Um estudo sobre as origens da Lógica Matemáitca

The present study has as objective to explaining about the origins of the mathematical logic. This has its beginning attributed to the autodidactic English mathematician George Boole (1815-1864), especially because his books The Mathematical Analysis of Logic (1847) and An Investigation of the Laws of Thought (1854) are recognized as the inaugural works of the referred branch. However, surprisingly, in the same time another mathematician called Augutus of Morgan (1806-1871) it also published a book, entitled Formal Logic (1847), in defense of the mathematic logic. Even so, times later on this same century, another work named Elements of Logic (1875) it appeared evidencing the Aristotelian logic with Richard Whately (1787-1863), considered the better Aristotelian logical of that time. This way, our research, permeated by the history of the mathematics, it intends to study the logic produced by these submerged personages in the golden age of the mathematics (19th century) to we compare the valid systems in referred period and we clarify the origins of the mathematical logic. For that we looked for to delineate the panorama historical wrapper of this study. We described, shortly, biographical considerations about these three representatives of the logic of the 19th century formed an alliance with the exhibition of their point of view as for the logic to the light of the works mentioned above. In this sense, we aspirated to present considerations about what effective Aristotelian´s logic existed in the period of Boole and De Morgan comparing it with the new emerging logic (the mathematical logic). Besides of this, before the textual analysis of the works mentioned above, we still looked for to confront the systems of Boole and De Morgan for we arrive to the reason because the Boole´s system was considered better and more efficient. Separate of this preponderance we longed to study the flaws verified in the logical system of Boole front to their contemporaries' production, verifying, for example, if they repeated or not. We concluded that the origins of the mathematical logic is in the works of logic of George Boole, because, in them, has the presentation of a new logic, matematizada for the laws of the thought similar to the one of the arithmetic, while De Morgan, in your work, expand the Aristotelian logic, but it was still arrested to her

Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics

Mãe-esposa e professora: educadoras no final do século XIX

This text is organized through discussions undertaken in the area of the History of Education in Rio Grande do Norte, circumscribed to the History of Women from the first decades of the Brazilian Republic, and to the analysis of what was expected of this education. We examined representations of women in Natal, between 1889 and 1914, with the goal of configuring relations between the sexes with the emphasis on moral, intellectual and pedagogical aspects required of these women. As documental sources we utilized the educational, civil and criminal Legislation, on a National scope, as well as on a State and Municipal scope. We circumscribed our search to the newspaper A República, in which we found literature that circulated in Natal in the form of pamphlets, short stories and poetry, as well as other texts by authors that were part of the corpus of analysis of this study, located in public and private archives in Rio Grande do Norte, such as the Historical and Geographic Institute of Rio Grande do Norte (IHGRN) and the State Public Archive of Rio Grande do Norte (APE-RN). The use of the indexing method and the propositions of Cultural History were the appropriate theoretical-methodological framework to complete studies of this nature. This operational perspective permitted us to elaborate nuances about this time of transition from the 19th to the 20th Century, and to spotlight the fire of the women from this period. The basis of the argument that related women to maternity and domesticity, and within the ideals of abnegation and religious leadership, aligned to a demand coming from the increase in the quantity of schools for women, allocated women as the most appropriate for superior in educational performance in the country, based on its foundations: primary education. Beyond the universe of formal education, the other side of women appeared in republican politics. The mother-spouse and the institutionalization of domestic education associated the female gender with the role of educator at home as well. Be it in the public sphere, as a teacher, or in private, as mother-spouse, female care is perceived in this configuration, as an educational base that the Republic, and in transition, bequeathed to the Brazilian 20th Century

Mariana , Pai contra mãe e O caso da vara : escravidão e chão histórico em Machado de Assis

Machado de Assis understood his time and brought his perception of Brazilian society in the 19th century, with its multiple aspects economy, politics, culture, amongst others - to the texts he wrote. Through the tensions lived in his novels and short stories, Machado displays Brazilian social reality and the changes it had been undergoing. Mariana and Pai contra mãe show the crisis of the slavery system, the relation of dependency, the treatment given to the captives and the lack of coherence of a country that intended to adopt Liberalism as an ideology, but which kept on living under the shadow of slavery and its consequences. A country where the priorities were given to the landlords, owners of slaves, in protection of their interests. O caso da vara tells about how the crias da casa little black girls who lived in the household and learned how to make spool embroidery were treated. What were the punishments for desobedience and how they were levelled out, how should be the behaviour of a child who lived as a social outcast. Thus, this paper aims at playing a game of mirrors between History and fiction. Not only to play it, but to analyze how Machado deals with the reflections of 19th century Brazil on his short stories

Gregório de Matos: do barroco à antropofagia

The exponential figure of Gregório de Matos e Guerra has been subject of many theoretical discussions through the years, since his apparition in a public place, in the 19th century, and even more, during the 20th century, when he was salvaged by the modernist vanguard. As a result, there are yet two antagonist points of view linked to Gregório de Matos, on one side, there some researchers who defend him, on the other, some of them attack him. The first ones say this poet from Bahia was the first literary voice in Brazil, from the Baroque basis, while the last ones say he is a merely plagiarist of the Spanish poets from the 17th century, without a real contribution to the development of Brazilian Literature. With this in mind, this thesis follows the perspective this poet is an anthropophagus-baroque, devouring cultures, with an active participation in the process of our cultural and literary identity. For that reason, it was made a literature review about the biography of this poet trying to break romantic descriptions, emphasizing some scientific facts that can contribute to present the baroque profile of this poet. In this sense, it was discussed the History of Literature focused on this creole poet, mainly based on the historians point of view about the Gregorian poetry in the formation of Brazilian Literature scenery. In the defense of the hypothesis that Gregório de Matos was our first anthropophagus, this work aims to analyze how his poetry reveals the intrinsic characteristics of Baroque and Anthropophagy, focusing its carnivalesque aspect, showing to the world, with a satiric tone, the idiosyncrasies of human life. In this way, analyzing this corpus in Spanish is the strength of this thesis because, besides it is previously unpublished, it contributes to the comprehension of the anthropophagy as a theoretical mechanism that explains the process of formation of our cultural literary identity. Then, we have Augusto de Campos (1968; 1978; 1984; 1986; 1988), Haroldo de Campos (1976; 2010a; 2010b; 2011), Severo Sarduy ([1988?]), Oswald de Andrade (1945; 1978; 2006), Mikhail Bakhtin (2010), Octavio Paz (1979), Segismundo Spina (1980; 1995; 2008), Afrânio Coutinho (1986a; 1986b; 1994), Affonso Ávila (1994; 1997; 2004; 2008), among others, to constitute this theoretical scenery. The Gregorian poetry, in this way, have contributed to the formation of baroque-anthropophagic scenery in Brazilian boundaries, with a special attention to the transition of time, because he is not only from the 17th century, established by the historiography, but his work is present nowadays due to the contemporaneously of his themes, centered to the eternal doubts of baroque man

Desventuras de Hypolita: luta contra a escravidão ilegal no sertão (Crato e Exu, século XIX)

This paper analyses the history of Hypolita Maria das Dores, mulatto woman, free born, was enslaved and, by an act of freedom, appealed to court to prove the illegitimacy of her captivity and regain their freedom and their children. The main scenarios of this social and legal struggle are Crato (Ceará) and Exu (Pernambuco), places where she lived in the 19th century. The main objective of this work is to understand how to set the tensions and alliances involving the struggle for freedom inside and outside justice, in differentiated provincial spaces. An approach that belongs to the field of the social history of slavery, we ll prioritize the narrative of life. In it, Hypolita is taken as the subject of her story, as she faces stately and patriarchal values in a slave society. The documentary corpus that allows such vertical investigative consists of parish registers, we examined the baptisms, marriages and death records; analyzed registry documents of postmortem inventories, petitions and crafts; reports of provincial presidents and, finally, the O Araripe s and O Cearense s journalistic information. The investigation of the case allowed the understanding of how, in space and time specific, freedom was understood, usurped and claimed by various social subjects in the frame of morals and justice institutionalized

Ícones urbanos na cidade de Natal: arquitetura e desenvolvimento urbano na cidade do sol e mar

Natal has come through major changes in the last 150 years, since the actions of city beautification, in the 19th century, until the present day, when such transformations start to have the objective of including the city in the competition for the attraction of the capital flows and consumption, domestically and in a foreign sense. It is thought that the first initiatives aimed at increasing tourism in Natal occurred in the 1960s, however, it became apparent that only from the 1980s was there a significant increase in tourist activities in Natal and the Metropolitan Region, especially on the east coast of the state of Rio Grande do Norte, leading to an expansion of the labour market, the significant increase of foreign investment, territorial changes of great impact and the production of buildings primarily intended for the hotel industry and second residence for European tourists. Since then, the incentives for tourist activity in the state have been maintained and even increased, based on tourism aimed at natural beauties, local cuisine and events, which transformed the tourist activity in one of the main sources of foreign exchange for the city of Natal. In the early 21st century, the construction of high-rise condominiums, monuments (including the designer ones), such as the Parque da Cidade, designed by Oscar Niemeyer, were already established. Also, shopping centers and, in order to host the World Cup, the new football stadium, the Arena das Dunas, among others, which were aimed at local and foreign consumers, especially European, stood out in the city. It is understood that these new buildings, monuments and also renovations and restorations that were deployed in the city of Natal aimed at constructing a new identity for the city, within the process of capitalist development and urban spectacle. It is considered that the monuments and the iconic buildings are attributes of the cities aimed at selling locations as goods, establishing a new urban environment, a new role as cities, which aimed at seeking greater autonomy from the nation-state. In this research, it was sought to analyze the architectural object, that is, buildings and monuments built or restored in Natal and its relevance to the city marketing promoted by the city itself. It was found that, indeed, such buildings and monuments are inserted in contemporary architectural production as a basis for increasing the competitive nature of Natal. In addition, they reveal a capitalist mode of production, supported by public resources, operating in the production of urban space with a view to repeating the hegemonic model of a competitive city