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

Um estudo sobre a concepção de paradoxo segundo o pensamento de Augustus de Morgan

This work aims to analyze the concept of "paradox" posed in the work of The Budget Paradox (1872) of mathematical and logical English Augustus De Morgan (1806-1871). Here it is important to note that a large part of this book consists of re-prints of a series of writings by the author in journal Athenaeum, where its performance as auditor of literature. The tests refer to some scientific work produced between the years 1489 and 1866 and the rules of selection for the composition of the work is, basically, the methodological aspects used in the completion or disclosed by such scholars. The concept of paradox is presented in two distinct moments. At first, we found a study of definitions for the term in a philosophical approach, characterizing it as something that requires further investigation; which was complemented with the classic examples of a scientific context. In the second, we present a concept advocated by De Morgan and, under this perspective, that he conceptualized the "paradox" is directly related to the non-usual methods employed in the formulation of new scientific theories. In this study some of these scientific concepts are detailed, where, through the redemption history, engaging in issues of our study Mathematics, Physics, of Logic, among others. Possession of the preliminary analysis and comparison with the design of De Morgan, it became possible to diagnose some limitations in the conceptualization suggested by the author. Further, evidenced, in front of the cases, the nonlinearity of the process of production of knowledge and hence the progress of science

Ecologia humana e manejo participativo da pesca do búzio Anomalocardia brasiliana (Gmelin, 1791) (Bivalvia: Veneridae) na Reserva de Desenvolvimento Sustentável Estadual Ponta do Tubarão (RN)

Coastal and marine protected areas are created to protect habitat, avoid biodiversity loss, and to help maintain viable fisheries. However, most of these areas in tropical countries occurs in impoverished regions and directly affect the livelihood and survival of coastal communities which directly depend on fisheries and shellfisheries. Therefore, socioeconomic and conservation goals overlap. In this context, fishers should have a central place in resource management. They are critical resource users and their behavior directly affects the system. Shellfish resources are important sources of food, employment and income to fishing communities in Latin America. But despite its widespread use for food and income, there is an urgent need of more research on shellfish management. This research discusses the artisanal fisheries of Venus clam (Anomalocardia brasiliana) (Gmelin, 1791) (Bivalvia: Veneridae) in Brazil, and points out strategies to improve the system. Venus clam is a small and commonly exploited species for food and income on the Brazilian coast. This research was carried out at Ponta do Tubarão Sustainable Development Reserve (Brazilian Northeast coast), where there was no information available about who harvest, where or how much Venus clam has been harvested, despite this resource being exploited for generations. Clam fishery follows the pattern of socio-economic invisibility that general clam exploitation has in Brazil. Methods used were interviews, participatory monitoring and focal follow observation from January 2010 to May 2011. Results include: (a) the identification of shell fishers, (b) how harvest and meat processing are performed (mollusk beds, time spent, gross and net production), (c) the analisis of shell fisher income and their economic sustentability, and (d) the involvement of shell fisher families in data gathering and analyses for the first time. Based on the acquired knowledge, we propose a new institutional arrangement for clam fishery including co-management, fisheries agreement, compensatory arrangements and improvements for the Venus clam value chain such as the establishment of a minimum price for clam meat. This research also includes two other results: a general description for Venus clam harvesting in the Brazilian Northeast coast and a specific discussion about co-management of Venus clam in Brazil. The first one was possible through the meeting of several shell fisherwomen from other states during activities promoted by People of the Tides (PoT) project. PoT was an international initiative aiming to develop coastal communities that depend on mollusk for their livelihood. The second one is a comparison between PoT and Venus clam management at Pirajubaé Marine Extractive Reserve (Santa Catarina). It evaluates the success and failures of these only two initiatives involving co-management of A. brasiliana in Brazil