Orientador: Antonio Carlos Carrera de Souza / Banca: Silvio Donizetti de Oliveira Gallo / Banca: Maria Rosa Rodrigues Martins de Camargo / Banca: Audria Alessandra Bovo / Banca: Antonio Sérgio Cobianchi / Resumo: Esta pesquisa tem como objetivo produzir diferença sobre a história do Curso de Licenciatura em Matemática em nosso país, pois procuramos ver e fazer ver através de quais práticas e discursos teve início o primeiro Curso de Licenciatura em Matemática no Brasil, criado na Faculdade de Filosofia, Ciências e Letras da Universidade de São Paulo no ano de 1934, e como essa criação reverbera ainda hoje em nossa Licenciatura em Matemática. Esta investigação de doutoramento buscou, como diria Michel Foucault, nosso principal teórico, fazer um diagnóstico do presente do Curso de Licenciatura em Matemática no Brasil, ou seja, produzir um olhar - o nosso olhar sobre este passado e sua força no presente - investigando o conceito de parresia - a coragem da verdade - dentro desse curso. Utilizamos como metodologia de investigação e escrita a arqueologia foucaultiana, pois a arqueologia nos possibilita colocar à vista as relações entre o ver e o dizer, entre o visível e o enunciável e que forças estão agindo no limiar deste processo. Permite-nos olhar a ressonância das práticas no discurso. Trata-se de uma descrição do discurso como objeto-monumento de um acontecimento. Desenvolver uma arqueologia, segundo Foucault, é produzir uma descrição histórica e filosófica sem o intuito de fazer julgamentos sobre os acontecimentos do passado com o olhar do presente. Através dos fragmentos utilizados - documentos escritos, tais como: discursos, leis, projetos políticos pedagógicos, atas e outros - descrevemos anarqueologicamente o desabrochar de ideias, a formulação de positividades, racionalidades para entender no presente como o passado se constituiu e como a construção desse passado faz vibrar atualmente forças de poder e resistência neste Curso, possibilitadas pela Coragem da Verdade / Abstract: This research aims to make difference on the history of Degree in Mathematics in our country, since we try to see and make it be seen through which practices and discourses started the first Degree in Mathematics in Brazil, created at the Faculty of Philosophy, Sciences and Languages and Literature of the University of São Paulo in 1934, and how this establishment reverberates in our Degree in Mathematics today. This doctoral research seeks, according to our main theorist, Michel Foucault, to make a diagnosis of the current Mathematics Degree Course in Brazil, that is, to create a look - our look of this past and its strength in the present - investigating the concept of parrhesia - the courage of the truth - within that course. Foucault's archeology was used as research methodology and writing, because archeology allows us to show the relationship between seeing and saying, between the visible and the expressible and what forces are acting on the threshold of this process. It allows us to look at the resonance of discourse practices. This is a description of discourse as an object-monument of an event. Developing an archeology, according to Foucault, is to produce a historical and philosophical description without the intention of making judgments about the events of the past with the look of the present. Through the fragments used - written documents such as speeches, laws, political pedagogical projects, minutes and others- we anarchaeologically describe the blossoming of ideas, formulation of positivities, rationales to understand at present how the past was constituted and how the construction of this past currently moves power strength and endurance present in this Course enabled by the Courage of the Truth / Doutor

Orientadores: Itala Loffredo D'Ottaviano, Jairo Jose da Silva / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas / Made available in DSpace on 2018-08-11T05:11:27Z (GMT). No. of bitstreams: 1 Santos_EberthEleuteriodos_D.pdf: 1563979 bytes, checksum: 4ce7cd812f548d70c8712c18785b0178 (MD5) Previous issue date: 2008 / Resumo: Georg Cantor foi um dos mais importantes matemáticos do final do século XIX. A idealização de sua teoria de conjuntos representa um marco no desenvolvimento da matemática. De fato, o aparecimento e o desenvolvimento dessa teoria tiveram profundas conseqüências que não se limitaram ao círculo da matemática. O debate científico que se seguiu a certos resultados como, por exemplo, a apresentação dos números transfinitos, reavivou uma discussão que remonta a antigas disputas ontológicas da filosofia présocrática, exatamente àquelas discussões que se voltavam para a afirmação do Ser como infinito. Essa discussão nasce na Grécia antiga e perpassa toda a história do pensamento ocidental. Conhecemo-la por meio de nomes como Anaximandro, Pitágoras, Parmênides, Platão, Aristóteles. Atravessando os séculos, essas idéias povoaram a mente de personagens como Bruno, Galileu, Leibniz, Kant e muitos outros. Nos séculos XIX e XX, os trabalhos de Cantor reavivaram e deram novo impulso ao tema. Esforçamo-nos em mostrar que estes trabalhos são absolutamente revolucionários. Motivados pelo filósofo da ciência Thomas Kuhn, concluímos que o aparecimento da Teoria de Conjuntos de Cantor representa a revisão de um antigo paradigma filosófico-matemático. Paradigma este que teve sua primeira elaboração lógica e filosófica com Aristóteles e que se desenvolveu como a maneira dominante de pensar a idéia de infinito. Destacamos que alguns dos aspectos apontados por Kuhn como sintomáticos de uma revolução científica estão presentes no trabalho de Cantor e que há, possivelmente, outras maneiras de argumentar em favor da qualidade revolucionária deste trabalho. Em um sentido mais amplo, foi-nos possível vislumbrar que o desenvolvimento da matemática também pode ser lido através do enfoque das revoluções, e o mais recente exemplo disto é representado pelo esforço intelectual de Cantor / Abstract: Georg Cantor is one of the most important mathematicians of the end of the 19th century. The idealization of the set theory represents a landmark in the development of mathematics. In fact, the creation and development of this theory had deep consequences not restricted only to the circle of mathematics. The scientific debate that followed some of the results, as for instance the presentation of the transfinite numbers, revived a quarrel that retraced old ontological disputes of the pre-Socratic philosophy, accurately topics like the being of the infinite. This quarrel is born in old Greece and crosses all the history of the occidental philosophical think. We know it through names like Anaximander, Pitagore, Parmmenides, Plato, Aristotle among others. Crossing the centuries, such ideas fill the mind of characters like Bruno, Galileo, Leibniz, Kant and others. In the 19th and 20th centuries, Cantor¿s works give a new life and color to the subject. In this thesis, we argue that these works are absolutely revolutionary. Based on Thomas Kuhn¿s conception, we conclude that the appearance of Cantor¿s set theory represents the disruption of one old philosophical-mathematical paradigm. Such a paradigm, that had its first logical and philosophical elaboration by Aristotle, had characterized the dominant way of thinking the concept of infinite. We have succeeded in detaching that some aspects pointed by Kuhn as symptomatic of a scientific revolution are present in Cantor¿s work and we also propose other ways to argue in favour of the revolutionary aspect of this work. In a more ample sense, we glimpse that the development of mathematics can also be understood by means of revolutions, whose more recent example seems to be the intellectual effort of Cantor / Doutorado / Doutor em Filosofia

Orientador: Fatima Regina Rodrigues Evora / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciências Huimanas / Made available in DSpace on 2018-08-21T20:51:35Z (GMT). No. of bitstreams: 1 Ramos_JosePortugaldosSantos_D.pdf: 2384313 bytes, checksum: e2f5697953843c457eadf3019953438a (MD5) Previous issue date: 2013 / Resumo: O propósito desta tese é explicar o método cartesiano por meio da lógica matemática que opera a sua constituição. Defende-se nesta pesquisa que, a partir dessa explicação do método, Descartes encontram meios que viabilizam a orientação de suas experimentações científicas. As experimentações científicas são iniciadas, então, quando Descartes encontra previamente uma determinada demonstração geométrica e visa, a partir desta, justificar os resultados da reconstrução de um fenômeno físico. No entanto, tal reconstrução requer outros meios da aplicação do método, pois neste momento trata-se da investigação de objetos que compõem um fenômeno físico. Nesta perspectiva, a aplicação do método de Descartes prescreve dois procedimentos de investigação científica, a saber, os procedimentos de redução e reconstrução. Sustenta-se nesta pesquisa que esses procedimentos requerem objetos manipuláveis que possibilitem, por meio do uso de suposições e analogias, a justificação experimental dos efeitos observados nos objetos físicos (ou seja, do fenômeno físico investigado). As obras de Descartes utilizadas nesta pesquisa são o Discurso do método e Ensaios complementares: A Geometria, a Dióptrica, os Meteoros, e ainda as Regras para orientação do espírito / Abstract: This thesis aims to explain the cartesian method through the mathematical logic which operates its constitution. It is defended in this thesis that, in this explanation of the method, Descartes finds geometric demonstrations that can guide his scientific experimentations. The scientific experimentations are started, so, when Descartes previously finds a particular geometrical demonstration and aims, through such demonstration, to justify the results of the reconstruction of physical phenomenon. However, such a reconstruction requires other means of the method's application, because in this moment it treats on the investigation of objects which compose a physical phenomenon. At this prospect, the application of Descartes' method prescribes two procedures of scientific enquiry, to wit, the ones of reduction and reconstruction. It is maintained in this thesis that such procedures require controllable objects which make possible, through suppositions and analogies, the experimental justification of the effects observed in the physics objects (i. e., as an investigated physical phenomenon). The works of Descartes used here are the Discourse on the Method and Complementary Essays: Geometry, Dioptrics, Meteors, and also Rules for the Direction of the Mind / Doutorado / Filosofia / Doutor em Filosofia

Doctorat en philosophie et lettres / info:eu-repo/semantics/nonPublished

No description available.

The fusion Ll ? Lr of two normal modal logics formulated in languages with disjoint sets of modal operators is the smallest normal modal logic containing Ll [ Lr. This paper proves that decidability, interpolation, uniform interpolation, and Halld?encompleteness are preserved under forming fusions of normal polyadic polymodal logics. Those problems remained open in [Fine & Schurz [3]] and [Kracht & Wolter [10]]. The paper defines the fusion `l ? `r of two classical modal consequence relations and proves that decidability transfers also in this case. Finally, these results are used to prove a general decidability result for modal logics based on superintuitionistic logics.

No description available.

The lower and upper independent, domination and irredundant numbers of the graph G = (V, E) are denoted by i ( G) , f3 ( G), 'Y ( G), r ( G), ir ( G) and IR ( G) respectively. These six numbers are called the domination parameters. For each of these parameters n:, we define six types of criticality. The graph G is n:-critical (n:+ -critical) if the removal of any vertex of G causes n: (G) to decrease (increase), G is n:-edge-critical (n:+-edge-critical) if the addition of any missing edge causes n: (G) to decrease (increase), and G is Ir-ER-critical (n:- -ER-critical) if the removal of any edge causes n: (G) to increase (decrease). For all the above-mentioned parameters n: there exist graphs which are n:-critical, n:-edge-critical and n:-ER-critical. However, there do not exist any n:+-critical graphs for n: E {ir,"f,i,/3,IR}, no n:+-edge-critical graphs for n: E {ir,"f,i,/3} and non:--ER-critical graphs for: E {'Y,/3,r,IR}. Graphs which are "I-critical, i-critical, "I-edge-critical and i-edge-critical are well studied in the literature. In this thesis we explore the remaining types of criticality. We commence with the determination of the domination parameters of some wellknown classes of graphs. Each class of graphs we consider will turn out to contain a subclass consisting of graphs that are critical according to one or more of the definitions above. We present characterisations of "I-critical, i-critical, "I-edge-critical and i-edge-critical graphs, as well as ofn:-ER-critical graphs for n: E {/3,r,IR}. These characterisations are useful in deciding which graphs in a specific class are critical. Our main results concern n:-critical and n:-edge-critical graphs for n: E {/3, r, IR}. We show that the only /3-critical graphs are the edgeless graphs and that a graph is IRcritical if and only if it is r-critical, and proceed to investigate the r-critical graphs which are not /3-critical. We characterise /3-edge-critical and r-edge-critical graphs and show that the classes of IR-edge-critical and r-edge-critical graphs coincide. We also exhibit classes of r+ -critical, r+ -edge-critical and i- -ER-critical graphs. / Mathematical Sciences / D. Phil. (Mathematics)

published_or_final_version / Mathematics / Master / Master of Philosophy

The lower and upper independent, domination and irredundant numbers of the graph G = (V, E) are denoted by i ( G) , f3 ( G), 'Y ( G), r ( G), ir ( G) and IR ( G) respectively. These six numbers are called the domination parameters. For each of these parameters n:, we define six types of criticality. The graph G is n:-critical (n:+ -critical) if the removal of any vertex of G causes n: (G) to decrease (increase), G is n:-edge-critical (n:+-edge-critical) if the addition of any missing edge causes n: (G) to decrease (increase), and G is Ir-ER-critical (n:- -ER-critical) if the removal of any edge causes n: (G) to increase (decrease). For all the above-mentioned parameters n: there exist graphs which are n:-critical, n:-edge-critical and n:-ER-critical. However, there do not exist any n:+-critical graphs for n: E {ir,"f,i,/3,IR}, no n:+-edge-critical graphs for n: E {ir,"f,i,/3} and non:--ER-critical graphs for: E {'Y,/3,r,IR}. Graphs which are "I-critical, i-critical, "I-edge-critical and i-edge-critical are well studied in the literature. In this thesis we explore the remaining types of criticality. We commence with the determination of the domination parameters of some wellknown classes of graphs. Each class of graphs we consider will turn out to contain a subclass consisting of graphs that are critical according to one or more of the definitions above. We present characterisations of "I-critical, i-critical, "I-edge-critical and i-edge-critical graphs, as well as ofn:-ER-critical graphs for n: E {/3,r,IR}. These characterisations are useful in deciding which graphs in a specific class are critical. Our main results concern n:-critical and n:-edge-critical graphs for n: E {/3, r, IR}. We show that the only /3-critical graphs are the edgeless graphs and that a graph is IRcritical if and only if it is r-critical, and proceed to investigate the r-critical graphs which are not /3-critical. We characterise /3-edge-critical and r-edge-critical graphs and show that the classes of IR-edge-critical and r-edge-critical graphs coincide. We also exhibit classes of r+ -critical, r+ -edge-critical and i- -ER-critical graphs. / Mathematical Sciences / D. Phil. (Mathematics)