“…cupiens mathematicam tractare infra radices metaphysice…” Roger Bacon sobre la abstracción matemática
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En algunos pasajes del Opus maius y del Opus tertium, Roger Bacon sostiene que los objetos matemáticos son los objetos inmediatos y adecuados del intelecto humano: en nuestra vida sensible, el intelecto se desarrolla fundamentalmente en torno a la cantidad. Comprendemos las cantidades y los cuerpos mediante una percepción del intelecto, porque sus formas pertenecen al intelecto, es decir, para nosotros la comprensión de las verdades matemáticas es prácticamente innata. Una reacción natural a estas afirmaciones consistirá en deducir una fuerte influencia pitagórica o platónica en la teoría del conocimiento matemático de Roger Bacon. Sin embargo, Bacon siempre ha seguido el punto de vista de Aristóteles, según el cual los números y las figuras no tienen una existencia real aparte de las sustancias sensibles ‒ y el conocimiento universal proviene también de la experiencia sensorial. Parece que la afirmación de Bacon de que la cantidad es el primer objeto del intelecto humano tiene su origen en una lectura original de un pasaje de Sobre la memoria y la reminiscencia de Aristóteles. En este trabajo se intentan aclarar las opiniones de Bacon sobre la abstracción matemática y la percepción intelectual de las formas matemáticas en sus cuestiones parisinas sobre la Física y el Liber de causis, la Perspectiva, el Opus maius, el Opus tertium, la Communia mathematica y la Geometria speculativa. Concluimos que Bacon consideraba la abstracción matemática como un modo de percepción de la estructura interna del mundo físico: la abstracción matemática no significa para Bacon un acto de separación de las formas ideales de la materia sensible, sino una posibilidad de intuición de la estructura interna del mundo sensible, facultad que es necesaria para la percepción humana del espacio y del tiempo.
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Bibliografía
Primary sources
Roger Bacon’s works
Letter to Pope Clement IV, edited and translated by N. Egel, Revista Española de Filosofía Medieval, 27/2 (2020): 143-174.
De viciis contractis in theologia, edited by R. Steele, Opera hactenus inedita Rogeri Baconi, fasc. 1 (Oxford: Clarendon Press, 1905).
Summulae Dialectices, edited by A. De Libera, “Les Summulae dialectices de Roger Bacon”, Archives d’Histoire Doctrinale et Littéraire du Moyen Âge 53 (1986): 139-289, and Archives d’Histoire Doctrinale et Littéraire du Moyen Âge 54 (1987): 171-278.
Qu. prime phil.: Questiones supra libros prime philosophie Aristotelis, edited by R. Steele and F. M. Delorme, Opera hactenus inedita Rogeri Baconi, fasc. 10. (Oxford: Clarendon Press, 1930).
Qu. octo phys.: Questiones supra libros octo physicorum aristotelis, edited by F. M. Delorme and R. Steele, Opera hactenus inedita Rogeri Baconi, fasc. 13. (Oxford: Clarendon Press, 1935).
Qu. lib. De causis: Questiones supra librum de causis, edited by R. Steele and F. M. Delorme, Opera hactenus inedita Rogeri Baconi, fasc. 12. (Oxford: Clarendon Press, 1935).
Opus maius, edited by J. H. Bridges, 3 vols. (Oxford and Edinburgh: Clarendon Press, 1897-1900).
Opus maius, Part IV, English translation by P. W. Dennis, Roger Bacon’s Mathematical Thought: A translation of Part IV of the Opus maius with Introduction and Commentary, by P. Willard Dennis, Ph Dissertation (Dallas: University of Texas, 2011).
Opus tertium, edited and translated into German, with notes, by N. Egel (Philosophische Bibbliothek Band 718) (Hamburg: Felix Meiner Verlag, 2019).
De multiplicatione specierum, edited and translated by D. C. Lindberg, Roger Bacon’s Philosophy of Nature (Oxford: Clarendon Press, 1983).
Communia Naturalium, edited by R. Steele, Opera hactenus inedita Rogeri Baconi, fasc. 2-4. (Oxford: Clarendon Press, 1910-1913).
Communia Mathematica, edited by R. Steele, Opera hactenus inedita Rogeri Baconi, fasc. 16. (Oxford: Clarendon Press, 1940).
Perspectiva, edited and translated into English by D.C. Lindberg, Roger Bacon and the Origins of Perspectiva in the Middle Ages (Oxford: Clarendon Press, 1996).
Geometria Speculativa, edited and translated into English by G. Molland, “Roger Bacon’s Geometria Speculativa”, in Vestigia Mathematica. Studies in medieval and early modern mathematics in honour of H.L.L. Busard, edited by M. Folkerts and J. P. Hogendijk, (Amsterdam: Rodopi B.V. Editions, 1993), 265-303.
Other Primary sources
Les auctoritates Aristotelis. Un florilège médiéval. Etude historique et édition critique par J. Hamesse (Philosophes Médiévaux 17) (Louvain: Presses Universitaires, 1974).
Avicenna’s Metaphysics (Avicenna Latinus): Liber de philosophia prima sive scientia divina, edited by S. Van Diet, 2 vols. (Louvain: E. Peters; Leiden: E. J. Brill, 1977).
Al-Kindi, De aspectibus: L’optique et la Catoptrique (Œuvres Philosophiques et Scientifiques d’Al-Kindi, vol.1; Islamic Philosophy Theology and Science. Texts and Studies, vol. 29), edited by R. Rashed (Leiden: E.J. Brill, 1997) – Liber Jacob Alkindi De causis diversitatum aspectus et dandis demonstrationibus geometris super eas, 439-523.
Pseudo-Bacon, Questiones super Libros IV Physicorum Aristotelis, edited by F. M. Delorme, Opera Hactenus Inedita Rogeri Baconi, fasc. 8 (Oxford: Clarendon Press, 1928).
Pseudo-Bacon, Questiones altere supra libros prime philosophie Aristotelis, edited by R. Steele and F. M. Delorme, Opera hactenus inedita Rogeri Baconi, fasc. 11 (Oxford: Clarendon Press, 1932).
Petrus Iohannis Olivi, O.F.M., Quaestiones in secundum librum Sententiarum, edited by B. Jansen, 3 vols., Bibliotheca Franciscana Scholastica Medii Aevi (Quaracchi: Collegium S. Bonaventurae, 1922-1926).
Moses Maimonides, Guide of the perplexed, translated by S. Pines, 2 vols. (Chicago: The University of Chicago Press, 1963).
Secondary sources
Bäck, Allan, Aristotle’s Theory of Abstraction (Heidelberg, New York, London: Springer, 2014).
Bérubé, Camille, La connaissance de l’individuel au Moyen Age (Montréal, Paris: Presses Universitaires de Montréal, Presses Universitaires de France, 1964).
Bloch, David, Aristotle on Memory and Recollection. Text, Translation, Interpretation, and Reception in Western Scholasticism (Leiden, Boston: Brill, 2007).
Cleary, John J., Aristotle in Mathematics. Aporetic Method in Cosmology and Metaphysics (Leiden, New York, Köln: E. J. Brill, 1995).
Crowley, Theodore, “Roger Bacon: The Problem of Universals in His Philosophical Commentaries”, Bulletin of the John Ryland's Library 34 (1951): 264-75.
Crisciani, Chiara, “Universal and particular in the Communia Naturalium: between ‘extreme realism’ and ‘experientia’”, in Roger Bacon’s Communia Naturalium. A 13th Century Philosopher’s Workshop, edited by P. Bernardini and A. Rodolfi (Micrologus Library) (Firenze: SISMEL-Edizioni di Galluzzo, 2014), 57-82.
Demange, Dominique, “Olivi et les Perspectivi. Les sources de la théorie olivienne de la vision” Oliviana 5 (2016): http://journals.openedition.org/oliviana/850.
Donati, Sylvia, “Pseudoepigrapha in the Opera hactenus inedita Rogeri Baconi? The Commentaries on the Physics and on the Metaphysics” in Les débuts de l’enseignement universitaire à Paris (1200-1245 environ), edited by O. Weijers and J. Verger (Turnhout: Brepols, 2013), 153-203.
Hackett, Jeremiah, “Roger Bacon (B. CA. 1214/20; D. 1292)”, in Individuation in Scholasticism. The Later Middle Ages and the Counter-Reformation, 1150-1650, edited by J. E. Gracia (Albany: State University of New York Press, 1994), 117-139.
Hackett, Jeremiah, “Roger Bacon on the classification of the sciences” in Roger Bacon and the Sciences. Commemorative essays, edited by J. Hackett (Leiden, New York, Köln: E. J. Brill, 1997), 49-65.
Hackett, Jeremiah, “Robert Grosseteste and Roger Bacon on the Posterior Analytics”, in Erkenntnis Und Wissenschaft/ Knowledge and Science: Probleme der Epistemologie in der Philosophie des Mittelalters/ Problems of Epistemology in Medieval Philosophy, edited by P. Antolic-Piper, A. Fidora and M. Lutz-Bachmann (Berlin and Boston: De Gruyter, 2004), 161-212.
Hackett, Jeremiah, “Roger Bacon on Animal Knowledge in the Perspectiva”, in Philosophical Psychology in Arabic Thought and The Latin Aristotelianism of the 13th Century, edited by L. X. Lòpez-Farjeat and J. A. Tellkamp (Paris: Vrin, 2013), 23-42.
Hackett, Jeremiah, “Motion, Time and Aevum in Roger Bacon’s Communia Naturalium: Context and Content”, in Roger Bacon’s Communia Naturalium. A 13th Century Philosopher’s Workshop, edited by P. Bernardini and A. Rodolfi (Micrologus Library) (Firenze: SISMEL-Edizioni di Galluzzo, 2014), 191-213.
Helmig, Christoph, “Aristotle’s Notion of Intelligible Matter”, Quaestio 7 (2007): 53-78.
Katz, Emily, “Geometrical Objects as Properties of Sensibles: Aristotle’s Philosophy of Geometry”, Phronesis 64 (2019): 465-513.
King, Peter, “Thinking about Things: Singular Thought in the Middle Ages” in Intentionality, Cognition, and Mental Representation in Medieval Philosophy, edited by G. Klima (New York: Fordham University Press, 2015), 104-121.
Lear, Jonathan, “Aristotle’s Philosophy of Mathematics”, The Philosophical Review 91/2 (1982): 161-192
Lička, Lukáš, “The Visual Process: Immediate or Successive? Approaches to the Extramission Postulate in 13th Century Theories of Vision”, in Medieval Perceptual Puzzles: Theories of Sense-Perception in the 13th and 14th Centuries, edited by E. Băltuță (Leiden: E. J. Brill, 2020), 73-110.
Lindberg, David C., Theories of Vision from Al-Kindi to Kepler (Chicago and London: University of Chicago Press, 1976).
Lindberg, David C., “On the Applicability of Mathematics to Nature: Roger Bacon and his Predecessors”, The British Journal for the History of Science 15/1 (1982): 3-25.
Maier, Anneliese, Metaphysische Hintergründe des Spätscholastischen Philosophie, Kap. 3 (“Das Problem Der Quantität oder der räumlischen Ausdehnung”) (Roma: Edizioni di Storia e Letteratura, 1955).
Maloney, Thomas, “The Extreme Realism of Roger Bacon”, The Review of Metaphysics 38 (1985): 807-837.
Maloney, Thomas, Three Treatments of Universals by Roger Bacon. A translation with introduction and notes (State University of New York at Binghamton: Center for Medieval and Early Renaissance Studies, 1989).
Molland, George, “Roger Bacon’s Knowledge of Mathematics” in Roger Bacon and the Sciences. Commemorative essays, edited by J. Hackett (Leiden, New York, Köln: E. J. Brill, 1997), 151-174.
Oelze, Anselm, Animal Rationality, Later Medieval Theories 1250-1350 (Leiden and New York: E. J. Brill, 2018).
Panti, Cecilia, “Natural Continuity and the Mathematical Proofs Against Indivisibilism in Roger Bacon’s De Celestibus (Communia Naturalium, II)” in Roger Bacon’s Communia Naturalium. A 13th Century Philosopher’s Workshop, edited by P. Bernardini and A. Rodolfi (Firenze: SISMEL-Edizioni di Galluzzo, 2014), 159-190.
Panti, Cecilia, “Non abest nec distat. Place and Movement of Angels according to Robert Grosseteste, Adam Marsh and Roger Bacon.” In Lieu, espace, mouvement: physique, métaphysique et cosmologie (XIIe-XVIe siècles). Actes du Colloque international Université de Fribourg (Suisse), 12-14 mars 2015, edited by T. Suarez-Nani, O. Ribordy and A. Petagine (Barcelona and Roma: FIDEM, 2017), 57-77.
Pereira, Michela, “Roger Bacon on Nature”, in The philosophy of science of Roger Bacon, Studies in Honour of Jeremiah Hackett, edited by N. Polloni and Y. Kedar (London and New York: Routledge, 2021), 17-35.
Raizman-Kedar, Yael, “The Intellect Naturalized: Roger Bacon on the Existence of Corporeal Species within the Intellect”, Early Science and Medecine 14 (2009): 131-157.
Risi, Vicenzo de, “Did Euclid Prove Elements I, 1? The Early Modern Debate on Intersections and Continuity”, in Reading Mathematics in the Early Modern Europe. Studies in the Production, Collection, and Use of Mathematical Books, ed. P. Beeley, Y. Nasifoglu and B. Wardhaugh (London: Routledge 2020), 12-32.
Sabra, Abdelhamid I., “Sensation and inference in Alhazen’s Theory of visual perception”, in Studies in Perception: Interrelations in the History of Philosophy and Science, edited by P. K. Machamer and R. G. Turnbull (Columbus: Ohio State University Press, 1978), 160-185 – reprint in Sabra, Abdelhamid I., Optics, Astronomy and Logic. Studies in Arabic Science and Philosophy (Aldershot: Ashgate Variorum, 1994).
Smith, A. Mark, “Spatial Representation in Medieval Visual Theory”, in Représentations et conceptions de l’espace dans la culture médiévale. Repräsentationsformen und Konzeptionen des Raums in der Kultur des Mittelalters, edited by T. Suarez-Nani and M. Rohde (Berlin and Boston: De Gruyter, 2011), 45-66.
Smith, A. Mark, From Sight to Light, The Passage from Ancient to Modern Optics (Chicago and London: University of Chicago Press, 2015).
Tachau, Katherine, Vision and Certitude in the Age of Ockham. Optics, Epistemology and the Foundations of Semantics. 1250-1345 (Leiden, New York, Köln: E. J. Brill, 1988)
Thom, René, Esquisse d’une sémiophysique. Physique aristotélicienne et théorie des catastrophes (InterEditions, 1988); translated into English by Vendla Meyer, Semiophysics: A Sketch, Aristotelian Physics and Catastrophe Theory (Redwood City, California: Addison-Wesley, 1990).