Lie, Nga Sze. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 103-111). / Abstracts in English and Chinese. / Abstract --- p.i / Chapter 1 --- Introduction and Preliminary Discussions --- p.1 / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.1.1 --- Overview of the Thesis --- p.2 / Chapter 1.1.2 --- Background --- p.3 / Chapter 1.1.3 --- About Chapter 3: Details of the Theory --- p.4 / Chapter 1.1.4 --- About Chapter 4: Defects of the Theory --- p.7 / Chapter 1.2 --- Preliminary Discussions --- p.12 / Chapter 1.2.1 --- number --- p.12 / Chapter 1.2.2 --- mathematical existence and abstract reality --- p.12 / Chapter 1.2.3 --- finite/infinite --- p.12 / Chapter 1.2.4 --- actually/potentially infinite --- p.13 / Chapter 1.2.5 --- denumerability --- p.13 / Chapter 1.3 --- Concluding Remarks --- p.14 / Chapter 2 --- Mapping Mathematical Philosophies --- p.15 / Chapter 2.1 --- Preview --- p.15 / Chapter 2.1.1 --- Nominalism --- p.16 / Chapter 2.1.2 --- Conceptualism --- p.16 / Chapter 2.1.3 --- Intuitionism --- p.17 / Chapter 2.1.4 --- Realism --- p.18 / Chapter 2.1.5 --- Empiricism --- p.19 / Chapter 2.1.6 --- Logicism --- p.19 / Chapter 2.1.7 --- Neo-logicism --- p.21 / Chapter 2.1.8 --- Formalism --- p.21 / Chapter 2.1.9 --- Practicism --- p.23 / Chapter 2.2 --- Central Problem of Philosophy of Mathematics --- p.23 / Chapter 2.3 --- Metaphysics --- p.24 / Chapter 2.3.1 --- Abstractism --- p.24 / Chapter 2.3.2 --- Abstractist Schools --- p.25 / Chapter 2.3.3 --- Non-abstractism --- p.25 / Chapter 2.3.4 --- Non-abstractist Schools --- p.26 / Chapter 2.4 --- Semantics --- p.26 / Chapter 2.4.1 --- Literalism --- p.26 / Chapter 2.4.2 --- Literalistic schools --- p.27 / Chapter 2.4.3 --- Non-literalism --- p.27 / Chapter 2.4.4 --- Non-literalistic schools --- p.27 / Chapter 2.5 --- Epistemology --- p.28 / Chapter 2.5.1 --- Scepticism --- p.28 / Chapter 2.5.2 --- Scepticist Schools --- p.28 / Chapter 2.5.3 --- Non-scepticism --- p.29 / Chapter 2.5.4 --- Non-scepticist Schools --- p.29 / Chapter 2.6 --- Foundations of Mathematics --- p.30 / Chapter 2.6.1 --- Foundationalism --- p.31 / Chapter 2.6.2 --- Foundationalist Schools --- p.32 / Chapter 2.6.3 --- N on-foundationalism --- p.33 / Chapter 2.6.4 --- Non-foundationalist schools --- p.33 / Chapter 2.7 --- Finitistic Considerations --- p.33 / Chapter 2.7.1 --- Finitism --- p.41 / Chapter 2.7.2 --- Finitist Schools --- p.42 / Chapter 2.7.3 --- Non-finitism --- p.44 / Chapter 2.7.4 --- Non-finitist Schools --- p.44 / Chapter 2.8 --- Finitistic Reconsiderations --- p.44 / Chapter 2.8.1 --- C-finitism --- p.45 / Chapter 2.8.2 --- C-finitist Schools --- p.45 / Chapter 2.8.3 --- Non-C-finitism --- p.46 / Chapter 2.8.4 --- Non-C-finitist Schools --- p.46 / Chapter 2.9 --- Concluding Remarks --- p.47 / Chapter 3 --- Principles of Transfinite Theory --- p.48 / Chapter 3.0.1 --- Historical Notes on Infinity --- p.48 / Chapter 3.0.2 --- Cantor´ةs Proof --- p.49 / Chapter 3.1 --- The Domain Principle --- p.51 / Chapter 3.1.1 --- Variables and Domain --- p.53 / Chapter 3.1.2 --- Attack and Defense --- p.54 / Chapter 3.2 --- The Enumeral Principle --- p.56 / Chapter 3.2.1 --- Cantor´ةs Ordinal Theory of Numbers --- p.58 / Chapter 3.2.2 --- A Well-ordered Set --- p.59 / Chapter 3.2.3 --- An Enumeral --- p.59 / Chapter 3.2.4 --- An Ordinal Number --- p.60 / Chapter 3.2.5 --- Attack and Defense --- p.60 / Chapter 3.3 --- The Abstraction Principle --- p.63 / Chapter 3.3.1 --- Cantor´ةs Cardinal Theory of Numbers --- p.64 / Chapter 3.3.2 --- An Abstract One --- p.65 / Chapter 3.3.3 --- One-one Correspondence --- p.65 / Chapter 3.3.4 --- A Cardinal Number --- p.65 / Chapter 3.3.5 --- Attack and Defense --- p.65 / Chapter 3.4 --- Concluding Remarks --- p.68 / Chapter 4 --- Problems in Transfinite Theory --- p.70 / Chapter 4.1 --- Structure and Procedure --- p.70 / Chapter 4.1.1 --- Free Mathematics --- p.72 / Chapter 4.1.2 --- Non-constructive Proof --- p.75 / Chapter 4.2 --- Number and Numerosity --- p.85 / Chapter 4.2.1 --- Weak Reductionism --- p.85 / Chapter 4.2.2 --- Non-Cantorian Sets --- p.87 / Chapter 4.2.3 --- Intension in an Extensional Theory --- p.89 / Chapter 4.3 --- Conceivability and Comparability --- p.95 / Chapter 4.3.1 --- Tension with Absolute Infinity --- p.95 / Chapter 4.4 --- Conclusion --- p.100 / Bibliography --- p.103

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: Michael B. Wrigley / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Filosofia e Ciencias Humanas / Made available in DSpace on 2018-07-21T09:22:59Z (GMT). No. of bitstreams: 1 Vilela_DeniseSilva_M.pdf: 5000035 bytes, checksum: 7f99d443a1b422dc4a4ff7bfeb08b4b0 (MD5) Previous issue date: 1996 / Resumo: Não informado / Abstract: Not informed. / Mestrado / Mestre em Filosofia

Cette recherche est une exploration des concepts de temps et de possible, au travers d'une conceptualité kierkegaardienne. Le point de départ est le moment d'une naissance qui, lorsque rapporté sur la question de la création de l'univers, impose d'emblée d'explorer le concept d'infini actuel, clarifié à l'aide de Cantor. L'Origine objective du monde est rapportée sur une décision subjective de l'individu. L'éternel retour comme thèse cosmologique est rejetée et resituée comme thèse existentielle et éthique, tout comme l'hypothèse de Dieu n'a un sens existentiel que comme condition de la passion, ce qui impose de revisiter la vérité comme subjectivité plutôt que comme objectivité ou adéquation entre la pensée et la chose. En conséquence, non seulement la réalité mais aussi la possibilité, qui correspond à l'avenir, est motivateur existentiel, c'est-à-dire moteur pour l'action.