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)

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)

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 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)

Research and practice about self-determination in the context of disability has centred on teaching skills and providing support to help people with impairments to be independent. However, limited research exists about the impact of Information and Communication Technologies, in particular social media and mobile devices, on the development of self-determination skills among people with disabilities. This paper presents the findings of a qualitative study which collected data from observations, a researcher diary, focus groups, individual interviews and data from social media. (...) The focus of the study was on young people with vision impairments who were transitioning to university life. The study found that the participants developed self-determination skills by using and adapting collaborative and interactive online tools and mobile devices according to their transition needs. This finding expands the understanding of the implications of new technologies for young people with disabilities’ personal development and the enhancement of self-determination. (shrink)

To explore social media use in New Zealand, a sample of 1001 adults aged 18 and over were surveyed in November 2021. Participants were asked about the frequency of their use of different social media platforms (text message included). This report describes how often each of the nine social media sites and apps covered in the survey are used individually on a daily basis. Differences based on key demographics, i.e., age and gender, are tested for statistical significance, and findings summarised.

In Bertrand Russell's 1903 Principles of Mathematics, he offers an apparently devastating criticism of the neo-Kantian Hermann Cohen's Principle of the Infinitesimal Method and its History (PIM). Russell's criticism is motivated by his concern that Cohen's account of the foundations of calculus saddles mathematics with the paradoxes of the infinitesimal and continuum, and thus threatens the very idea of mathematical truth. This paper defends Cohen against that objection of Russell's, and argues that properly understood, Cohen's views of limits and infinitesimals (...) do not entail the paradoxes of the infinitesimal and continuum. Essential to that defense is an interpretation, developed in the paper, of Cohen's positions in the PIM as deeply rationalist. The interest in developing this interpretation is not just that it reveals how Cohen's views in the PIM avoid the paradoxes of the infinitesimal and continuum. It also reveals some of what is at stake, both historically and philosophically, in Russell's criticism of Cohen. (shrink)

The COVID-19 pandemic highlighted the importance of internet access across various aspects of life, from remote work and online education to healthcare services and social connections. As we transition to a post-pandemic era, a pressing need arises to update our understanding of the multifaceted nature of internet access. This study is one of the first attempts to do so. Using survey data from New Zealand adult internet users (n=960), it compares internet connection types, frequency of internet use at home, social (...) media use, and concerns about online risk between people with and without disabilities. Results show people with disabilities have restricted fibre access and higher wireless broadband (a much slower connection type). People with disabilities use social media platforms less and are more concerned about certain online risks. The findings highlight persistent disparities in internet access for people with disabilities in the post-pandemic era. Implications of the study are discussed. (shrink)

Es conocido que el Teorema de Completitud de Gödel, el Teorema del Colapso Transitivo de Mostowski y el Principio de Reflexión son resultados muy útiles en las investigaciones de Lógica matemática y/o los Fundamentos de la matemática. El objetivo de este trabajo es presentar algunas demostraciones clásicas de tales resultados: Dos del Teorema de Completitud de Gödel, una del Teorema del Colapso Transitivo de Mostowski y una del Principio de Reflexión. Se aspira que estas notas sean de utilidad para estudiar (...) dichas pruebas. Vale la pena resaltar que entre los métodos matemáticos que se utilizan en tales demostraciones se encuentran: (1) La técnica de construcción de modelos a partir de constantes (o "método del conjunto maximal consistente con un conjunto de testigos" de Henkin) y (2) el Principio de inducción matemática en varias versiones [ (2.1) Inducción matemática sobre los números naturales y (2.2) Inducción transfinita ((2.2.1) Inducción transfinita sobre conjuntos bien ordenados cualesquiera, por ejemplo sobre un cardinal infinito Alef_alfa, (2.2.2) Inducción transfinita sobre una clase de conjuntos bien ordenada, por ejemplo sobre la "clase de todos los ordinales, finitos o infinitos", y (2.2.3) Inducción transfinita sobre relaciones bien fundamentadas, por ejemplo sobre la "relación de pertenencia" entre conjuntos)]. (shrink)

While children’s experiences of online risks and harm is a growing area of research in New Zealand, public discussion on the matter has largely been informed by mainstream media’s fixation on the dangers of technology. At best, debate on risks online has relied on overseas evidence. However, insights reflecting the New Zealand context and based on representative data are still needed to guide policy discussion, create awareness, and inform the implementation of prevention and support programmes for children. This research report (...) presents findings from a quantitative study regarding different aspects related to risks and online safety. It looks at the online experiences that children find bothersome and upsetting and explores the hurtful behaviours they encounter or engage in, both online and in person. Evidence regarding exposure to different types of potentially harmful online content is also presented. Another relevant contribution is the insights related to excessive internet use.The findings presented in this report are based on data from 2,061 New Zealand children aged 9-17. We hope the findings will contribute to the development of policies, practices and services designed to support New Zealand children to safely take advantage of the opportunities available to them online. (shrink)

About thirty years ago, when the Internet started to be commercialised, access to the medium became a topic of research and debate. Up-to-date evidence about key predictors, such as age, is crucial because of the Internet's ever-changing nature and the challenges associated with gaining access to it. This paper aims to give an overview of New Zealand's Internet access trends and how they relate to age. It is based on secondary analysis of data from a larger online panel survey with (...) 1,001 adult respondents. The Chi-square test of independence and Cramer's V were used in the analysis. The study provides new evidence to understand the digital divide. Specifically, it uncovers a growing disparity in the quality of Internet connectivity. Even though fibre is the most common type of broadband connection at home, older adults are less likely to have it and more likely to use wireless broadband, which is a slower connection type. Additionally, a sizable majority of people in all age categories have favourable opinions on the Internet. Interestingly, this was more prevalent among older people, although they report an increased concern about the security of their personal information online. The implications of the results are discussed and some directions for future research are proposed. (shrink)

European Journal of Philosophy, Volume 30, Issue 1, Page 148-168, March 2022.

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)

In her paper, The case for physician assisted suicide: not proven, Bonnie Steinbock argues that the experience with Oregon’s Death with Dignity Act fails to demonstrate that the benefits of legalising physician assisted suicide outweigh its risks. Given that her verdict is based on a small number of highly controversial cases that will most likely occur under any regime of legally implemented safeguards, she renders it virtually impossible to prove the case for physician assisted suicide. In this brief paper, we (...) suggest some ways that may enable us to weigh the risks and benefits of legalisation more fairly and, hopefully, allow us to close the case for physician assisted suicide. (shrink)

Consider the claims that representations of physical laws are intersubjective, and that they ultimately provide the foundation for all other intersubjective knowledge. Those claims, as well as the deeper philosophical commitments that justify them, constitute rare points of agreement between the Marburg School neo-Kantians Paul Natorp and Ernst Cassirer and their positivist rival, Ernst Mach. This is surprising, since Natorp and Cassirer are both often at pains to distinguish their theories of natural scientific knowledge from positivist views like Mach’s, and (...) often from Mach’s views in particular. Thus the very fact of this agreement between the Marburg School neo-Kantians and their positivist stalking horse points to a deep current of ideas that runs beneath the whole of the post-Kantian intellectual context they shared. (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)

Introduction to the Special Volume, “Method, Science and Mathematics: Neo-Kantianism and Analytic Philosophy,” edited by Scott Edgar and Lydia Patton. At its core, analytic philosophy concerns urgent questions about philosophy’s relation to the formal and empirical sciences, questions about philosophy’s relation to psychology and the social sciences, and ultimately questions about philosophy’s place in a broader cultural landscape. This picture of analytic philosophy shapes this collection’s focus on the history of the philosophy of mathematics, physics, and psychology. The following (...) essays uncover, reflect on, and exemplify modes of philosophy that are engaged with these allied disciplines. They make the case that, to the extent that analytic philosophers are still concerned with philosophy’s ties to these disciplines, we would do well to pay attention to neo-Kantian views on those ties. (shrink)

This research report presents findings about the extent and nature of digital self-harm among New Zealand teens. Digital self-harm is broadly defined here as the anonymous online posting or sharing of mean or negative online content about oneself. The report centres on the prevalence of digital self-harm (or self-cyberbullying) among New Zealand teens (aged 13-17), the motivations, and outcomes related to engaging in this behaviour. The findings described in this report are representative of the teenage population of New Zealand by (...) gender, ethnicity and age. Key findings are: Overall, 6% of New Zealand teens have anonymously posted mean or negative content online about themselves in the past year. Teenagers’ top reasons for this behaviour were: making a joke, wanting to show resilience, looking for friends’ sympathy, and seeking reassurance of friendship. By exploring the nature and extent of this behaviour, we are providing the online safety community, schools and parents with insights about a complex and, to some extent, hidden phenomenon involving New Zealand teens. (shrink)

Over the last ten years the sharing of nude images or videos (sometimes known as “sexting”) by young people has emerged as a concern. Despite this, no research had been conducted on the prevalence of the sharing of nudes among young New Zealanders. This study addresses this and raises important questions for all those with a role in supporting young people’s healthy development. We believe this report makes an important contribution to the overall understanding of young people’s experience of these (...) behaviours. However, it only provides a snapshot, and more work is required to understand how best to support young people as they navigate the challenges and potential risks. This report is being released as part of a larger project exploring young people’s experiences of digital risk and harm, carried out by a partnership between Netsafe and the Ministry for Women. (shrink)

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

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

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

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

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.

While children’s interaction with digital technologies is a matter of interest around the world, evidence based on nationally representative data about how integrated these tools are in children’s everyday life is still limited in New Zealand. This research report presents findings from a study that explores children’s internet access, online skills, practices, and opportunities. This report is part of Netsafe’s research project Ngā taiohi matihiko o Aotearoa - New Zealand Kids Online, and our first publication as a member of Global (...) Kids Online. Generating insightful, reliable evidence about New Zealand children’s online experiences is vital to develop adequate support that reflects children’s experiences and needs. This, in turn, will help them to manage online risks and potential harm from behaviours such as cyberbullying, harassment, and other forms of abuse and intimidation. (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)

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 .

The physiologist Johannes Müller’s doctrine of specific nerve energies had a decisive influence on neo-Kantian conceptions of the objectivity of knowledge in the 1850s - 1870s. In the first half of the nineteenth century, Müller amassed a body of experimental evidence to support his doctrine, according to which the character of our sensations is determined by the structures of our own sensory nerves, and not by the external objects that cause the sensations. Neo-Kantians such as Hermann von Helmholtz, F.A. Lange, (...) and Otto Liebmann took Müller’s doctrine to have far-reaching consequences for their epistemologies. Over the course of the 1850s - 1870s, these three neo-Kantians, each in his own way, argued that reflection on Müller’s doctrine ruled out a certain conception of the objectivity of knowledge. It ruled out the view that knowledge is objective in virtue of affording us information about objects in a mind-independent external world. -/- This paper traces how Helmholtz, Lange, and Liebmann developed their arguments for this view, and how each developed his own alternative conception of objectivity, according to which objectivity has nothing to do with a mind-independent world. Finally, the paper concludes by considering why these arguments modelled on Müller’s doctrine would have been so powerful against rival post-Hegelian conceptions of objectivity, especially those of scientific materialists like Ludwig Büchner. (shrink)

Are there any truly ontologically random events? This paper argues that randomness is an unavoidably epistemic concept and therefore ascription of ontological randomness to any particular event or series of events can never be justified.

Research on transition to higher education and young people with disabilities has increased in recent years. However, there is still limited understanding of transition issues and how digital technologies, such as social media and mobile devices, are used by this group of students to manage these issues. This article presents the findings of an empirical study that addressed this matter based on young people’s views and experiences. The qualitative study was conducted in the context of a group of students with (...) vision impairments transitioning to a New Zealand university. The findings draw from observations, a researcher diary, focus groups, individual interviews, and data from social media. The study shows that, like their non-disabled peers, the students actively engaged with interactive and collaborative digital technologies to make sense, individually and collectively, of different transition issues before, during and after the first academic trimester of their university journey. (shrink)

Some commentators on Hermann Cohen have remarked on what they take to be a puzzle about the origins of his mature anti-psychologism. When Cohen was young, he studied a kind of psychology, the Völkerpsychologie of Moritz Lazarus and Heymann Steinthal, and wrote apparently psycholgistic accounts of knowledge almost up until the moment he first articulated his anti-psychologistic neo-Kantianism. To be sure, Cohen's mature anti psycholgism does constitute a rejection of certain central commitments of Völkerpsychologie. However, the relation between Völkerpsychologie and (...) Cohen's mature anti-psychologism is not one of straightforward opposition. This paper argues that Cohen had significantly less distance to travel than it appears to get from his early Völkerpsychologie to his mature anti-psychologism. In particular, this paper argues that Cohen always had an anti-psychologistic account of knowledge, even during the period when he was studying Völkerpsychologie, and further, that key features of his Völkerpsychologie partly shaped his mature account of knowledge. Finally, the paper identifies how Cohen’s views did change over the transition from his völkerpsychological period to his later anti-psychologism. It thus identifies what changes in Cohen’s views do need to be explained. (shrink)

Research suggests that parents tend to largely underestimate their child’s engagement in risky and/or hurtful behaviours as well as their experiences of harm online. While helpful, the available international evidence is not only limited but also does not reflect the New Zealand context. In addition, understanding parental knowledge of the online experiences of children is important as parents play a critical role in helping their child to prevent or deal with bothering experiences and risky behaviours as well as providing children (...) with emotional support when things go wrong online. To help close the gap of New Zealand-based evidence on the topic, this factsheet presents findings from a quantitative study conducted with New Zealand parents and their children. The objectives of the study are to measure parental knowledge of children’s experiences of risks and harm online, and to compare parents’ level of awareness with their child’s self-reported experiences. The study found a mismatch between parents’, caregivers’ and whānau awareness and their children’s reports of bothering or upsetting experiences online. (shrink)

Government agencies in New Zealand are not required to systematically collect data on online hate speech, thus, there is a lack of longitudinal evidence regarding this phenomenon. This report presents trends in personal experiences of and exposure to online hate speech among adult New Zealanders based on nationally representative data. The findings from this study are also compared with results from a similar research study conducted in 2018. In addition, this report explores people’s perceptions about other issues related to hate (...) speech. The goal of this study is to fill some knowledge gaps regarding the extent and nature of hate speech in New Zealand. It also seeks to provide reliable and robust evidence to inform public conversation on the topic and the implementation of strategies and activities to ensure all New Zealanders, no matter what their characteristics, are safe online to benefit from the multiple opportunities of the digital environment. (shrink)

ABSTRACT A number of authors have recently advanced a ‘disjunctivist’ view of the rationalising explanation of action, on which rationalisations of the form ‘S A’d because p’ are explanations of a fundamentally different kind from rationalisations of the form ‘S A’d because she believed that p’. Less attempt has been made to explicitly articulate the case against this view. This paper seeks to remedy that situation. I develop a detailed version of what I take to be the basic argument against (...) disjunctivism, drawing on a framework of explanatory proportionality. The disjunctivist cannot reject this framework, I argue, because they need it to respond to another challenge, from psychological individualism. As I explain, however, the proportionality-based challenge is not in principle insurmountable, and I outline a number of ways in which a case for disjunctivism might be developed in response to it. The paper thus clarifies the dialectic around disjunctivism about the rationalisation of action and, specifically, what advocates of the view must do in order to make a compelling case for it. (shrink)

In 'Weak agnosticism defended' Graham Oppy set out to ’show that agnosticism can be so formulated that it is no less philosophically respectable than theism and atheism’. Oppy begins by differentiating between strong agnosticism, which obliges rational persons to suspend judgment on the question of God’s existence, and weak agnosticism, which allows rational persons to do so. Weak agnosticism is thus the philosophical position that it is possible and rational - but not obligatory - to suspend judgment on the question (...) of God’s existence. The question I discuss in this paper is whether one can consistently practice agnosticism, as opposed to merely suspending judgment regarding the existence of God? Does acceptance of the the sis that ’agnosticism can be so formulated that it is no less philosophically respectable than theism and atheism’ entail the possibility of actual consistent practice of agnosticism? (shrink)

This paper considers George A. Reisch’s account of the role of Cold War political forces in shaping the apolitical stance that came to dominate philosophy of science in the late 1940s and 1950s. It argues that at least as early as the 1930s, Logical Empiricists such as Rudolf Carnap already held that philosophy of science could not properly have political aims, and further suggests that political forces alone cannot explain this view’s rise to dominance during the Cold War, since political (...) forces cannot explain why a philosophy of science with liberal democratic, anti-communist aims did not flourish. The paper then argues that if professionalization is understood in the right way, it might point toward an explanation of the apolitical stance of Cold War philosophy of science. (shrink)

A growing number of young people with disabilities is pursuing university education. Available research on the impact of Information and Communication Technologies on this matter has mainly focused on assistive technologies and their compensatory role for the adjustment of this group of students to the tertiary setting. However, limited research has looked at the role played by digital technologies such as social media and mobile devices in the transition to university, a critical period of change for all students but more (...) challenging for those with impairments. This paper presents the findings of an empirical study that investigated the experiences of students with vision impairments aged 18 to 24 who were transitioning to a New Zealand university. The findings draw from observations, a researcher diary, focus groups, individual interviews, and data from social media. The study found that new technologies play several enabling roles that help students to manage diverse transition challenges. These roles not only include aspects such as impairment compensation, communication, information, and learning but also support arrangement, collaboration, and social connection and participation. By incorporating in the analysis the potential of digital tools, the article updates and expands the understanding of the role of ICTs in higher education from experiences and views of young people with vision impairments. (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)

La siguiente ponencia-taller tiene por finalidad explicar cómo podría aplicarse el Método de George Polya para resolver problemas (matemáticos) en el contexto de la Lógica Matemática, especialmente en la lógica Matemática elemental (la lógica de primer orden con identidad). Es una propuesta pedagógica experimental (además de las ya existentes) que tal vez pueda ser útil para la enseñanza de la lógica matemática en ciencias o en humanidades. Dicha ponencia se presentó (vía web) con motivo de la celebración del Día Mundial (...) de Lógica 2022 en dos ocasiones: En la Universidad Central de Venezuela (Venezuela) y en la Universidad Mayor de San Andrés (Logic & Analytics Group - La Paz y La Sociedad Científica de Filosofía de la UMSA, Bolivia). Es un proyecto pedagógico en construcción. (shrink)

In its recent statement 'Sex Selection and Preimplantation Genetic Diagnosis', the Ethics Committee of the American Society of Reproductive Medicine concluded that preimplantation genetic diagnosis for sex selection for non-medical reasons should be discouraged because it poses a risk of unwarranted gender bias, social harm, and results in the diversion of medical resources from genuine medical need. We critically examine the arguments presented against sex selection using preimplantation genetic diagnosis. We argue that sex selection should be available, at least within (...) privately funded health care. (shrink)

Brian Garrett claims, in defence of Gaunilo’s Perfect Island and contra Plantinga, that ‘Properly understood, the great-making qualities of an island are maximal’. This article demonstrates that they are not, thus ‘the greatest conceivable island’ remains an incoherent concept and Gaunilo’s parody fails.

This article introduces Transition 2.0, a paradigm shift designed to study and support students with disabilities' transition to higher education. Transition 2.0 is the result of a qualitative study about how a group of young people with vision impairments used digital technologies for their transition to university. The findings draw from observations, a researcher diary, focus groups, individual interviews, and data from social media. The article discusses a conventional view of transition, referred to here as Transition 1.0, which has dominated (...) disability-related research and service provision in higher education. It counters this view by further developing the conceptual framework for Transition 2.0. The findings expand current conceptual approaches to transition by incorporating in the analysis the role played by digital tools such as social media and mobile devices. They also provide a new lens through which to study and understand student engagement in higher education. (shrink)

This paper explores the integration of multiple intelligences and artificial intelligence (AI) in language learning, focusing on its potential to enhance personalization and engagement. Drawing from existing research and studies conducted in various contexts, including the Philippines, this study aims to contribute to the understanding of the benefits, challenges, and effectiveness of this integration. The paper begins with an introduction that highlights the background and significance of integrating multiple intelligences and AI in language learning, identifying research gaps, objectives, research questions, (...) and the theoretical framework. A literature review provides an overview of multiple intelligences theory by Howard Gardner, the role of AI in language learning, and identifies gaps in the existing literature. The methodology section outlines the research design and approach, participant selection, data collection methods, validity and reliability measures, and ethical considerations. Findings and results are presented through the analysis of qualitative data, exploring emergent themes and patterns. The discussion section critically examines the identified research gaps, discusses the validity and reliability of the study, addresses the scope and limitations, and explores the implications of the findings for theory, practice, and future research. The conclusion summarizes the key findings and contributions of the study, reflects on the achievement of research objectives, offers recommendations for further research, and provides final remarks tying together the main points of the study. This paper contributes to the existing body of knowledge by providing insights into the integration of multiple intelligences and AI in language learning and its impact on personalization, engagement, and language learning outcomes. (shrink)

A critique of J. L. Schellenberg's argument from Divine Hiddenness: Schellenberg's conclusion that since apparently there are 'capable inculpable non-believers in God' the cognitive problem of divine hiddenness is actually an argument for the non-existence of God. Schellenberg's conclusion seems at least partly based on his misunderstanding or disregard of significant aspects of the Judeo-Christian tradition and certain assumptions, especially regarding nature of religious belief as well as primacy and instrumentality of reason. I suggest that given the kind of God (...) proposed by the Judeo-Christian tradition it is not necessary that reasonable non-belief in His existence be impossible; moreover it may even be the case that possibility of reasonable non-belief is necessary given the nature and purposes of God as proposed by the Judeo-Christian tradition. (shrink)

Since transition to higher education emerged as a research topic in the early 1970s, scholarly inquiry has focused on students without impairments and, what is more, little attention has been paid to the role of digital technologies. This article seeks to address this knowledge gap by looking at the university experiences of a group of first-year students with vision impairments from New Zealand, and the way they use digital tools, such as social media and mobile devices, to manage their transition-related (...) challenges. The article summarises the findings from a longitudinal qualitative project which was methodologically informed by action research (AR). The article explores and discusses scholarly inquiry of transition to university and introduces a conceptual framework which includes five overlapping stages, the transition issues faced by the students and the roles played by digital technologies. The article updates and expands the theoretical understanding of transition to higher education and provides empirical evidence for practitioners to support the needs, inclusion, and participation of young people with disabilities in the tertiary setting. (shrink)

The transport sector is one of the largest sources of greenhouse gas emissions in New Zealand. To address this issue, the government is planning a set of actions to be implemented in the next 15 years. One of these actions deals with transport emissions and targets for a reduction in light vehicle travel. However, to achieve this goal, there is a need for both an updated assessment of effective interventions and an analysis of their relevance and applicability to the New (...) Zealand context. This report seeks to close the gap by conducting a narrative literature review of a collection of existing literature, supplemented with some targeted searches. With the focus on evidence relevant to New Zealand’s largest and fastest growing urban environments, the report identified 24 publicly available research outputs from around the world (mainly from Western European countries). The papers assessed differ not only in the type of research method and analysis applied but also the form of intervention (s) evaluated, the duration of the intervention and follow-up periods, the characteristics of the population groups or intervention sites studied, the measures, results and metrics relevant to New Zealand, and the outcomes of the interventions. Although these differences may represent a challenge in terms of comparability and transferability, they also provide opportunities and lessons for policy-and decision-makers. Finally, the report discusses the implications of the review and its findings and provides some directions and recommendations for future research, policy and practice for the measurement and evaluation of interventions. (shrink)