Scientiae Studia 11 (2):391-416 (2013)

Authors
Jacintho Del Vecchio Junior
University of São Paulo
Abstract
Este texto introduz a tradução do discurso de intitulado "Sobre os números transfinitos" ("Über transfinite Zahlen"), proferido por Henri Poincaré em 27 de abril de 1909, na Universidade de Göttingen. Após uma breve apresentação do pensamento do autor acerca dos fundamentos da aritmética, procura-se citar os aspectos mais relevantes da chamada crise dos fundamentos da matemática, para então introduzir a reformulação do conceito de predicatividade aventada no referido discurso sobre números transfinitos, contribuição compreendida como um recurso teórico necessário para a superação dos paradoxos relativos à teoria dos conjuntos. Com isso, pretende-se evidenciar o papel central do texto publicado nesta edição para o desenvolvimento da concepção matemática de Henri Poincaré. This article provides an introduction to the translation of the lecture entitled "On transfinite numbers" ("Über transfinite Zahlen"), given by Henri Poincaré at the University of Göttingen on April 27, 1909. Following a short presentation of Poincaré's views on the foundations of arithmetic, it identifies the aspects of the so-called crisis of the foundations of mathematics that are most relevant for understanding his reconstruction of the concept of predicativity, which is intended to be a theoretical resource that may overcome the paradoxes of set theory. In doing so, the article highlights the central role of this text in the process of maturation of Poincaré's views on the foundations of mathematics
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References found in this work BETA

On Some Difficulties in the Theory of Transfinite Numbers and Order Types.Bertrand Russell - 1906 - Proceedings of the London Mathematical Society 4 (14):29-53.
On Some Difficulties in the Theory of Transfinite Numbers and Order Types.Harold Chapman Brown - 1906 - Journal of Philosophy, Psychology and Scientific Methods 3 (14):388-390.
Contributions to the Founding of the Theory of Transfinite Numbers.Cassius J. Keyser - 1916 - Journal of Philosophy, Psychology and Scientific Methods 13 (25):697-697.

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