Robert Halifax, un calculador de sombras de Oxford
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Resumen
En su Comentario a las Sentencias de Pedro Lombardo, cuestión 1, Robert Halifax OFM presenta un argumento óptico notablemente original e inventivo. Compara dos pares de cuerpos luminosos y opacos con dos conos de sombra hasta que los cuerpos luminosos alcanzan el cenit. Al situar en los conos de sombra a dos seres humanos en movimiento cuya evolución moral es paralela al tamaño de las sombras, Halifax crea un teatro de sombras sin precedentes, dotado matemáticas y los teoremas del movimiento derivados del Tratado de las Proporciones de Thomas Bradwardine. Este artículo es un primer intento de analizar este experimento imaginario y las matemáticas del infinito por él implicadas. Él muestra además que la óptica ha tenido nuevos objetivos a través de su conexión con los teoremas del movimiento de los Calculadores de Oxford.
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ARTÍCULOS
Bibliografía
Bibliography
Manuscripts
Paris, Bibliothèque Nationale de France, Lat. 15880
Vaticano, Biblioteca Apostolica Vaticana, Lat. 1111
Primary sources
Johannes de Sacro Bosco, Opusculum de sphaera mundi (Paris: Jean Petit, 1495).
Richard Kilvington, Quaestiones super libros Ethicorum, edited by M. Michałowska (Leiden: Brill, 2016).
The Sophismata of Richard Kilvington, edited by N. Kretzmann and B. E. Kretzmann (Oxford: Oxford University Press, 1990).
Thomas of Bradwardine, His Tractatus de proportionibus. Its Significance for the Development of Mathematical Physics, edited and translated by H. Lamar Crosby, Jr. (Madison (WI): The University of Wisconsin Press, 1955).
Thomas Bradwardine, Traité des rapports entre les rapidités dans les mouvements, translated by S. Rommevaux (Paris: Les Belles Lettres, 2010).
Secondary sources
Chen-Morris, Raz, Measuring Shadows: Keplerʼs Optics of Invisibility (University Park, PA: Penn State University Press, 2016).
Clagett, Marshall, The Science of Mechanics in the Middle Ages (Madison, WI: The University of Wisconsin Press, 1959).
Courtenay, William J., “Some Notes on Robert of Halifax OFM”, Franciscan Studies 33 (1977): 135-142.
De la théologie aux mathématiques. Lʼinfini au XIVe siècle, edited by J. Biard and J. Celeyrette (Paris: Les Belles Lettres, 2005).
Dictionary of Medieval Latin from British Sources, 3 vols., prepared by R. K. Ashdowne, D. R. Howlett and R. E. Latham (Oxford: Oxford University Press, 2018).
Di Liscia, Daniel A., “Perfections and Latitudes. The Development of the Calculatorsʼ Tradition and the Geometrisation of Metaphysics and Theology”, in Quantifying Aristotle. The Impact, Spread, and Decline of the Calculatores Tradition, edited by D. A. Di Liscia and E. D. Sylla (Leiden: Brill, 2022), 278-327.
Genest, Jean-François, “Les premiers écrits théologiques de Bradwardine: textes inédits et découvertes récentes”, in Mediaeval Commentaries on the Sentences of Peter Lombard, edited by G. Evans (Leiden: Brill, 2002), 395-421.
Jung, Elżbieta, and Podkoński, Robert, Towards the Modern Theory of Motion: Oxford Calculators and the New Interpretation of Aristotle (Łódż: Łódż University Press, 2020).
Lička, Lukáš, “Shadows in Medieval Optics, Practical Geometry, and Astronomy: On a Perspectiva Ascribed to Thomas Bradwardine”, Early Science and Medicine 27 (2022): 179-223.
Lukács, Edit Anna, “Calculations in Thomas Bradwardineʼs De causa Dei, Book I”, in Quantifying Aristotle. The Impact, Spread, and Decline of the Calculatores Tradition, edited by D. A. Di Liscia and E. D. Sylla (Leiden: Brill, 2022), 106-125.
Lukács, Edit Anna, “Robert Halifax on the Middle Act of the Will”, forthcoming.
Michałowska, Monika, “Kilvingtonʼs Use of Physical and Logical Arguments in Ethical Dilemmas”, Documenti e studi sulla tradizione filosofica medievale 22 (2011): 467-494.
Molland, George, “The Geometrical Background to the ʻMerton Schoolʼ”, The British Journal for the History of Science 4, 2 (1968): 108-125.
Murdoch, John E., “The Medieval Language of Proportions: Elements of the Interaction with Greek Foundations and the Development of New Mathematical Techniques”, in Scientific Change. Historical studies in the intellectual, social and technical conditions for scientific discovery and technical invention, from antiquity to the present, edited by A. C. Crombie (New York: Basic Books, 1963), 237-271.
Murdoch, John E. and Sylla, Edith D., “The Science of Motion”, in Science in the Middle Ages, edited by D. C. Lindberg (Chicago: Chicago University Press, 1978), 206-264.
Murdoch, John E., “Subtilitates Anglicanae in Fourteenth-Century Paris: John of Mirecourt and Peter Ceffons”, in Machautʼs World. Science and Art in the Fourteenth Century, edited by M. P. Cosman and B. Chandler (New York: New York Academy of Sciences, 1978), 51-86.
North, John D., Stars, Minds and Fate. Essays in Ancient and Medieval Cosmology (London: The Hambledon Press, 1989).
Quantifying Aristotle. The Impact, Spread, and Decline of the Calculatores Tradition, edited by D. A. Di Liscia and E. D. Sylla (Leiden: Brill, 2022).
Rosier-Catach, Irène, “Roger Bacon and Grammar”, in Roger Bacon and the Sciences. Commemorative Essays, edited by J. Hackett (Leiden: Brill, 1997), 67-102.
Roudaut, Sylvain, La mesure de lʼêtre: Le problème de la quantification des formes au Moyen Âge (ca. 1250-1370) (Leiden: Brill, 2022).
Sylla, Edith D., “The Oxford Calculators”, in The Cambridge History of Later Medieval Philosophy. From the Rediscovery of Aristotle to the Disintegration of Scholasticism, 1100–1600, edited by N. Kretzmann, A. Kenny, J. Pinborg and E. Stump (Cambridge: Cambridge University Press, 1982), 540-563.
Manuscripts
Paris, Bibliothèque Nationale de France, Lat. 15880
Vaticano, Biblioteca Apostolica Vaticana, Lat. 1111
Primary sources
Johannes de Sacro Bosco, Opusculum de sphaera mundi (Paris: Jean Petit, 1495).
Richard Kilvington, Quaestiones super libros Ethicorum, edited by M. Michałowska (Leiden: Brill, 2016).
The Sophismata of Richard Kilvington, edited by N. Kretzmann and B. E. Kretzmann (Oxford: Oxford University Press, 1990).
Thomas of Bradwardine, His Tractatus de proportionibus. Its Significance for the Development of Mathematical Physics, edited and translated by H. Lamar Crosby, Jr. (Madison (WI): The University of Wisconsin Press, 1955).
Thomas Bradwardine, Traité des rapports entre les rapidités dans les mouvements, translated by S. Rommevaux (Paris: Les Belles Lettres, 2010).
Secondary sources
Chen-Morris, Raz, Measuring Shadows: Keplerʼs Optics of Invisibility (University Park, PA: Penn State University Press, 2016).
Clagett, Marshall, The Science of Mechanics in the Middle Ages (Madison, WI: The University of Wisconsin Press, 1959).
Courtenay, William J., “Some Notes on Robert of Halifax OFM”, Franciscan Studies 33 (1977): 135-142.
De la théologie aux mathématiques. Lʼinfini au XIVe siècle, edited by J. Biard and J. Celeyrette (Paris: Les Belles Lettres, 2005).
Dictionary of Medieval Latin from British Sources, 3 vols., prepared by R. K. Ashdowne, D. R. Howlett and R. E. Latham (Oxford: Oxford University Press, 2018).
Di Liscia, Daniel A., “Perfections and Latitudes. The Development of the Calculatorsʼ Tradition and the Geometrisation of Metaphysics and Theology”, in Quantifying Aristotle. The Impact, Spread, and Decline of the Calculatores Tradition, edited by D. A. Di Liscia and E. D. Sylla (Leiden: Brill, 2022), 278-327.
Genest, Jean-François, “Les premiers écrits théologiques de Bradwardine: textes inédits et découvertes récentes”, in Mediaeval Commentaries on the Sentences of Peter Lombard, edited by G. Evans (Leiden: Brill, 2002), 395-421.
Jung, Elżbieta, and Podkoński, Robert, Towards the Modern Theory of Motion: Oxford Calculators and the New Interpretation of Aristotle (Łódż: Łódż University Press, 2020).
Lička, Lukáš, “Shadows in Medieval Optics, Practical Geometry, and Astronomy: On a Perspectiva Ascribed to Thomas Bradwardine”, Early Science and Medicine 27 (2022): 179-223.
Lukács, Edit Anna, “Calculations in Thomas Bradwardineʼs De causa Dei, Book I”, in Quantifying Aristotle. The Impact, Spread, and Decline of the Calculatores Tradition, edited by D. A. Di Liscia and E. D. Sylla (Leiden: Brill, 2022), 106-125.
Lukács, Edit Anna, “Robert Halifax on the Middle Act of the Will”, forthcoming.
Michałowska, Monika, “Kilvingtonʼs Use of Physical and Logical Arguments in Ethical Dilemmas”, Documenti e studi sulla tradizione filosofica medievale 22 (2011): 467-494.
Molland, George, “The Geometrical Background to the ʻMerton Schoolʼ”, The British Journal for the History of Science 4, 2 (1968): 108-125.
Murdoch, John E., “The Medieval Language of Proportions: Elements of the Interaction with Greek Foundations and the Development of New Mathematical Techniques”, in Scientific Change. Historical studies in the intellectual, social and technical conditions for scientific discovery and technical invention, from antiquity to the present, edited by A. C. Crombie (New York: Basic Books, 1963), 237-271.
Murdoch, John E. and Sylla, Edith D., “The Science of Motion”, in Science in the Middle Ages, edited by D. C. Lindberg (Chicago: Chicago University Press, 1978), 206-264.
Murdoch, John E., “Subtilitates Anglicanae in Fourteenth-Century Paris: John of Mirecourt and Peter Ceffons”, in Machautʼs World. Science and Art in the Fourteenth Century, edited by M. P. Cosman and B. Chandler (New York: New York Academy of Sciences, 1978), 51-86.
North, John D., Stars, Minds and Fate. Essays in Ancient and Medieval Cosmology (London: The Hambledon Press, 1989).
Quantifying Aristotle. The Impact, Spread, and Decline of the Calculatores Tradition, edited by D. A. Di Liscia and E. D. Sylla (Leiden: Brill, 2022).
Rosier-Catach, Irène, “Roger Bacon and Grammar”, in Roger Bacon and the Sciences. Commemorative Essays, edited by J. Hackett (Leiden: Brill, 1997), 67-102.
Roudaut, Sylvain, La mesure de lʼêtre: Le problème de la quantification des formes au Moyen Âge (ca. 1250-1370) (Leiden: Brill, 2022).
Sylla, Edith D., “The Oxford Calculators”, in The Cambridge History of Later Medieval Philosophy. From the Rediscovery of Aristotle to the Disintegration of Scholasticism, 1100–1600, edited by N. Kretzmann, A. Kenny, J. Pinborg and E. Stump (Cambridge: Cambridge University Press, 1982), 540-563.