Beta integrals for several non-integer values of the exponents were calculated by Leonhard Euler in 1730, when he was trying to find the general term for the factorial function by means of an algebraic expression. Nevertheless, 70 years before, Pietro Mengoli (1626–1686) had computed such integrals for natural and half-integer exponents in his Geometriae Speciosae Elementa (1659) and Circolo(1672) and displayed the results in triangular tables. In particular, his new arithmetic–algebraic method allowed him to compute the quadrature of the circle. (...) The aim of this article is to show how Mengoli calculated the values of these integrals as well as how he analysed the relation between these values and the exponents inside the integrals. This analysis provides new insights into Mengoli’s view of his algorithmic computation of quadratures. (shrink)

The introduction of a new analytical method, due fundamentally to François Viète and René Descartes and the later dissemination of their works, resulted in a profound change in the way of thinking and doing mathematics. This change, known as process of algebrization, occurred during the seventeenth and early eighteenth centuries and led to a great transformation in mathematics. Among many other consequences, this process gave rise to the treatment of the results in the classic treatises with the new analytical method, (...) which allowed new visions of such treatises and the obtaining of new results. Among those treatises is the Arithmetic of Diophantus of Alexandria which was written, using the new algebraic language, by the French mathematician Jacques Ozanam, who in addition to profusely increasing the original problems of Diophantus, solved them in a general way, thus obtaining many geometric consequences. The work is handwritten, it has never been published, it has been lost for almost 300 years, and the known references show its importance. We will show that Ozanam’s manuscript was quoted as an important work on several occasions by others mathematicians of the time, among whom G. W. Leibniz stands out. Once the manuscript has been located, our aim in this article is to show and analyze this work of Ozanam, its content, its notation and its structure and how, through the new algebraic method, he not only solved and expanded the questions proposed by Diophantus, but also introduced a connection between the algebraic solutions and what he called geometric determinations by obtaining loci from the solutions. (shrink)

Na sua “última lição”, reiterou-nos José Esteves Pereira “a flagrante actualidade do pensamento de Ortega y Gasset”. Nesta nossa breve reflexão, a partir de obra A Rebelião das Massas, explicitaremos como isso para nós se verifica.

O objetivo deste artigo é apresentar um dispositivo conceitual desde Laclau e Lacan que permita abordar o fenômeno político nomeado como populismo. Para isso, primeiro, estabeleceremos a definição dos conceitos utilizados. Em segundo lugar, estabeleceremos o contraponto entre populismo, neoliberalismo e fascismo. Finalmente, apresentaremos o populismo como uma possibilidade de saída de crise política, social e econômica. Devemos salientar que o texto esteve intencionalmente elaborado para um debate com uma defesa do liberalismo como saída de crise política, social e (...) econômica. Palavras-chave: Populismo. Identificação. Afetos. Laclau. Lacan. (shrink)

Curso evolutivo -- Anacronismo fehaciente -- La dictadura -- El Estado -- Federalismo -- Evolucion verdadera -- Cataclismo social -- Nuestra labor.

Das Buch zeigt, in welcher Weise Heidegger und Wittgenstein die Grundlagen der traditionellen Philosophie sowie der Psychologie einer Kritik unterziehen. Der Schwerpunkt liegt dabei auf dem jeweiligen Frühwerk und wie dort die Problemkreise Sprache, Ethik und Leben miteinander verbunden sind. Konvergenzen ihres Philosophierens liegen u.a. darin, dass sie jeweils eine semantische Bewegung ausmachen, die die Grenzen der individuellen Welt umschreibt, dass sich bei beiden ein Appell an das Ethos der Verschwiegenheit findet, der eine Verknüpfung zwischen Sprache und Ethik nahelegt, und (...) dass das Leben für beide Philosophen eine ethische Bedeutung gewinnt. (shrink)

Este trabalho analisa a repercussão social do cartaz do “Salão do Livro da Região Sul e Sudeste do Pará”, evento da Feira Pan-Amazônica do Livro de 2018, para compreender como o processo de resposta social (BRAGA, 2006) impôs uma mudança institucional por parte da Secretaria de Cultura do Estado. O país homenageado foi a Colômbia e a peça de divulgação destacava uma mulher negra carregando livros na cabeça, representação das palenqueras. O fato gerou repercussão nas redes sociais e na mídia (...) local e nacional. Os protestos voltaram-se contra a reiteração de uma imagem que inferioriza as mulheres negras, reproduzindo colonialidades de gênero, poder e saber. O corpuscompõe-se de postagens no Facebooke de matérias jornalísticas veiculadas em abril de 2018. Duas técnicas metodológicas foram usadas: a netnografia (RECUERO, 2012; KOZINETS, 2014) e a aplicação de um questionário online, por meio do Facebook e Whatsapp. (shrink)

Heideggers Frage nach dem Wesen der planetarischen Technik ist mehr und anderes als eine reine Technikkritik. Sie erfasst die Formationen der alles umfassenden Technik als Grundform der Seinsverlassenheit und eines veranderten Weltverhaltnisses nach dem Ende der Metaphysik. Der Band zeichnet Heideggers Technikphilosophie in ihren immanenten Verweisungszusammenhangen nach. Er befragt Heideggers Technikbegriff auch vor dem Horizont der ungeahnten Perspektiven, die Anthropotechniken und Digitalisierung seither eroffnen.

Após afirmar que os dois sentidos aristotélicos do ato são insuficientes para dizer o ente tal como este se encontra na realidade, o trabalho mostra como o novo sentido que Lúlio atribuiu à noção de ato permitiu-lhe superar a limitação própria dos conhecimentos obtidos mediante as operações da faculdade cognoscitiva e alcançar, com ajuda de sua Ars, o ato de ser dos entes.

Apresentam-se, em forma de sintética perspectiva histórica, alguns dos temas principais da metafisica do ser, de modo a mostrar a articulação do pensamento filosófico desde Parmênides a Tomás de Aquino, salientando-se no fim de cada período as conquistas que ficaram em aberto. A seguir, expõe-se a metafisica Juliana, afirmando-se que esta seguramente consistiria numa tentativa de continuar a especulação e o aprofundamento sobre o ato de Ser, a partir do ponto alcançado pela especulação anterior. O trabalho pode ser visto portanto (...) como uma chave para a leitura das obras lulianas. (shrink)

This study is divided in three parts. First, it shows which are the specific truths of Christianism, that distinguish it from other monotheistic religions. In the second part, establish the lullian metaphysics´suppositions that consent to embrace this truths. Finally, the third part is an attempt to expose the arguments and demonstrations characteristic of Lullian theory of knowledge.

Esta comunicación muestra que elpensamiento del filósofo mallorquín avanza conrelación ai estado de la doctrina tradicional sobrelas nociones clásicas de naturaleza y personaporque arranca de su teoria de las Dignidades,según la cual el ser se presenta como actividadformalizada. Si "pensar", "escuchar" y "ver" sonactos, lo son por el acto de ser, y tendrá que seréste, el acto en primer lugar diferenciado.Además, la importante teoria Juliana de las obraspropias y apropiadas permite una explicación dela naturaleza humana muy consistente con larealidad. Se (...) empieza por explicar cómo surge elhombre por su acto de ser. Según Llull, e! hombreradica en e! "soy", un "acto común" que conectaalma y cuerpo. La naturaleza humana es la únicaque reúne en si todo lo criado y es gracias a ellaque las criaturas pueden alcanzar su fin. Sedemuestra que el alma existe, es criada, y es máspor su fin que por su esencia, y es, porconsiguiente, eterna. Finalmente, Llull dice queexiste en nosotros un entender interior ypripligenio, siempre en acto, por media del cualtenemos noticia de nuestro ser, del ser de lascosas y de Dios. (shrink)

Estudam-se realidades básicas da moral - o ente, o ato de ser e a causalidade eficiente intrínseca - e se conclui que se harmonizam apenas com aquelas metafísicas denominadas do ser. que concebem o ser como a primeira perfeição à qual se reduzem todas as outras. Critica-se a posição essencialista. Examina-se a noção de ser implícita nos escritos de Tomás de Aquino que, por superar a concepção formalista do ser, permite uma compreensão adequada da vida moral.,Da mesma maneira, a noção (...) do ser que se extrai da obra de Raimundo Lúlio não difere essencialmente daquelas apresentadas pelas metafisicas do ser, e por isso a moral Juliana sobre ela assente é permanente e adequada à pessoa humana. (shrink)

This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise hypotheses. These pragmatic (...) versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais. (shrink)

Organizational ethics and institutional theories are extended by recovering Weberian and Pre-Weberian theorizing that emphasized the joining of ethics and institutional theories. Understanding how ethics and institutional systems influence each other can advance our understanding of the nature and causes of structural organizational ethics issues and help guide potential reforms. We consider the interplay of these elements during the recession of 2008–2009, highlighting how structural ethics problems may have to be addressed at the institutional levels and not solely the individual (...) or organizational levels. (shrink)

This paper offers theoretical explanations for why “guided touch” or manual touch with verbal communication can be an effective way of treating the body and the mind. The active inference theory suggests that chronic pain and emotional disorders can be attributed to distorted and exaggerated patterns of interoceptive and proprioceptive inference. We propose that the nature of active inference is abductive. As such, to rectify aberrant active inference processes, we should change the “Rule” of abduction, or the “prior beliefs” entailed (...) by a patient’s generative model. This means pre-existing generative models should be replaced with new models. To facilitate such replacement—or updating—the present treatment proposes that we should weaken prior beliefs, especially the one at the top level of hierarchical generative models, thereby altering the sense of agency, and redeploying attention. Then, a new prior belief can be installed through inner communication along with manual touch. The present paper proposes several hypotheses for possible experimental studies. If touch with verbal guidance is proven to be effective, this would demonstrate the relevance of active inference and the implicit prediction model at a behavioral level. Furthermore, it would open new possibilities of employing inner communication interventions, including self-talk training, for a wide range of psychological and physical therapies. (shrink)

This paper introduces the category of b-frames as a new tool in the study of complete lattices. B-frames can be seen as a generalization of posets, which play an important role in the representation theory of Heyting algebras, but also in the study of complete Boolean algebras in forcing. This paper combines ideas from the two traditions in order to generalize some techniques and results to the wider context of complete lattices. In particular, we lift a representation theorem of Allwein (...) and MacCaull to a duality between complete lattices and b-frames, and we derive alternative characterizations of several classes of complete lattices from this duality. This framework is then used to obtain new results in the theory of complete Heyting algebras and the semantics of intuitionistic propositional logic. (shrink)

Using an alternative to Tarskian semantics for first-order logic known as possibility semantics, I introduce an approach to nonstandard analysis that remains within the bounds of semiconstructive mathematics, i.e., does not assume any fragment of the Axiom of Choice beyond the Axiom of Dependent Choices. I define the Fr´echet hyperreal line †R as a possibility structure and show that it shares many fundamental properties of the classical hyperreal line, such as a Transfer Principle and a Saturation Principle. I discuss the (...) technical advantages of †R over some other alternative approaches to nonstandard analysis and argue that it is well-suited to address some of the philosophical and methodological concerns that have been raised against the application of nonstandard methods to ordinary mathematics. (shrink)

Bernard Bolzano (1781–1848) is commonly thought to have attempted to develop a theory of size for infinite collections that follows the so-called part–whole principle, according to which the whole is always greater than any of its proper parts. In this paper, we develop a novel interpretation of Bolzano’s mature theory of the infinite and show that, contrary to mainstream interpretations, it is best understood as a theory of infinite sums. Our formal results show that Bolzano’s infinite sums can be equipped (...) with the rich and original structure of a non-commutative ordered ring, and that Bolzano’s views on the mathematical infinite are, after all, consistent. (shrink)

This research characterizes and compares the job satisfaction of fitness professionals in Portugal between genders, ages, professional experience, professional title, and educational qualifications. A total of 401 fitness professionals answered the online questionnaire Job Satisfaction Scale, which has 16 factors rated on a Likert scale with seven levels. The statistical analysis comprises descriptive and statistical tests to compare the results of two or more groups. Overall, the results demonstrated that fitness professionals were moderately satisfied with their work. The lower degrees (...) of job satisfaction were concerning salary, opportunities for promotion, and stability at work. The highest levels of job satisfaction were related to the freedom to choose their work method, their work colleagues, the physical conditions of their workplace, and the opportunity to use their competencies. There were no differences in job satisfaction in terms of gender and a few differences between professional title and between educational levels. Regarding age and professional experience, the results showed significant differences in almost all factors, suggesting that, as fitness professionals get older and more experienced, their job satisfaction is greater. The results of this study suggest that even though fitness professionals are, in general, moderately satisfied with their work, some aspects can be improved by employers to increase their satisfaction levels. Such findings would assist employers in guiding the job satisfaction of their employees with consequent enhancements in the services provided by fitness professionals, which can increase participants’ retention in exercise fitness activities. (shrink)

In this paper we present a theoretical framework to understand the underlying psychological mechanism involved in human-Companion Robot interactions. At first, we take the case of Sexual Robotics, where the psychological dynamics are more evident, to thereafter extend the discussion to Companion Robotics in general. First, we discuss the differences between a sex-toy and a Sexual Robots, concluding that the latter may establish a collusive and confirmative dynamics with the user. We claim that the collusiveness leads to two main consequences, (...) such as the fixation on a specific and atypical type of sexual interaction, called paraphilic, and to the infantilization of the user, which we explain through the theoretical framework of “object-relation theory”. We argue that these dynamics may degrade to an infantile stage the relational abilities of users, extending this argument to Companion Robots in general. Then, we enquire if and how the relational dynamics enacted in HRI may shift to human relations: we discuss the analogy with virtual reality concluding that, under certain condition, a symbolic shift might happen. In the last part of this work, we propose an experimental setup to verify if a collusive and confirmative interaction with a Companion Robot can, over time, impact on the user’s ability to manage relational frustration. (shrink)

Morphological EvoDevo is a field of biological inquiry in which explicit relations between evolutionary patterns and growth or morphogenetic processes are made. Historically, morphological EvoDevo results from the coming together of several traditions, notably Naturphilosophie, embryology, the study of heterochrony, and developmental constraints. A special feature binding different approaches to morphological EvoDevo is the use of formalisms and mathematical models. Here we will introduce anatomical network analysis, a new approach centered on connectivity patterns formed by anatomical parts, with its own (...) concepts and tools specifically designed for the study of morphological EvoDevo questions. Riedl’s concept of burden is tightly related to the use of anatomical networks, providing a nexus between the evolutionary patterns and the structural constraints that shape them. (shrink)

Trois dossiers distincts, mais complémentaires, et rattachés à la ville d’Éphèse sont convoqués pour éclairer des cas concrets de transmission de pratiques, de savoirs ou de vocabulaire rituels. Tout d’abord, les associations dionysiaques d’Éphèse permettent d’aborder la question des référents à partir desquels se constitue un rituel, vu que chaque association est un cas unique, au profil cultuel particulier. Ensuite, l’examen de la Lettre aux Éphésiens d’Ignace d’Antioche souligne l’utilisation par un des premiers auteurs chrétiens d’un vocabulaire associatif et mystérique (...) pour véhiculer son message chrétien. Cela suppose une large diffusion et une connaissance partagée de pratiques rituelles. Enfin, une inscription d’Éphèse met en lumière le rôle du hiérophante public comme indispensable « passeur de tradition » dans l’exécution des rites publics par les magistrats et insiste sur la séparation des tâches et des savoirs en matière rituelle. La mise en parallèle de ces trois cas permet de remettre en question la distinction entre un savoir proprement cultuel et des connaissances fondées plus largement sur des références culturelles : dans un savoir religieux en action, c’est le rite effectif qui devient lui-même référence culturelle. (shrink)