A difícil aceitação dos números negativos: um estudo da teoria dos números de Peter Barlow (1776-1862)

The present study seeks to present a historico-epistemological analysis of the development of the mathematical concept of negative number. In order to do so, we analyzed the different forms and conditions of the construction of mathematical knowledge in different mathematical communities and, thus, identified the characteristics in the establishment of this concept. By understanding the historically constructed barriers, especially, the ones having ontologicas significant, that made the concept of negative number incompatible with that of natural number, thereby hindering the development of the concept of negative, we were able to sketch the reasons for the rejection of negative numbers by the English author Peter Barlow (1776 -1862) in his An Elementary Investigation of the Theory of Numbers, published in 1811. We also show the continuity of his difficulties with the treatment of negative numbers in the middle of the nineteenth century

Fundamentos da filosofia moral de Peter Singer

This research aims to reconstruct and explain the argument proposed by Peter Singer to justify the principle of equal consideration of interests (PECI). The PECI is the basic normative principle according to people should consider the interests of all sentient beings affected when somebody taking a moral decision. It is the join that Singer proposes between universalizability and the principle of equal consideration of interests that constitutes a compelling reason to justify it. The universalizability requires to disregard the numerical differences, putting yourself in other people s shoes, and to consider preferences, interests, desires and ideals of those affected. Singer joins universalizability to normative principle and molds the form and content of his theory. The first chapter introduces the discussion will be developed in this essay. The second chapter deals the historical and philosophical viewpoint from which Singer starts his studies. The third chapter is about the Singer s critiques of naturalism, intuitionism, relativism, simple subjectivism and emotivism. The fourth chapter exposes the design of universal prescriptivism proposed by R. M. Hare. The universal prescriptivism indicates, in the Singer s viewpoint, a consistent way to create the join between the universalizability and PECI. It highlights also the criticism designed by J. L. Mackie and Singer himself to universal prescriptivism. The second part of this chapter shows briefly some of the main points of the classical conception of utilitarianism and its possible relationship with the theory of Singer. The fifth chapter introduces the Singer s thesis about the origin of ethics and the universalizability as a feature necessary to the point of view of ethic, and the way which this argument is developed to form the PECI. The sixth chapter exposes the main distinctions that characterize the PECI. Finally the seventh chapter provides a discussion about the reasons highlighted by Singer for one who wants orient his life according to the standpoint of ethics. This structure allows explaining the main ideas of the author concerning the theoretical foundations of his moral philosophy

A eletricidade chega à cidade: inovação técnica e a vida urbana em Natal (1911-1940)

Dans les premières décennies du XXème siècle, un groupe d intellectuels brésiliens a pris pour soi la mission de conduire la nation aux chemins du progrès, en réfléchissant sur les transformations des villes et, souvent, en proposant et en mettant en avant des actions et mesures qui dirigeraient la modernisation du pays. Dans ce contexte, la ville apparaissait comme un synonyme de progrès en opposition à la campagne, en donnant emphase à la construction du Brésil urbain. À Natal, celui-ci a été une période de sensible modification dans l espace urbain, en suivant les préceptes de l hygiénisme et de l esthétique racionaliste, qui ont orienté les réformes entreprises dans beaucoup de villes brésiliennes. Les élites politiques et socioéconomiques de la capitale du Rio Grande do Norte ont developpé le discours en faveur de la modernisation qui avait pour objectif de justifier les interventions dans la ville et l introduction de l infra-structure de services urbains, par exemple, les services d illumination et de transport, qui à partir de 1911, ont commencé à être stimulés par l électricité. Cette modernisation est matérialisée par de nouveaux équipements et services, par des espaces remodelés en accord avec la rationalité technique de l urbaniste, pour l utilisation de nouvelles sources d énergie (gaz, électricité), en plus de la croissance de la population résidente en ville. Cependant, nous ne pouvons pas oublier que la construction de la ville moderne est passée tant par des transformations physiques, matérielles, comme par l absorption de valeurs, symboles, gestes, vocabulaires, objets, adoptions de nouvelles normes de comportement et par la formation de nouvelles sensibilités sur l espace urbain et la vie en ville. De cette manière, les nouvelles normes technologiques, comme l électricité, ont rendu possible des transformations dans la structure matérielle de la ville et en vie urbaine dans ses plus divers aspects. Ce travail propose d analyser la relation entre énergie électrique et la vie urbaine à Natal entre 1911 et 1940, en prenant en compte, pour cela, les actions d intervention de l État sur l espace urbain et les perceptions d intellectuels face aux transformations urbaines dont ils étaient les témoins. À partir de cette analyse, nous cherchons à préciser les efforts gouvernementaux pour la manutention des services d électricité et conservation des équipements urbains; comprendre comment l utilisation d énergie électrique a aidé à produire de nouvelles situations quotidiennes et comment elle a été perçue, traduite en sentiments et perceptions fondées dans la cohabitation avec cette innovation technique. Les élites locales désiraient diffuser des habitudes considerées modernes, en construisant une identification avec la manière de vie urbaine, fortement inspirée dans la vie dans les villes Européennes et Américaines. L électricité a rendu possible des expériences et sensations qui allaient caractériser l habitant de la ville

Natal, outra cidade : o papel da Intendência Municipal no desenvolvimento de uma nova ordem urbana(1904-1929)

The present work regards, as its subject, the management of the urban space. It aims to survey the role assumed by the Conselho de Intendência Municipal de Natal (Municipal Stewardship Council of Natal) in the formation of a new urban order between the years of 1904 and 1929. For a better comprehension of the object of research, the milestone of the time span analyzed in this work was receded to the year of 1890, specifically at the first chapter of this dissertation. In this chapter, we will turn our attention towards an analysis of the referred council, on the regulation of its operation, the relations of this institution with the state government and its mechanisms of action in the city, among other topics. In the next chapter, we will delve into an elite who administrated the city of Natal during the first republic, understanding that the analysis of the formation of a modern city project by the Municipal Stewardship undergoes the comprehension of those who leaded this institution. In the third chapter, we will examine the limits of the municipal management to put into practice its projects to the upraise of a new Natal, between the years of 1904 and 1921. The last chapter, on its turn, presents a new Stewardship, reformulated after a process of administrative streamlining, and a city that transforms itself, especially during the O Grady tenure by receiving major constructions, which alter its main features. We will regard, as the main resources of this study, articles from the daily newspapers A República (The Republic) and Diário de Natal (Daily Natal), dictums, announcements, laws, state decrees and the messages disclosed by the state government. To build a way of analysis, we make use of authors such as Anthony Giddens, Peter Burke and Laurent Vidal, among many others who discuss concepts related to the proposed theme