Submitted by Luanna Matias (lua_matias@yahoo.com.br) on 2015-02-05T13:54:15Z No. of bitstreams: 2 Tese - Humberto de Assis Clímaco - 2014.pdf.pdf: 1818373 bytes, checksum: 66d3ffcf4b0148b8b63434e115149cb9 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2015-02-05T14:08:32Z (GMT) No. of bitstreams: 2 Tese - Humberto de Assis Clímaco - 2014.pdf.pdf: 1818373 bytes, checksum: 66d3ffcf4b0148b8b63434e115149cb9 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) / Made available in DSpace on 2015-02-05T14:08:32Z (GMT). No. of bitstreams: 2 Tese - Humberto de Assis Clímaco - 2014.pdf.pdf: 1818373 bytes, checksum: 66d3ffcf4b0148b8b63434e115149cb9 (MD5) license_rdf: 23148 bytes, checksum: 9da0b6dfac957114c6a7714714b86306 (MD5) Previous issue date: 2014-05-30 / Taking part of the research line Grounds of the Educational Process of Post-graduate program in education of Universidade Federal de Goiás, this thesis reflects, in an original way, on the core issues the fundamentals of core issues of the today‘s mathematical education, opening new horizons for this area of knowledge. It discusses the transformation of the relationship between intuition and concept in the philosophy of mathematics occurred in the early nineteenth century, when the nature of mathematical knowledge has undergone such profound changes that mathematics came to be called Pure Mathematics, a subject that is relevant to understand the contradiction between simplicity and clarity sought by the creators of Pure Mathematics to make it a language, and the difficulty and lack of meaning with which it is often seen in schools. The way of conceiving knowledge was profoundly changed by this transformation, and in particular changed the meaning of intuition. Kant's work has been discussed in this thesis due to the constructive role that the philosopher attributed, in its critical period, to the intuition of the knower subject; with the work of Kant, a genetic issue, about the origins and the conditions in which knowledge occurs, was inaugurated in philosophy, whence derives the importance that gained in its system the subject's ability to perceive objects through the notions of space and time, as conditions for any knowledge. Kant concludes that what makes knowledge possible is the fact that for its development contributes the subject‘s intuition and constructive action, and that this is how he achieves the concept, general representation, based on intuition, particular representation. Bolzano sought to eliminate from the investigations on the theory of science the study of the conditions and origins of knowledge, which he considered as a social issue that should be written in an order that would allow it to be communicated. Therefore, Bolzano denied that space and time could support language and mathematics, and sought to found principles able to reorganize knowledge in a hierarchical structure in which more conceptual truths could not be substantiated by more intuitive ones. Although Bolzano has not investigated the learning process itself, the importance he gave to education was so great that in his most important work, the Doctrine of Science, Wissenschaftslehre, he defined science as determined organized knowledge so as to compose a textbook. The philosophical, scientific and cultural consequences of the Industrial Revolution that occurred in the early nineteenth century, were studied in this thesis because it was in the context of its emergence that emerged deep processes, on the one hand, to create a public knowledge through the reorganization of universities, the emergence of large Polytechnics who needed graduate engineers in large scale, proliferation of publications with educational concerns; and, on the other hand, a search for reorganizing knowledge created or arisen in previous centuries in a hierarchical manner according to principles, which led to a search for treating in a theoretical manner the knowledge hitherto seen as a set of isolated truths. The study of the authors treated in the thesis, especially Kant and Bolzano, were made based on their original works, and any recourse to commentators did not substitute a careful reading of their ones. / Inserida na linha Fundamentos dos Processos Educativos do Programa de PósGraduação da Universidade Federal de Goiás, esta tese reflete de maneira original sobre os fundamentos de questões centrais para a Educação Matemática na atualidade, abrindo novos horizontes para esta área do conhecimento. Discute a transformação da relação entre intuição e conceito na filosofia da matemática ocorrida no início do século XIX, quando a natureza do conhecimento matemático passou por modificações tão profundas que a matemática passou a ser chamada de Matemática Pura, tema que é relevante para compreender a contradição entre a simplicidade e a clareza buscadas pelos criadores da Matemática Pura ao torná-la uma linguagem, e a dificuldade e a falta de significados com que ela costuma ser vista nas escolas. A forma de conceber o conhecimento foi alterada profundamente por esta transformação, e em particular mudou o significado da intuição. A obra de Kant foi discutida devido ao papel construtivo que o filósofo atribuiu, em seu período crítico, à intuição do sujeito; com a obra de Kant, inaugurou-se na filosofia uma questão genética, sobre as origens e as condições em que ocorre o conhecimento, donde deriva a importância que adquiriu em seu sistema a capacidade do sujeito de perceber objetos por meio das noções de espaço e de tempo, consideradas condições para qualquer conhecimento. Kant conclui que o que torna o conhecimento possível é o fato de que para sua elaboração contribui a intuição e a ação construtiva s do sujeito, e que é assim que ele alcança o conceito, representação geral, partindo da intuição, representação particular . Bolzano procurou eliminar das investigações sobre a teoria da ciência o estudo das condições e das origens do conhecimento, que ele considerou como algo social que deveria ser escrito numa ordem que permitisse que ele fosse comunicado . Por isso, negou que espaço e tempo pudessem fundamentar a linguagem e a matemática, e procurou criar princípios aptos a reorganizar o conhecimento numa estrutura hierárquica em que as verdades mais conceituais não pudessem ser fundamentadas pelas mais intuitivas. Embora Bolzano não tenha investigado o processo de aprendizagem em si, a importância que ele deu à educação foi tão grande que em sua mais importante obra, Doutrina da Ciência, Wissenschaftslehre, ele definiu a ciência como determinado conhecimento organizado de maneira a compor um livro didático. As consequências filosóficas, científicas e culturais da Revolução Industrial, ocorrida no início do século XIX, foram estudadas nesta tese porque foi no contexto de sua emergência que surgiram processos profundos, de um lado, de publicização do conhecimento por meio da reorganização das universidades, do surgimento das grandes Escolas Politécnicas que precisavam for mar engenheiros em larga escala, da proliferação de publicações com preocupações educacionais ; e de outro de busca por reorganizar o conhecimento surgido nos séculos anteriores de maneira hierarquizada de acordo com princípios, o que levou a uma busca por tratar de maneira teórica o conhecimento até então visto como um conjunto de verdades isoladas. O estudo dos autores tratados na tese, sobretudo as obras de Kant e de Bolzano, for am feitas com base em seus originais, e o eventual recurso a comentadores não substituiu a leitura de suas obras.

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Texte remanié de: Dissertation--Universität Innsbruck, 2003. / Bibliogr. p. [499]-509.

Dissertation--Universität Innsbruck, 1993. Titre de soutenance : Die Stadt Brixen 1918-1939. / Contient des documents en italien. Bibliogr. p. 353-359.

Texte remanié de: Diss.--Philosophische Fakultät--München--Ludwig-Maximilians-Universität, 1990. / Bibliogr. p. 485-539. Index.

In my opinion, compactness is the most important concept in mathematics. We 'll track it from the one-dimensional real line in calculus to infinite dimensional spaces of functions and surfaces and see what it can do.

The early Husserl wants to know what logic is, or what we should call ‘logic.’ He poses the question in a way that knowingly encompasses both what the 19th century (after Kant but before Frege) and the 20th century (since Frege) call ‘logic.’ But that he asks the question, and with such scope, has yet to be widely recognized. In particular, Husserl scholars still lack an overview of how Husserl’s early, explicitly logical inquiries, driven more by this single question than any worry about doctrinal consistency, does at least two things at once: probe what will later be called ‘pure phenomenology’ or ‘transcendental logic,’ and delimit logic as a positive yet mathematical discipline. With the aim of providing the neglected overview of this project, this dissertation takes the measure of Husserl’s two-volume Logical Investigations (1900-01) in four studies. Chapter I argues that the first volume, the Prolegomena to Pure Logic (1900), intends at once to resolve a 19th-century conflict and to establish logic’s possibility as its own discipline, all by means of demonstrating the confusion of psychologism (the view that empirical psychology could set the terms for logic as a discipline). Chapter II then contends that most of the Prolegomena’s first chapter falls outside this intention, departing from the book’s Bolzano-inspired argumentative framework yet thereby anticipating Husserl’s later ‘transcendental logic.’ Chapter III presents Frege and Husserl as two images of indecision as to how it falls to logic to know truth’s laws. Chapter IV concludes by expounding Husserl’s conception of logic as noetics, the self-clarification of knowing, thus completing the picture of Husserl’s indecision, while also laying groundwork to track the development of his thinking after the Logical Investigations.

This work deals with a basic question of modern science and it is its indefectibility. Quality of education is reduce to an evaluation of conformity to a common known knowledge and its quantity representation. Seeds of this long process go back to an ancient academia of Gondisapur established in an Arabic world. Author proclaims that the main goal of philosophy is to show, that this is not the only way of thinking and in the same time that the main goal and power of phenomenology is to apply the transcendental epoche to overcame the truth in its regularization shape. The hardcore of modern science is located in the world of mathematics and a lot of thinkers find the Math as a land of pure sureness - the core of this work in an opposite proofs, that in fact nowadays math is all, but the correct way of thinking. The two examples are explicit: the Pythagorean Theorem and the Sum of the geometric row. This work brings a quite new view on the mathematical problem of "the point" and "the nothing" as a border of things. In the second part uses as a frame of its topic the first 18 §§ of the work "Paradoxes of the infinite" by Czech mathematician of German mother tongue Bernard Bolzano. The important idea of this study is a new ontological view on the set of prime numbers.

CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / O trabalho traz inicialmente uma abordagem histÃrica, da GrÃcia (com os pitagÃricos), com o matemÃtico Eudoxo, fazendo referÃncia a talvez à maior obra matemÃtica, os livros de Euclides. Em seguida, trazemos definiÃÃes e construÃÃes sobre os nÃmeros reais com um corpo completo, os conceitos de Ãnfimo, supremo, sequÃncias infinitas com destaque as convergentes, sequÃncia de Cauchy e os trÃs teoremas fundamentais para o curso de cÃlculo, o teorema do anulamento, do valor intermediÃrio e de Weierstrass. Logo apÃs, definimos mÃtrica e espaÃo mÃtrico no plano, mostramos que o processo de comparar um segmento arbitrÃrio com outro fixado como unidade nos conduz aos diversos tipos de nÃmeros reais positivos: inteiros, racionais e irracionais, onde a noÃÃo de segmento comensurÃvel à explicada. O cÃlculo de Ãrea para figuras planas, onde sÃo apresentadas as fÃrmulas usuais para as Ãreas dos polÃgonos mais simples, apresentamos uma aplicaÃÃo, a fÃrmula de Pick, sem demonstraÃÃo do teorema, simples, divertida, prÃtica e eficiente para o cÃlculo de Ãrea, um conteÃdo da disciplina de matemÃtica presente em todo o ensino bÃsico do Brasil sempre presente em avaliaÃÃes externas como a OBMEP. / The work initially brings a historical approach, Greece (with the Pythagoreans), with the mathematician Eudoxus, referring to perhaps the greatest mathematical work, Euclidâs books. Then bring definitions and constructions of the real numbers as a complete body, the concepts of tiny, supreme, infinite sequences especially the convergent, Cauchy sequences and the three fundamental theorems for the calculus course, the annulment of the theorem, the intermediate value and Weierstrass. Soon after, we define metric and metric space in the plan, we show that the process of comparing an arbitrary segment with another set as unit leads to various types of positive real numbers: integers, rational and irrational, where the notion of measurable and immeasurable segment is explained. The area calculation for plane figures, where the usual formulas for the areas of simple polygons are presented, we present and application, Pickâs formula, without demonstration of the theorem, simple, fun, practical and efficient for area calculation, one this mathematical discipline of content throughout basic education in Brazil always present in external evaluation as OBMEP.

This diploma thesis is focused on the part of the work of important philosopher and mathematician Bernard Bolzano, which is currently rather neglected. It is his utopian writing On the best state. The aim of my thesis is to find out (through the analysis of the selected representatives of the utopian genre from the 16th to half of the 19th century and their consequent comparison with Bolzano's utopia), where to put the book On the best state in context of European utopian thought. In Czech literature Bolzano's writing is considered to be an example of rationalistic utopia of Enlightenment; however this statement hasn't been proven by deeper comparative analysis. That's why this diploma thesis tries to review this statement in order to either confirm it or define newly the position of Bolzano's book in the history of political utopianism. The thesis is divided into four chapters. The first one gives basic introduction to Bolzano's professional and personal life, which is necessary for better understanding of his political thought. The second part analyzes important European utopias of Renaissance, Enlightenment as well as the utopias of the first half of the 19th century. The main part of this thesis is the chapter three, where are discussed selected political, economical and social aspects of the...