems that can then be adopted/adapted by the diverse communities for the respective knowledge technologies and practices. This is achieved by means of a formal–indeed, mathematical–approach to epistemological matters a.k.a. formal epistemology. The corresponding application focus is on knowledge systems implementable as computer programs. (shrink)

To most of us – believers and non-believers alike – the possibility of a perfect God co-existing with the kinds of evil that we see calls out for explanation. It is unsurprising, therefore, that the belief that God must have justifying reasons for allowing all the evil that we see has been a perennial feature of theistic thought. Recently, however, a growing number of authors have argued that the existence of a perfect God is compatible with the existence of gratuitous (...) evil. Given powerful, millenia-long sensibilities about power and love and justice, it isn’t hard to find that suggestion simply incredible. Nonetheless, in this paper I will argue that the most prominent theistic alternatives to what has seemed incredible to most of us throughout most of history are themselves patently unacceptable for the theist as well. On any of the most widely accepted accounts of how God could have justifying reasons for permitting some evils, God’s existence means that we have justifying reasons for perpetrating and allowing every evil that we see. That's hard to swallow too. If I’m right about all of this, then two competing outcomes seem to present themselves as a possible result. On the one hand, for the theist, the apparently outrageous suggestion that the existence of a perfect God is compatible with gratuitous evil no longer looks like it faces a formidable, hard-to-resist alternative. On the other hand, some like me might think that my arguments go no distance at all towards dispelling the incredibility of the gratuitous evil nouvelle vague. On this line, theism may seem now to be between the rock and the hard place: it seems hard to make sense of the existence of a perfect God whether or not He has justifying reasons for allowing all the evil that we see. (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)

Christopher Hookway has been influential in promoting engagement with pragmatist and naturalist perspectives from classical and contemporary American philosophy. This book reflects on Hookway’s work on the American philosophical tradition and its significance for contemporary discussions of the understanding of mind, meaning, knowledge, and value. -/- Hookway’s original and extensive studies of Charles S. Peirce have made him among the most admired and frequently referenced of Peirce’s interpreters. His work on classical American pragmatism has explored the philosophies of William James, (...) John Dewey, and Josiah Royce, and examined the influence of pragmatist ideas outside of the United States. Additionally, Hookway has participated in a number of celebrated exchanges with some of the most high-profile figures of twentieth- and twenty-first-century philosophy, including Karl-Otto Apel, Philip Pettit, Hilary Putnam, and W.V.O. Quine, through which his treatments of a large range of topics in epistemology and the philosophies of mind and language have been developed and promoted. The chapters in this book—which include contributions from several of Hookway’s former students and colleagues—include studies of Hookway’s engagement with the works of Peirce, James, and Dewey, his contributions to virtue epistemology, and his discussions of hope and pragmatist metaphysics. -/- Pragmatic Reason will be of interest to researchers and advanced students working on American philosophy, the history of analytic philosophy, and epistemology. (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 paper I present reasons for us to accept the hypothesis that suspended judgment has correctness conditions, just like beliefs do. Roughly put, the idea is that suspended judgment about p is correct when both p and ¬p might be true in view of certain facts that characterize the subject’s situation. The reasons to accept that hypothesis are broadly theoretical ones: it adds unifying power to our epistemological theories, it delivers good and conservative consequences, and it allows us to (...) assess processes of reasoning involving attitudes of suspended judgment. (shrink)

Paul Silva has recently argued that doxastic justification does not have a basing requirement. An important part of his argument depends on the assumption that doxastic and moral permissibility have a parallel structure. I here reply to Silva's argument by challenging this assumption. I claim that moral permissibility is an agential notion, while doxastic permissibility is not. I then briefly explore the nature of these notions and briefly consider their implications for praise and blame.

Not focusing on the history of classical logic, this book provides discussions and quotes central passages on its origins and development, namely from a philosophical perspective. Not being a book in mathematical logic, it takes formal logic from an essentially mathematical perspective. Biased towards a computational approach, with SAT and VAL as its backbone, this is an introduction to logic that covers essential aspects of the three branches of logic, to wit, philosophical, mathematical, and computational.

Se lleva a cabo un planteamiento del estatus de la naturaleza en el ordenamiento jurídico como sujeto y objeto de derechos. Para lograr este objetivo, los autores se valen de una metodología inductiva a partir de un análisis descriptivo desde la doctrina, jurisprudencia y normas primarias. Con ello, se busca, en primer lugar, responder a la cuestión de si es posible o no que un ordenamiento jurídico contemple derechos de la naturaleza; en segundo lugar, se pretende evidenciar cómo el reconocimiento (...) de derechos sobre la naturaleza por parte de la jurisprudencia en Colombia cuenta con presupuestos comunes pese a que aún no se contemplan reglas claras sobre la asignación de derechos a la naturaleza. Al final, se realiza un llamado de atención para comprender esta figura más como un instrumento que el Estado debe utilizar a favor de la naturaleza, que como un decálogo de derechos. (shrink)

Given plausible assumptions about the nature of evidence and undercutting defeat, many believe that the force of the evidential problem of evil depends on sceptical theism’s being false: if evil is...

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)

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)

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)

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)

A survey of innateness in cognitive science, focusing on (1) what innateness might be, and (2) whether concepts might be innate.

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 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)

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)

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)

A. Newell and H. A. Simon were two of the most influential scientists in the emerging field of artificial intelligence (AI) in the late 1950s through to the early 1990s. This paper reviews their crucial contribution to this field, namely to symbolic AI. This contribution was constituted mostly by their quest for the implementation of general intelligence and (commonsense) knowledge in artificial thinking or reasoning artifacts, a project they shared with many other scientists but that in their case was theoretically (...) based on the idiosyncratic notions of symbol systems and the representational abilities they give rise to, in particular with respect to knowledge. While focusing on the period 1956-1982, this review cites both earlier and later literature and it attempts to make visible their potential relevance to today's greatest unifying AI challenge, to wit, the design of wholly autonomous artificial agents (a.k.a. robots) that are not only rational and ethical, but also self-conscious. (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 article’s objetive is to present four application examples of Herbrand’s theorem to decide the validity of reasoning on first order language, in accordance whit Church’s Undecidability’s theorem. Also, to tell which is the principal problem around it. The logical resolution calculus will be worked on this article, which is a method used in artificial intelligence.

Genera, typically hand-in-hand with their branching species, are essential elements of vocabulary-based information constructs, in particular scientific taxonomies. Should they also feature in formal ontologies, the highest of such constructs? I argue in this article that the answer is “Yes” and that the question posed in its title also has a Yes-answer: The way medieval ontologists sliced up the world into genera does matter to formal ontology. More specifically, the way Dietrich of Freiberg, a Latin scholastic, conceived and applied strictly (...) generic criteria to slice up the world into its entities can provide some guidelines to the field of formal ontology with respect to not only its contents, but also its scope. In particular, Dietrich's information criterion plays here a central role. (shrink)

The gulf between philosophical and formal ontology can and should be bridged. In this Editorial, I elaborate briefly on this subject.

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)

¿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)

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 .

Why should we avoid incoherence? An influential view tells us that incoherent combinations of attitudes are such that it is impossible for all of those attitudes to be simultaneously vindicated by the evidence. But it is not clear whether this view successfully explains what is wrong with certain akratic doxastic states. In this paper I flesh out an alternative response to that question, one according to which the problem with incoherent combinations of attitudes is that it is impossible for all (...) of those attitudes to be simultaneously knowledgeable. This alternative response explains what is wrong with akratic combinations of attitudes using commonly accepted epistemological theses. The paper still shows how this proposal is able to explain the badness of incoherent combinations involving the absence of attitudes, suspended judgment and credence. These explanations deploy the notions of knowledge and being in a position to know, instead of the notion of responding properly to the evidence. Finally, I suggest that this picture can be generalized to the realm of practical rationality as well. (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)

An analysis of--yet another--case of academic failure in multi- and interdisciplinarity. An editorial of the Journal of Knowledge Structures & Systems.

2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory to cognitive modeling, and (...) they are today in more demand than ever, due to the realization that inconsistency and vagueness in knowledge bases and information processes are not only inevitable and acceptable, but also perhaps welcome. The main modern applications of (any) logic are to be found in the digital computer, and we thus require the practical knowledge how to computerize—which also means automate—decisions (i.e. reasoning) in many-valued logics. This, in turn, necessitates a mathematical foundation for these logics. This book provides both these mathematical foundation and practical knowledge in a rigorous, yet accessible, text, while at the same time situating these logics in the context of the satisfiability problem (SAT) and automated deduction. The main text is complemented with a large selection of exercises, a plus for the reader wishing to not only learn about, but also do something with, many-valued logics. (shrink)

Deontological evidentialism is the claim that we ought to form and maintain our beliefs in accordance with our evidence. In this paper, I criticize two arguments in its defense. I begin by discussing Berit Broogard’s use of the distinction between narrow-scope and wide-scope requirements against W.K. Clifford’s moral defense of. I then use this very distinction against a defense of inspired by Stephen Grimm’s more recent claims about the moral source of epistemic normativity. I use this distinction once again to (...) argue that Hilary Kornblith’s criticism of Richard Feldman’s defense of is incomplete. Finally, I argue that Feldman’s defense is insensitive to the relation between normative requirements and privileged values: values that have normative authority over us. (shrink)

Aesthetic subjectivism takes the truth of aesthetic judgments to be relative to the individual making that judgment. Despite widespread suspicion, however, this does not mean that one cannot be wrong about such judgments. Accordingly, this does not mean that one cannot gain higher-order evidence of error and fallibility that bears on the rationality of the aesthetic judgment in question. In this paper, we explain and explore these issues in some detail.

In this paper, I offer two counterexamples to the so-called ‘Uniqueness Thesis.’ As one of these examples rely on the thesis that it is possible for a justified belief to be based on an inconsistent body of evidence, I also offer reasons for this further thesis. On the assumption that doxastic justification entails propositional justification, the counterexamples seem to work.

Logic arguably plays a role in the normativity of reasoning. In particular, there are plausible norms of belief/disbelief whose antecedents are constituted by claims about what follows from what. But is logic also relevant to the normativity of agnostic attitudes? The question here is whether logical entailment also puts constraints on what kinds of things one can suspend judgment about. In this paper I address that question and I give a positive answer to it. In particular, I advance two logical (...) norms of agnosticism, where the first one allows us to assess situations in which the subject is agnostic about the conclusion of a valid argument and the second one allows us to assess situations in which the subject is agnostic about one of the premises of a valid argument. (shrink)