Representação Matemática e Crítica às Teorias Indivisibilistas em Thomas Bradwardine
Resumo
Em seu tratado De continuo, escrito entre 1325 e 1343, Thomas Bradwardine (1290-1349) afirma que o contínuo da natureza (movimento, tempo, lugar e temperatura) pode ser representado e medido pelo contínuo matemático (linha superfície e sólido). No espaço geométrico, tal medida é possibilitada pelo uso de pontos (discretos, indivisíveis) como marcas do contínuo que se pretende medir. Como Aristóteles, Bradwardine compreende que o contínuo não pode ser constituído por indivisíveis. A despeito deste compromisso com Aristóteles, Bradwardine sugere que os pontos que marcam a representação matemática do contínuo da natureza representam partes do contínuo marcado. Em meu artigo, procuro mostrar como Bradwardine pode afirmar, ao mesmo tempo, que o contínuo da natureza pode ser representado pelo contínuo geométrico e, também, que esta representação não é a admissão de indivisíveis como partes componentes do contínuo.Palavras-chave: Contínuo. Atomismo. Thomas Bradwardine. Aristóteles.
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Referências
ARISTOTLE. The Complete Works of Aristotle: The Revised Oxford Translation. 2 vols, Princeton: Princeton University Press, 1995.
BRADWARDINE, T; GENET, J-F; TACHAU, K. (eds.). “La Lecture de Thomas Bradwardine sur les Sentences”. Archives d’Histoire Doctrinale et Littéraire du Moyen Age, t. 57, 1990-1991: 301-306.
BRADWARDINE; SAVILLE, H. (eds.). De causa Dei contra Pelagium et de virtute causarum ad suos Mertorenses libri tres... Londres, 1618.
DE LIBERA, A. La philosophie médiévale. Paris: PUF, 1995.
DOLNIKOWSKI, W. Thomas Bradwardine: A View of Time and a Vision of Eter-nity in Fourteenth-Century Thought. Leiden: Brill Academic Publishers, 1997.
GRANT. Source Book in Medieval Science. Harvard: Harvard University Press, 1974.
LIVESEY, S. Metabasis: The Interrelationship of the Science in Antiquity and the Middle Age. Ph.D. Thesis. Los Angeles: University of California, 1982.
LIVESEY, S. T. Theology and Science in the Fourteenth Century: Three Questions on the Unity and Subalternation of the Science from John of Reading’s Com-mentary on the Sentences. Leiden: E. J. Brill, 1989.
LIVESEY, S. “The Oxford Calculatores, Quantification of Qualities, Aristotle’s Prohibition of Metabasis”. Vivarium, XXIV, n. 1, 1986.
MURDOCH, J. E. Geometry and the Continuum in Fourteenth Century: A Philosophical Analysis of Thomas Bradwardine’s “Tractatus de Continuo”. Ph.D. Thesis. University of Wisconsin, 1957.
MURDOCH, J. “From Social into Intellectual Factors: An Aspect of the Unitary Character of Late Medieval Learning”. In: MURDOCH; SYLLA (eds.). The Cultural Context of Medieval Learning. Dordrecht: Reidel, 1975: 271-339.
MURDOCH, J. “Infinity and Continuity”. In: KRETZMAM; KENNY; PIN-BORG (eds.). Cambridge History of Later Medieval Philosophy. Cambridge: Cambridge University Press, 2003: 564-591.
O’BRIEN, D. Democritus Weight and Size: An Exercise in the Reconstruction of Early Greek Philosophy. Paris/Leiden: Les Belle Lettres/Brill, 1981.
SYLLA, E. “Thomas Bradwardine’s De continuo and the Structure of Fourteenth-Century Learning”. In: SYLLA; McVAUGH (eds.). Texts and Contexts in Ancient and Medieval Science: Studies on the Occasion of John E. Murdoch’s Seventieth Birthday. Leiden: E. J. Brill, 1997: 148-186.
BRADWARDINE, T; GENET, J-F; TACHAU, K. (eds.). “La Lecture de Thomas Bradwardine sur les Sentences”. Archives d’Histoire Doctrinale et Littéraire du Moyen Age, t. 57, 1990-1991: 301-306.
BRADWARDINE; SAVILLE, H. (eds.). De causa Dei contra Pelagium et de virtute causarum ad suos Mertorenses libri tres... Londres, 1618.
DE LIBERA, A. La philosophie médiévale. Paris: PUF, 1995.
DOLNIKOWSKI, W. Thomas Bradwardine: A View of Time and a Vision of Eter-nity in Fourteenth-Century Thought. Leiden: Brill Academic Publishers, 1997.
GRANT. Source Book in Medieval Science. Harvard: Harvard University Press, 1974.
LIVESEY, S. Metabasis: The Interrelationship of the Science in Antiquity and the Middle Age. Ph.D. Thesis. Los Angeles: University of California, 1982.
LIVESEY, S. T. Theology and Science in the Fourteenth Century: Three Questions on the Unity and Subalternation of the Science from John of Reading’s Com-mentary on the Sentences. Leiden: E. J. Brill, 1989.
LIVESEY, S. “The Oxford Calculatores, Quantification of Qualities, Aristotle’s Prohibition of Metabasis”. Vivarium, XXIV, n. 1, 1986.
MURDOCH, J. E. Geometry and the Continuum in Fourteenth Century: A Philosophical Analysis of Thomas Bradwardine’s “Tractatus de Continuo”. Ph.D. Thesis. University of Wisconsin, 1957.
MURDOCH, J. “From Social into Intellectual Factors: An Aspect of the Unitary Character of Late Medieval Learning”. In: MURDOCH; SYLLA (eds.). The Cultural Context of Medieval Learning. Dordrecht: Reidel, 1975: 271-339.
MURDOCH, J. “Infinity and Continuity”. In: KRETZMAM; KENNY; PIN-BORG (eds.). Cambridge History of Later Medieval Philosophy. Cambridge: Cambridge University Press, 2003: 564-591.
O’BRIEN, D. Democritus Weight and Size: An Exercise in the Reconstruction of Early Greek Philosophy. Paris/Leiden: Les Belle Lettres/Brill, 1981.
SYLLA, E. “Thomas Bradwardine’s De continuo and the Structure of Fourteenth-Century Learning”. In: SYLLA; McVAUGH (eds.). Texts and Contexts in Ancient and Medieval Science: Studies on the Occasion of John E. Murdoch’s Seventieth Birthday. Leiden: E. J. Brill, 1997: 148-186.
