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

O processo avaliativo institucional de desempenho do sistema público municipal de Teresina-PI (2001 a 2005): entre a lógica da excelência e a lógica da aprendizagem

This work focalize the institutional and educational evaluation, aiming to investigate the Municipal System Institutional Evaluation Performance of Teresina City Piauí (2001-2005), and to reflect about Institutional System Performance and its contribution to compose a new learning evaluation practice. In this sense, classifies elements about the evaluation practice in two Elementary Education municipal public schools, involving Education Municipal Bureau technicians as managers, pedagogues, teachers and students. Based on the ethnographic studies principles in the educational area, the work employs investigative procedures like document analysis, interviews with groups and individuals and also participator s comments. Intending to comprehend the complexity produced by the institutional and education evaluation processes, the wok reveals the Institutional Evaluation legal and educational political basis and the several positions assumed by the Learning Evaluation, as a classification tool or as a learning enhancement. This work points, as results, to a evaluation culture bipolarity carried out by the Municipal Education System as a explicit control and regulation toll, related to the classification and learning in a interaction process that operates both in the pressure and the reflection, as a culture practice established between excellence of logic and learning. The evaluation history has been construct on the evaluation actions dialectics, joint simultaneously between the Institutional Evaluation Performance and the learning evaluation. The senses, meanings and actions bipolarity is a interaction process product sustained between the institutional evaluation, under the scholar ranking application, and the learning evaluation. In this relativity, the teacher evaluation practice is found, ruled by interesting, thoughts and actions on the school evaluation, allowing a higher security and support to the learning results. Grounded in the researched reality, its possible to say that the teacher s evaluation practice is diversified, with different characteristics, when it is done in the learning search and in the learning intention. In the first case, reflects, rearranges and constructs new actions that lead the student to produce learning. In the second, shows the will, the wish of learning, but is a weak action, producing a not really significant learning and development; as a result, remains the mark approach as a determinant in the student future. The work s hope is to contribute not just to rethink these two evaluations dimensions the institutional and the learning ones but also to organize the school and to improve the pedagogic process

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