Platão e Aristóteles na filosofia da matemática
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Data
2010-01-13
Autores
Barbosa, Gustavo [UNESP]
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Editor
Universidade Estadual Paulista (Unesp)
Resumo
O objetivo dessa pesquisa é participar da discussão acerca das diferentes concepções de Platão e Aristóteles a respeito da natureza e do estatuto ontológico dos entes matemáticos. Enquanto Platão situa o âmbito ontológico dos entes matemáticos entre dois mundos, o sensível e o inteligível, Aristóteles nega o caráter supra-sensível dos objetos matemáticos e oferece como resposta a sua filosofia empirista da matemática. Aristóteles teria dirigido duras críticas contra Platão e os acadêmicos nos dois últimos livros da Metafísica, M e N, respectivamente. Desde a antiguidade, vários autores sustentam que tais críticas referem-se às “doutrinas não-escritas” de Platão, que seriam cursos por ele ministrados na Academia, cujo teor ele não quis escrever por considerar que somente à dialética oral caberia o ensinamento dos primeiros princípios. Utilizando uma metodologia de pesquisa filosófica e também a história da filosofia e da matemática, foram abordados diversos textos, que vão desde livros e artigos atuais, até as próprias obras de Platão e Aristóteles relacionadas ao tema. Como parte das reflexões finais, o presente trabalho destaca a importância da exegese para uma correta interpretação das filosofias da matemática de Platão e Aristóteles e ainda das relações entre elas.
The research aim is the discussion about Plato and Aristotle’s different conceiving about the nature and the ontological status of mathematical entities. While Plato located the ontological scope of mathematical entities between two worlds, the sensible and the intelligible, Aristotle denies the character “super-sensible” of the mathematical entities and offers in response his own empiricist philosophy of mathematics. Aristotle would have direct harsh criticism to Plato and the academics in two last books of his Metaphysics, M and N, respectively. Since ancient times several authors argue that these criticism refer to “unwritten doctrines” of Plato, that they would be courses that he taught at the Academy, whose contents he did not want to write because he had believe that only oral dialectic should teach the first principles. Using a philosophical methodology of research and also the history of philosophy and mathematics several texts were discussed, like current books and articles as well as works of Plato and Aristotle about the theme. As part of final reflection, the present work highlights the exegesis importance for a correct interpretation of the mathematics philosophy from Plato and Aristotle and even the relationships between them.
The research aim is the discussion about Plato and Aristotle’s different conceiving about the nature and the ontological status of mathematical entities. While Plato located the ontological scope of mathematical entities between two worlds, the sensible and the intelligible, Aristotle denies the character “super-sensible” of the mathematical entities and offers in response his own empiricist philosophy of mathematics. Aristotle would have direct harsh criticism to Plato and the academics in two last books of his Metaphysics, M and N, respectively. Since ancient times several authors argue that these criticism refer to “unwritten doctrines” of Plato, that they would be courses that he taught at the Academy, whose contents he did not want to write because he had believe that only oral dialectic should teach the first principles. Using a philosophical methodology of research and also the history of philosophy and mathematics several texts were discussed, like current books and articles as well as works of Plato and Aristotle about the theme. As part of final reflection, the present work highlights the exegesis importance for a correct interpretation of the mathematics philosophy from Plato and Aristotle and even the relationships between them.
Descrição
Palavras-chave
Matemática - Filosofia, Platão, Aristóteles, Exegese, Philosophy of mathematics, Exegesis
Como citar
BARBOSA, Gustavo. Platão e Aristóteles na filosofia da matemática. 2009. 134 f. Dissertação (mestrado) - Universidade Estadual Paulista, Instituto de Geociências e Ciências Exatas, 2009.