Proof assistants are software-based tools that are used in the mechanization of proof construction and validation in mathematics and computer science, and also in certified program development. Different such tools are being increasingly used in order to accelerate and simplify proof checking, and the Coq proof assistant is one of the most well known and used in large-scale projects. Language and automata theory is a well-established area of mathematics, relevant to computer science foundations and information technology. In particular, context-free language (...) theory is of fundamental importance in the analysis, design, and implementation of computer programming languages. This work describes a formalization effort, using the Coq proof assistant, of fundamental results of the classical theory of contextfree grammars and languages. These include closure properties (union, concatenation, and Kleene star), grammar simplification (elimination of useless symbols, inaccessible symbols, empty rules, and unit rules), the existence of a Chomsky Normal Form for context-free grammars and the Pumping Lemma for context-free languages. The result is an important set of libraries covering the main results of context-free language theory, with more than 500 lemmas and theorems fully proved and checked. As it turns out, this is a comprehensive formalization of the classical context-free language theory in the Coq proof assistant and includes the formalization of the Pumping Lemma for context-free languages. The perspectives for the further development of this work are diverse and can be grouped in three different areas: inclusion of new devices and results, code extraction, and general enhancements of its libraries. (shrink)

An attention shift from a stationary to a changing object has to occur in feature space, in order to bind these stimuli into a unitary percept. This time-consuming shift leads to the perception of a changing stimulus further ahead along its trajectory. This attentional framework is able to accommodate the flash-lag effect in its multiple empirical manifestations.

O artigo pretende tratar, de forma resumida, como a filosofia de Hegel, ao contrário de boa parte das interpretações canônicas, tenta dar conta dos problemas reais da política e sociedade alemãs. Da mesma forma a filosofia sartreana tenta dar respostas do mesmo cunho à cena concreta da vida francesa. Tendo em vista esses dois fatores apresenta-se o pensamento hegeliano, a sua recepção por Sartre e os possíveis aportes entre as duas teorias.

The Hilbert space formalism is a powerful language to express many cognitive phenomena. Here, relevant concepts from signal detection theory are recast in that language, allowing an empirically testable extension of the quantum probability formalism to psychophysical measures, such as detectability and discriminability.

Nesse artigo analisamos alguns aspectos do Programa Um Computador por Aluno (UCA), recentemente implantado na rede municipal de ensino de Erechim (RS), buscando apresentar reflexões sobre as possibilidades desse Programa à formação docente e lançando luzes para as implicações dessa formação nos processos de ensino e aprendizagem e na promoção da inclusão digital na escola pública. Nosso estudo sinaliza que a inclusão digital tornou-se desafio e compromisso no referido município, ao tempo que a formação tecnológica de professores é entendida como (...) prioridade para que essa inclusão se concretize. O estudo mostra que mudanças estruturais e pedagógicas são vislumbradas pelos professores, os quais sugerem a necessidade de formação tecnológica contínua para que possam mudar suas práticas, e, ainda, que a inclusão digital é entendida pelos gestores e docentes como via para a qualificação dos processos de ensino e aprendizagem. Para tanto, entendemos que o processo de inclusão digital precisa fomentar novas formas de conhecimento e participação social para professores e estudantes. (shrink)

Scientific inquiry possibly shares with people's ordinary understanding the same evolutionary determinants, and affect-laden intuitions that shape moral judgments also play a decisive role in decision-making, planning, and scientific reasoning. Therefore, if ordinary understanding does differ from scientific inquiry, the reason does not reside in the fact that the former (but not the latter) is endowed with moral considerations.

The main objective of this work is to understand the daily practices of user management in post-reformist devices in the Brazilian mental health field. Through Foucault's genealogical work on government practices, understood as forms of conducting the behavior of others, it is possible to open a possible field for the study of the practices of psi knowledge, considering them as forms of management that act by through the free and natural acts of individuals. More specifically, our goal is to examine (...) day-to-day practices on some reformist devices such as CAPS through user files. Basically, two driving models have been found in the new devices: 1) Cases with frank intervention of production of commitments and agreements with users, seeking the entry of this to varied activities and political leadership ; 2) Cases with little response from the user, in which the forms of conduction are implemented by policies of inclusion of family members and close reference characters in the management of the patient's life. (shrink)

This paper intents to analyze the influence of John Dewey’s ideas in the movement that defended the educationl renovation in Brazil at the end of the 1920s and in the 1930s. For this, it explains two trends of that movement: the first is described by the metaphor of industrial or mechanical efficiency, whose emphasis was in the power derived from the disciplinary idea of progress, which was embedded in the process of rationalization of the social relations submitted by a factory (...) model; the second, developed by influence of Dewey, is characterized by a project of democratization of society and school that prevented the individual massification and the adoption of the rationalizing model inspired by the factory without any criticism. When Dewey was put in the center of the debate on political, pedagogical and social goals of the Brazilian New School, he was called to introduce a series of concepts that helped to find the balance between the respect for individuality and the observation of the social needs. (shrink)

For the philosopher Ivan Illich, society became a set of systems rather than a group of people. As such, society depersonalizes life and brings the need for open non-systematized spaces where people can act and interact outside their typical roles. On the other hand, an absence of formal structures may simply open spaces for the informal reproduction of society’s already well-established structures. Given this conjuncture, can systems be designed to foster personal expression? The answer I found in cybernetics is self-organization, (...) a process of adaptation to a context that can grow different organizations depending on what this context provides. This implies that personal expression is a concern in society’s emergent organizations, calling for meta planning to design the context of some of society’s self-organization processes. The cybernetician Gordon Pask argued that depersonalization follows from non-conversational communications, like the ones that develop in large committees. In response, Pask’s fellow cybernetician Stafford Beer proposed a meeting protocol called Team Syntegrity allowing large groups to subdivide into small integrated discussion groups. While Beer’s work has been extensively discussed in existent literature, this article presents the results of four experiments conducted by using variations of Beer’s protocol to understand both the ease with which it can be adapted to different situations, and the implications of its conversational structure on personal expression. The experiment’s realization demonstrates that the protocol’s preparation is laborious and hard to adapt in a timely manner in situations where participant numbers fluctuate. Automation of these processes, however, offers possibilities to use the approach in loosely organized groups. Automation can also help choosing the most appropriate protocol for particular situations through the manipulation of its configuration. Despite difficulties, the protocol offers promise for different purposes, encouraging personal expression in a way that reverberates with others’ personal perspectives. (shrink)

Elementos para uma psicopedagogia da cultura digital 1 Resumo: a cultura digital é um paradigma emergente que coloca questões a serem tratadas pelas mais diversas áreas do conhecimento. A educação é uma das áreas mais questionadas, exigindo-se dela uma constante renovação para acompanhar as mudanças que o mundo digital provoca no processo de aprendizagem. A psicopedagogia da cultura digital é uma proposta epistemológica de reflexão sobre o processo de aprendizagem permeado por desafios informacionais e comunicacionais. Nesta pesquisa, fazendo análise de (...) bibliografia no campo da psicopedagogia, mas também da teoria da comunicação e da filosofia da mente, propomos um quadro teórico que visa fundamentar tais exigências epistemológicas em educação. Apresentamos, por fim, alguns elementos teóricos, advindos das demandas da cultura digital, que permitem-nos pensar um outro paradigma psicopedagógico e outra abordagem da aprendizagem. Palavras-chave: Educação. Cultura Digital. Psicopedagogia. Epistemologia. Fundamentos da Educação. Elements towards a Psychopedagogy of Digital Culture Abstract: digital culture is an emerging paradigm that poses questions to be addressed by the most diverse areas of knowledge. Education is one of the most questioned areas, requiring a constant renewal to accompany the changes that the digital world causes in the learning process. The psychopedagogy of digital culture is an epistemological proposal of reflection on the learning process permeated by informational and communicational challenges. In this paper, making bibliographic analysis in the field of psychopedagogy, but also in the theory of communication and the philosophy of mind, we propose a theoretical framework that aims to base such epistemological demands on education. Finally, we present some theoretical elements, coming from the demands of digital culture, which allow us to think of another paradigm psychopedagogic and another approach to learning. Keywords: Education. Digital Culture. Psychopedagogy. Epistemology. Foundations of Education. Elementos hacia una Psicopedagogía de la Cultura Digital Resumen: La cultura digital es un paradigma emergente que pone cuestiones a ser tratadas por distintas áreas del conocimiento. La educación es una de las más cuestionadas, exigiéndose de ella una renovación continua a fin de acompañar los cambios que el mundo digital provoca en el proceso de aprendizaje. La psicopedagogía de la cultura digital es una propuesta epistemológica de reflexión sobre el mismo proceso de aprendizaje, traspasado por retos informacionales y comunicacionales. En esta recerca, haciendo uso de análisis bibliográfica en el campo de la psicopedagogía, así come de la teoría de la comunicación y de la filosofía de la mente, proponemos un cuadro teórico que intenta fundamentar tales exigencias epistemológicas en educación. Presentamos, al fin, algunos elementos teóricos, desde las demandas de la cultura digital, que nos permiten pensar otro paradigma psicopedagógico y otro abordaje del aprendizaje. Palabras clave: Educación. Cultura digital. Psicopedagogía. Epistemología. Fundamentos de la educación. Data de registro: 23/01/2021 Data de aceite: 22/09/2021 1 Pesquisa desenvolvida com financiamento CAPES. (shrink)

Este artigo propõe-se a discutir a possibilidade de utilizar as tecnologias digitais online e as redes sociais como espaço de aprendizagem digital de uma maneira que favoreça a aprendizagem cooperativa entre os estudantes, alicerçado na Epistemologia Genética de Jean Piaget. Este estudo foi baseado em uma pesquisa-ação, nas aulas de Matemática, realizada com estudantes do ensino médio integrado em informática do IFRS – Campus Osório (RS), em 2011 e 2012-1. Os estudantes demonstraram apropriação deste espaço de aprendizagem digital, como o (...) Facebook, e apontaram que este potencializa a aprendizagem cooperativa no que tange à disciplina de Matemática, por ações colaborativas com a professora. (shrink)

O presente artigo busca analisar, a partir da leitura da obra De Quaerendo Deum, como a questão da luz se faz central no processo de elevação intelectual a partir do sensível na obra cusana. Nele iremos mostrar como a luz é o elo que guia o objeto sensível até o intelecto e o intelecto até Deus. Tomado esse objetivo, o artigo será dividido em duas partes, na primeira iremos abordar a questão central da obra De Docta Ignorantia, que é os (...) limites de se conhecer propriamente Deus e as essências das coisas. Vai se buscar a partir daí apresentar os fundamentos para o que será o papel da experiência estética em Cusa. A constatação do nosso limite em conhecer verdadeiramente o infinito e a Verdade geradora não são postos por Cusa como forma de desestimular a conjectura sobre elas, pelo contrário, é a partir dessa constatação que nos é possível, pela ignorância esclarecida, buscar mais propriamente nos aproximarmos, ainda que nunca cheguemos, dessas Verdades. Tomada essa base fundamental, trabalharemos no segundo tópico o ponto central aqui proposto, a saber, a importância da luz nesse processo. Focados principalmente na obra cusana De Quaerendo Deum iremos articular os conceitos de teofania e a importância da luz. A teofania será central para o conceito de anagogia através da contemplação estética, fundamentando como pode-se buscar conjecturar sobre o Criador a partir de sua manifestação na criação. Longe de ser um panteista a teoria cusana busca expressar que, apesar de inacessível em sua totalidade devido a sua própria natureza, o Deus cusano não se esconde, mas sim se manifesta na sua criação, sendo possível conjecturar sobre Ele a partir da percepção sensível sobre os objetos criados. Nesse sistema, a luz será explorada tanto enquanto luz sensível, como também enquanto a luz interior e principalmente a luz como manifestação e ligação com a divindade a partir do intelecto humano, dessa forma vai se mostrar como todo o processo de elevação a partir da contemplação sensível tem a presença da luz como parte essencial. Palavras chave: Cusa. Estética. Luz. Teofania. (shrink)

Name der Zeitschrift: Semiotica Jahrgang: 2016 Heft: 209 Seiten: 301-321.

Os escritos de Evágrio Pôntico, monge do século IV, embora não constituindo um sistema filosófico, são de capital importância para compreendermos o desenvolvimento da cultura ocidental. No presente trabalho, todavia, operamos um corte epistemológico diferente. Buscamos na sua obra Tratado Prático, primeira parte de uma trilogia de teologia espiritual, elementos de uma doutrina psicológica que, é o que pretendemos demonstrar, se constitui em verdadeira terapêutica. Assim, exploramos alguns conceitos fundamentais dessa obra, tais como os de impassibilidade, de pensamentos passionais, e (...) o de paixões, e também doutrinas importantes, como a da divisão tripartite da alma e a demonologia evagriana. (shrink)

Schools have been the main context for physical activity and sedentary behavior interventions among adolescents, but there is inconsistent evidence on whether they also improve dimensions of the health−related quality of life. The aim of this study was to evaluate the effects of a school-based active lifestyle intervention on dimensions of HRQoL. A secondary aim was to verify whether sex, age, and HRQoL at baseline were moderators of the intervention effect. A cluster-randomized controlled trial was conducted at three control and (...) three intervention schools in Florianopolis, Brazil. All students from 7th to 9th grade were invited to participate. A school year intervention, designed primarily to increase PA and reduce SB, included strategies focused on teacher training on PA, SB, and nutrition, and availability of teaching materials related to these contents; environmental improvements ; and education strategies, with the availability of folders and posters regarding PA, SB, and nutrition. Participants and the research staffs were not blinded to group assignment, but a standardized evaluation protocol was applied at baseline and after the intervention using the KIDSCREEN−27 to assess HRQoL across five dimensions. Mixed linear models were performed to evaluate the effect of the Movimente intervention on the five HRQoL dimensions. Of the 921 students who answered the questionnaire at baseline, 300 and 434 completed the study in control and intervention groups, respectively. The results revealed no significant effects of the intervention on any HRQoL dimensions. A reduction of the school environment dimension was observed in both the control and intervention groups. Sensitivity analyses showed that students in the highest baseline tertiles of HRQoL in any dimension had a reduction in their respective scores from pre- to post-intervention in both school groups. In conclusion, our results demonstrated no intervention effect on HRQoL dimensions and those students with the highest levels of HRQoL at baseline on all dimensions reduced from pre to post-intervention.Clinical Trial RegistrationThe trial is registered at the Clinical Trial Registry. (shrink)

Brazilian writer Carolina Maria de Jesus (1914–1977) was born in a rural community and spent most of her life in a slum. Despite this, her literary work achieved remarkable editorial success, having its value recognized by critics and academic circles. This paper analyzes Carolina Maria de Jesus’s autobiographical narratives in the light of John Dewey’s aesthetic theory, with the purpose of investigating the factors responsible for the development of her aesthetic sensitivity – intellectual and emotional dispositions favorable to involvement with (...) artistic practices. The results suggest that Carolina Maria de Jesus’s literary skills, which express not only individual but also collective yearnings, resulted from the incentive she received to think about things that do not exist and from her relationship with people who favored the formation of a personality open to varied experiences. Such results are presented as requirements for a democratic and humanist education that aims at the flowering of aesthetic sensitivity and encourages educators and students to believe in their creative potential. (shrink)

In A moral theory of sports, Richard J. Severson examines modern sports and modern morality from the lens of evolutionary psychology. The author’s primary goals are to interpret modern sport as...

This work relates L. S. Vygotsky’s theory to the rhetorical and poetic pedagogy, which is a set of educational ideas and practices derived from the philosophical-educational tradition initiated by the Sophists. It is verified that the Vygotskyan concepts contribute to broaden the foundations of poetic and rhetorical pedagogy, presenting a psychology of language that integrates decorum, kairos and antilogical argumentation within aesthetic experiences; communication sustains knowledge and reflection of reality, aiming at the strengthening of the individual’s identity, the education of (...) the creative subject and the improvement of the collective. It is considered that the rhetorical and poetic character of Vygotsky’s theory encourages the contemporary school to be a space for investigation and search for creative solutions, contradicting the measurementist pedagogical tendencies that dehumanize education. (shrink)

Este trabalho tem como objetivo apresentar e discutir a filosofia da experiência de John Dewey, enfatizando suas concepções sobre experiência, experiência educativa e propósito. Além disso, apresentar e discutir como os projetos de programação desenvolvidos por crianças no Scratch podem ser entendidos como um propósito no contexto de sua filosofia, o que nos levou a relacionar o conceito de propósito construído por Dewey à ideia de projeto pessoal desenvolvida por Papert, no âmbito do construcionismo. Tal relação se torna importante para (...) ampliar as investigações que tratam problemáticas relacionadas ao ensino de programação na educação básica. A fim de exemplificar as possíveis relações, apresentamos um projeto de programação desenvolvido por um aluno do quinto ano do ensino fundamental, reconhecendo nele os pressupostos teóricos da teoria de Dewey discutidos no texto, relacionando-os às ideias de Papert. (shrink)

Neste artigo, abordamos o processo de construção da educação das relações raciais a partir de uma perspectiva analítica que tem como elemento central a história da educação dos negros, no Brasil. Dessa forma, construímos um percurso que trata de diferentes momentos em relação ao processo de incorporação dos negros à sociedade brasileira, especificamente o tráfico de africanos escravizados, a abolição da escravidão e a constituição do movimento negro como sujeito coletivo. Analisamos esses eventos procurando destacar seu significado educacional e suas (...) implicações na construção do movimento negro como um agente transformador da sociedade. O ponto culminante da análise foi o processo de aprovação da Lei 10.639/2003 e a construção de uma política pública voltada para reconfiguração da educação das relações raciais. Destacamos esse processo como uma das mais importantes transformações pela qual passou a educação brasileira, sobretudo no que diz respeito ao reconhecimento da diversidade, o combate ao racismo e às desigualdades raciais. (shrink)

We aimed to characterize the age of onset of training, age at menarche, menstrual periodicity, and performance perception during the menstrual cycle and examined the impact of these reproductive variables on body composition, morphology, and body weight satisfaction in Brazilian elite futsal players. The study consisted of 115 female Brazilian elite futsal players from the top national teams. Data were collected during the twentieth Women’s Brazil Futsal Cup. Players were interviewed and self-reported their age of onset of training, age at (...) menarche, menstrual periodicity, and the menstrual period, where they performed best. We also asked for what they considered to be their ideal body weight as well as information related to their training. Subsequently, anthropometric measurements were performed to estimate the body composition and determine morphological characteristics. Fifty-nine players were postmenarche-trained and 52 were premenarche-trained. Eighteen, 65, and 28 were classified as early, normal, and late menarche, respectively. Only 11 and 1 had irregular menstrual cycles and were amenorrheic, respectively. Seventy-three, 23, and 9 reported that their game performance was the best at the follicular phase, menses, and luteal phase of the menstrual cycle, respectively. No associations between the four reproductive-related variables were found. Postmenarche-trained players had significant lower age at menarche and higher percentage body fat. The somatotype profile registered lower ectomorphy rate for the postmenarche-trained participants after controlling for covariates. Early menarche group presented higher sum of six skinfold thickness and endomorphy rate compared to normal and late menarche groups. No differences were found when menstrual periodicity groups and best performance groups were compared, except for higher femur width in the regular menstrual cycle group compared to the irregular one. The association between body weight satisfaction and the four reproductive-related variables were not observed. Premenarche-trained Brazilian elite futsal players had the menarche later than the postmenarche-trained athletes. Most of the participants had menarche age classified as “normal,” presented “regular” menstrual cycles and perceived to perform better during the follicular phase of the menstrual cycle. (shrink)

Em um de seus últimos artigos publicados na Folha de S. Paulo, Ferreira Gullar defendeu a necessidade de se reinventar uma nova utopia para o tempo presente: “por isso mesmo, o fim do regime comunista provocou um vazio ideológico, que necessita ser preenchido, uma vez que a sociedade humana, sem utopia, torna-se inviável”. Trata-se da última dentre tantas reviravoltas em sua saudosa trajetória intelectual. Diante disso, discutimos aqui uma das principais contribuições para esse debate, presente Em um rabo de foguete: (...) trauma e cultura política em Ferreira Gullar, de Marcus Vinícius Furtado da Silva Oliveira. Neste livro, o autor procurou identificar e interpretar várias dessas reviravoltas presentes na vida intelectual do poeta e crítico literário maranhense. Notoriamente, algo que poderia enfraquecer o argumento de uma de suas teses centrais - no caso, o cancelamento das utopias em Ferreira Gullar – ao contrário, acabou por trazer ainda mais relevância para o trabalho, coincidentemente publicado no mesmo ano do texto de Gullar. (shrink)

Recent experiments have shown that people iconically modulate their prosody corresponding with the meaning of their utterance. This article reports findings from a story reading task that expands the investigation of iconic prosody to abstract meanings in addition to concrete ones. Participants read stories that contrasted along concrete and abstract semantic dimensions of speed and size. Participants read fast stories at a faster rate than slow stories, and big stories with a lower pitch than small stories. The effect of speed (...) was distributed across the stories, including portions that were identical across stories, whereas the size effect was localized to size-related words. Overall, these findings enrich the documentation of iconicity in spoken language and bear on our understanding of the relationship between gesture and speech. (shrink)

The leader integrity literature has described how professional behavior influences perceptions of integrity, yet behavior in leaders’ personal lives potentially affects those perceptions. The present paper examined how personal life behavior affects leaders. We assessed high profile political sex scandals to explore the research questions of how indiscretions in personal life affect leaders and how leaders recover from public revelations of sexual indiscretions. The results revealed that whether politicians survived the scandal depended on the degree to which the indiscretion deviated (...) from accepted norms, the degree to which the behavior departed from the politician’s expressed values, the leader’s political power, and whether the leader fully engaged in atonement under conditions when denying the allegations is not possible. These components were inter-related such that atonement was possible if the behavior was neither too extreme nor out of character and the leader had sufficient political power. The model was then tested with a sample of business executives engaged in sex scandals, finding support for its elements. (shrink)

The paper offers an account of luck, fate, and fortune. It begins by showing that extant accounts of luck are deficient because they do not identify the genus of which luck is a species. That genus of properties, the tychic, alert an agent to occasions on which the external world cooperates with or frustrates their goal-achievement. An agent’s sphere of competence is the set of goals that it is possible for them to reliably achieve. Luck concerns occasions on which there (...) is a mismatch between attempt and result; in bad luck the external world thwarts goal-achievement within the agent’s sphere of competence, in good luck the external world assists goal-achievement beyond the agent’s sphere of competence. Fateful events are those where, more passively, the agent finds the external world achieving or frustrating their goals. Fortune concerns the contraction and expansion of the agent’s sphere of competence. Eight reasons are given for accepting the account; its theoretical virtues and various things it explains. Lastly, three objections are answered; that the tychic properties relate to well-being rather than agency, that there are alternative theories of fortune available in the contemporary literature, that the account draws arbitrary distinctions between synonyms. (shrink)

This book includes detailed critical analysis of a wide variety of versions of the indispensability argument, as well as a novel approach to traditional views about mathematics.

Let X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }$$\end{document} be a set of outcomes, and let I\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{I }$$\end{document} be an infinite indexing set. This paper shows that any separable, permutation-invariant preference order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} on XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{X }^\mathcal{I }$$\end{document} admits an additive representation. That is: there exists a linearly ordered abelian group R\documentclass[12pt]{minimal} (...) \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document} and a ‘utility function’ u:X⟶R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$u:\mathcal{X }{{\longrightarrow }}\mathcal{R }$$\end{document} such that, for any x,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document} which differ in only finitely many coordinates, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∑i∈Iu-u≥0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{i\in \mathcal{I }} \left[u-u\right]\ge 0$$\end{document}. Importantly, and unlike almost all previous work on additive representations, this result does not require any Archimedean or continuity condition. If \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$$$\end{document} also satisfies a weak continuity condition, then the paper shows that, for anyx,y∈XI\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x},\mathbf{y}\in \mathcal{X }^\mathcal{I }$$\end{document}, we have x≽y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{x}\succcurlyeq \mathbf{y}$$\end{document} if and only if ∗∑i∈Iu≥∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u\ge {}^*\!\sum _{i\in \mathcal{I }}u$$\end{document}. Here, ∗∑i∈Iu\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\sum _{i\in \mathcal{I }} u$$\end{document} represents a nonstandard sum, taking values in a linearly ordered abelian group ∗R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}^*\!\mathcal{R }$$\end{document}, which is an ultrapower extension of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal{R }$$\end{document}. The paper also discusses several applications of these results, including infinite-horizon intertemporal choice, choice under uncertainty, variable-population social choice and games with infinite strategy spaces. (shrink)

Why should music be of interest to cognitive scientists, and what role does it play in human cognition? We review three factors that make music an important topic for cognitive scientific research. First, music is a universal human trait fulfilling crucial roles in everyday life. Second, music has an important part to play in ontogenetic development and human evolution. Third, appreciating and producing music simultaneously engage many complex perceptual, cognitive, and emotional processes, rendering music an ideal object for studying the (...) mind. We propose an integrated status for music cognition in the Cognitive Sciences and conclude by reviewing challenges and big questions in the field and the way in which these reflect recent developments. (shrink)

This article uses differing interpretations of a thread of narrative taken from Orwell’s Nineteen Eighty-Four as a springboard to exploring the connection between philosophical truth and political liberalism. It argues that while no positive connection exists between realist truth and political liberalism, minimal negative connections do exist between Rorty’s humanistic account of truth and a basic commitment to democratic and liberal frameworks. It sees these minimal connections as limiting in their failure to provide a politics that moves beyond an exclusive (...) concern with liberty and democracy to more substantive political issues of equality and justice. However, it also sees them as reassuring in showing how acceptance of Rorty’s humanistic account of truth in no way necessitates adopting his own ethnocentric political stance. (shrink)

Arts of Allusion: Object, Ornament, and Architecture in Medieval Islam By GravesMargaret S., xi + 339 pp. Price HB £55.00. EAN 978–0190695910.

Our visual experience seems to suggest that no continuous curve can cover every point of the unit square, yet in the late 19th century Giuseppe Peano proved that such a curve exists. Examples like this, particularly in analysis received much attention in the 19th century. They helped to instigate what Hans Hahn called a ‘crisis of intuition’, wherein visual reasoning in mathematics came to be thought to be epistemically problematic. Hahn described this ‘crisis’ as follows : " Mathematicians had for (...) a long time made use of supposedly geometric evidence as a means of proof in much too naive and much too uncritical a way, till the unclarities and mistakes that arose as a result forced a turnabout. Geometrical intuition was now declared to be inadmissible as a means of proof … "Avoiding geometrical evidence, Hahn continued, mathematicians aware of this crisis pursued what he called ‘logicization’, ‘when the discipline requires nothing but purely logical fundamental concepts and propositions for its development’. On this view, an epistemically ideal mathematics would minimize, or avoid altogether, appeals …. (shrink)

In der "Transzendentalen Ästhetik" der KrV will Kant zeigen, daß Raum und Zeit Anschauungsformen und daher keine Eigenschaften der Dinge an sich sind. Es scheint jedoch, als übersehe er dabei die Möglichkeit, daß Raum und Zeit Anschauungsformen und zugleich Eigenschaften der Dinge an sich sein könnten. Dagegen soll hier gezeigt werden, daß Kants Beweis durchaus schlüssig ist. Dabei kommt es zunächst darauf an, die genaue Struktur des Kantischen Beweises zu verstehen. Darauf folgt eine Diskussion der Kantischen Begriffe Anschauung sowie Form (...) der Anschauung und reine Anschauung, in der sich unter anderem herausstellt, daß Kants Anschauungsbegriff im Sinne der aktuellen Philosophie des Geistes "externalistisch" konzipiert ist. Dies erlaubt es dann, den Schluß auf die Idealität von Raum und Zeit tatsächlich als Folgerung aus Kants vorhergehenden Ausführungen zu verstehen. Abschließend geht es um einige der Konsequenzen, die sich aus dieser Interpretation für das Verständnis des transzendentalen Idealismus ergeben. (shrink)

The Golden Rule has received remarkably little philosophical discussion. No book has ever been written on it, and articles devoted to it have been exceedingly few, and usually not very searching. It is usually mentioned, where it is mentioned at all, only in passing, and most of these passing remarks have either been false, trite, or misleading, though some of them, as we shall see, have certainly been interesting enough. Considering its obvious importance and its almost universal acceptance, this dearth (...) of philosophical discussion is unfortunate, and also somewhat surprising. One of the things I hope to show about it, though only incidentally, is that there are problems connected with it of the utmost subtlety, worthy of the attention of even the most minute philosophers. (shrink)