Palabras clave
Matemáticas
filosofía de las matemáticas
ciencia moderna
Piccolomini
Clavius
Barozzi
Pereira
filosofía de las matemáticas
ciencia moderna
Piccolomini
Clavius
Barozzi
Pereira
Cómo citar
De la subordinación a la hegemonía. Sobre la legitimación epistemológica de las matemáticas en la filosofía natural en el siglo XVII. (2013). Civilizar, 13(25), 157-176. https://doi.org/10.22518/16578953.135
Resumen
Este artículo analiza la legitimación epistemológica de las matemáticas en la filosofía natural en el siglo XVII. En el Renacimiento se alegó que las matemáticas no cumplían con los criterios aristotélicos de cientificidad, ya que no explicaban las causas eficientes y finales. Así, sus críticos inspirados en la tradición aristotélica rechazaron los primeros intentos de matematizar la filosofía natural. Se examinan las condiciones epistemológicas implicadas en el debate sobre la cientificidad de las matemáticas y su pertinencia para la filosofía natural. Se hace un recorrido historiográfico de la matematización de la naturaleza para ofrecer nuevos elementos de ponderación respecto a una caracterización históricamente más contextual y filosóficamente más conceptual del surgimiento de la ciencia moderna.
Referencias
Aristóteles. (1988). Tratados de Lógica: (Órganon) II: sobre la interpretación. Analíticos primeros. Analíticos segundos. Madrid: Gredos.
Aristóteles. (1995). Física (Trad. G. De Echandía). Madrid: Gredos.
Barrow, I. (1734). The Usefulness of Mathematical
Learning Explained and Demonstrated: Being Mathematical Lectures Read in the Public Schools of Cambridge. Londres: S. Austen.
Biagioli, M. (1989). The social status of Italian mathematicians, 1450-1600. History of Science, 27, 41-95.
Biancani, G. (1615). De mathematicarum natura dissertatio. Bolonia: B. Cocchi.
Blay, M. (1998).Reasoning with the Infinite: From the Closed World to the Mathematical Universe. Chicago: University Press.
Clark, S. (1997). Thinking with Demons: The idea of witchcraft in early modern Europe. Oxford: Clarendon Press.
Clavius, C. (1612). Opera mathematica (Vols.1-5). Mainz: Reinhard Eltz.
Crombie, A. C. (1952). Augustine to Galileo: The History of Science, A.D. 400-1650. London: Falcon.
Dear, P. (1987). Jesuit mathematical science and the reconstitution of experience in the early seventeenth century. Studies in History and Philosophy of Science, 18(2), 133-175.
Dear, P. (1995). Discipline and Experience. The
Mathematical Way in the Scientific Revolution. Chicago: University Press.
Dear, P. (1998). The Mathematical Principles of
Natural Philosophy: Toward a Heuristic Narrative for the Scientific Revolution. Configurations, 6(2), 173-193.
Dobbs, B. J. (2000). Newton as Final cause and
First Mover. En M. Osler (Ed.), Rethinking the scientific revolution (pp. 25-39). New York, NY: Cambridge University Press.
Feldhay, R. (1998). The use and abuse of mathematical entities: Galileo and the Jesuits
revisited. En P. K. Machamer (Ed.), The Cambridge companion to Galileo (pp. 80-145). Cambridge: Cambridge University Press.
Funkenstein, A. (1986). Theology and the scientific
imagination from the Middle Ages to the seventeenth century. Princeton: Princeton University Press.
Gingras, Y. (2001). What did Mathematics do to Physics? History of Science, 39, 383-416.
Guicciardini, N. (1989). The development of Newtonian calculus in Britain, 1700-1800. New York: Cambridge University Press.
Hall, A. R. (1981). From Galileo to Newton. New York: Dover.
Hall, M. B. (1952). The Establishment of the Mechanical Philosophy. Bruges: St. Catherine Press.
Heath, T. L. (1956). The Thirteen Books of Euclid’s Elements. New York: Dover Publications.
Jardine, N. (1986). Epistemology of the sciences. En C. B. Schmitt, Q. Skinner & E. Kessler (Eds.), The Cambridge history of Renaissance philosophy (pp. 685-711). Cambridge: Cambridge University Press.
Koyré, A. (1965). The significance of the Newtonian
synthesis. En Newtonian studies (pp. 3-24). Cambridge: Cambridge University Press.
Koyré, A. (1994). From the Closed World to the
Infinite Universe. Baltimore: Johns Hopkins University Press.
Koyré, A. (1997). La aportación científica del Renacimiento. En Estudios de historia del pensamiento científico (pp. 41-50). México: Siglo XXI Editores.
Mancosu, P. (1992). Aristotelian Logic and Euclidean
Mathematics: Seventeenth Century Developments of the Quæstio de Certitudine Mathematicarum. Studies in History and Philosophy of Science, 23(2), 241-265.
Mancosu, P. (1996). Philosophy of Mathematics
and Mathematical Practice in the Seventeenth Century. New York: Oxford University Press.
Moran, B. T. (2005). Distilling Knowledge: Alchemy,
Chemistry, and the Scientific Revolution. Cambridge: Harvard University Press.
Newman, W. R. (2006). Atoms and Alchemy:
Chymistry and the experimental origins of the scientific revolution. Chicago: University of Chicago Press.
Newman, W. R., & Grafton, A. (2001). Secrets of Nature: Astrology and Alchemy in Early Modern Europe. Cambridge: MIT Press.
Ochoa, F. (2001). Newton heteróclito: Problemas
y límites del historiar a Sir Isaac Newton. Estudios de Filosofía, 24, 63-78.
Ochoa, F. (2012). Mathematics, Natural Philosophy,
and Providential Theology: An inquiry into the ontological problem of the causation of gravity force in Newton’s physics. (Tesis Doctoral, Instituto de Filosofía, Universidad de Antioquia).
Orozco, S. (2007). Modelos interpretativos del corpus newtoniano: Tradiciones historiográficas del siglo XX. Estudios de Filosofía, 35, 227-256.
Orozco, S. (2009). Isaac Newton y la reconstitución
del palimpsesto divino. Medellín: Editorial Universidad de Antioquia.
Osler, M. J. (2000). Rethinking the Scientific Revolution. Cambridge: Cambridge University Press.
Pereira, B. (1591). De communibus omnium rerum naturalium principiis et affectionibus, libriquindecim. Venetiis: Andream Muschium.
Piccolomini, A. (1576). La prima parte della filosofía naturale. Roma: Daniel Zaneti, & Compagni.
Pycior, H. (1997). Symbols, Impossible Numbers,
and Geometric Entanglements: British Algebra Through the Commentaries on Newton’s Universal Arithmetick. New York: Cambridge University Press.
Roux, S. (2010). Forms of Mathematization (14th-17th Centuries). Early Science and Medicine, 15(4-5), 319-337. doi: 10.1163/157338210X516242
Scheiner, C. (1614). Disquisitiones mathematicae
de controuersii set nouitatibus astronomicis. Ingolstadii: Elisabetham Angermariam.
Smiglecki, M. (1618). Logica Martini Smiglecii:
Selectis disputationi bus et quaestioni bus illustrata. Ingolstadii: Eder.
Smolarski, D. C. (2002a). Historical Documents,
Part II.Two Documents on Mathematics. Science in Context, 15(3), 465- 470. doi:10.1017/S0269889702000583
Smolarski, D.C. (2002b). Historical Documents,
Part I. Sections on mathematics from the various editions of the Ratio Studiorum. Science in context, 15(3), 459-464.doi: 10.1017/S0269889702000571
Sorell, T. (1993).The Rise of Modern Philosophy: The Tension between the new and traditional philosophies from Machiavelli to Leibniz. Oxford: Clarendon Press.
Vickers, B. (1984). Occult and Scientific Mentalities in the Renaissance. Cambridge: Cambridge University Press.
Wallis, J. (1693-1699). Johannis Wallis Oxoniensi Opera mathematica: tribus volumini buscontenta. Oxford: Theatro Sheldoniano.
Yolder, J. G. (1988). Unrolling time: Christiaan Huygens and the Mathematization of Nature. Cambridge: Cambridge University Press.
Aristóteles. (1995). Física (Trad. G. De Echandía). Madrid: Gredos.
Barrow, I. (1734). The Usefulness of Mathematical
Learning Explained and Demonstrated: Being Mathematical Lectures Read in the Public Schools of Cambridge. Londres: S. Austen.
Biagioli, M. (1989). The social status of Italian mathematicians, 1450-1600. History of Science, 27, 41-95.
Biancani, G. (1615). De mathematicarum natura dissertatio. Bolonia: B. Cocchi.
Blay, M. (1998).Reasoning with the Infinite: From the Closed World to the Mathematical Universe. Chicago: University Press.
Clark, S. (1997). Thinking with Demons: The idea of witchcraft in early modern Europe. Oxford: Clarendon Press.
Clavius, C. (1612). Opera mathematica (Vols.1-5). Mainz: Reinhard Eltz.
Crombie, A. C. (1952). Augustine to Galileo: The History of Science, A.D. 400-1650. London: Falcon.
Dear, P. (1987). Jesuit mathematical science and the reconstitution of experience in the early seventeenth century. Studies in History and Philosophy of Science, 18(2), 133-175.
Dear, P. (1995). Discipline and Experience. The
Mathematical Way in the Scientific Revolution. Chicago: University Press.
Dear, P. (1998). The Mathematical Principles of
Natural Philosophy: Toward a Heuristic Narrative for the Scientific Revolution. Configurations, 6(2), 173-193.
Dobbs, B. J. (2000). Newton as Final cause and
First Mover. En M. Osler (Ed.), Rethinking the scientific revolution (pp. 25-39). New York, NY: Cambridge University Press.
Feldhay, R. (1998). The use and abuse of mathematical entities: Galileo and the Jesuits
revisited. En P. K. Machamer (Ed.), The Cambridge companion to Galileo (pp. 80-145). Cambridge: Cambridge University Press.
Funkenstein, A. (1986). Theology and the scientific
imagination from the Middle Ages to the seventeenth century. Princeton: Princeton University Press.
Gingras, Y. (2001). What did Mathematics do to Physics? History of Science, 39, 383-416.
Guicciardini, N. (1989). The development of Newtonian calculus in Britain, 1700-1800. New York: Cambridge University Press.
Hall, A. R. (1981). From Galileo to Newton. New York: Dover.
Hall, M. B. (1952). The Establishment of the Mechanical Philosophy. Bruges: St. Catherine Press.
Heath, T. L. (1956). The Thirteen Books of Euclid’s Elements. New York: Dover Publications.
Jardine, N. (1986). Epistemology of the sciences. En C. B. Schmitt, Q. Skinner & E. Kessler (Eds.), The Cambridge history of Renaissance philosophy (pp. 685-711). Cambridge: Cambridge University Press.
Koyré, A. (1965). The significance of the Newtonian
synthesis. En Newtonian studies (pp. 3-24). Cambridge: Cambridge University Press.
Koyré, A. (1994). From the Closed World to the
Infinite Universe. Baltimore: Johns Hopkins University Press.
Koyré, A. (1997). La aportación científica del Renacimiento. En Estudios de historia del pensamiento científico (pp. 41-50). México: Siglo XXI Editores.
Mancosu, P. (1992). Aristotelian Logic and Euclidean
Mathematics: Seventeenth Century Developments of the Quæstio de Certitudine Mathematicarum. Studies in History and Philosophy of Science, 23(2), 241-265.
Mancosu, P. (1996). Philosophy of Mathematics
and Mathematical Practice in the Seventeenth Century. New York: Oxford University Press.
Moran, B. T. (2005). Distilling Knowledge: Alchemy,
Chemistry, and the Scientific Revolution. Cambridge: Harvard University Press.
Newman, W. R. (2006). Atoms and Alchemy:
Chymistry and the experimental origins of the scientific revolution. Chicago: University of Chicago Press.
Newman, W. R., & Grafton, A. (2001). Secrets of Nature: Astrology and Alchemy in Early Modern Europe. Cambridge: MIT Press.
Ochoa, F. (2001). Newton heteróclito: Problemas
y límites del historiar a Sir Isaac Newton. Estudios de Filosofía, 24, 63-78.
Ochoa, F. (2012). Mathematics, Natural Philosophy,
and Providential Theology: An inquiry into the ontological problem of the causation of gravity force in Newton’s physics. (Tesis Doctoral, Instituto de Filosofía, Universidad de Antioquia).
Orozco, S. (2007). Modelos interpretativos del corpus newtoniano: Tradiciones historiográficas del siglo XX. Estudios de Filosofía, 35, 227-256.
Orozco, S. (2009). Isaac Newton y la reconstitución
del palimpsesto divino. Medellín: Editorial Universidad de Antioquia.
Osler, M. J. (2000). Rethinking the Scientific Revolution. Cambridge: Cambridge University Press.
Pereira, B. (1591). De communibus omnium rerum naturalium principiis et affectionibus, libriquindecim. Venetiis: Andream Muschium.
Piccolomini, A. (1576). La prima parte della filosofía naturale. Roma: Daniel Zaneti, & Compagni.
Pycior, H. (1997). Symbols, Impossible Numbers,
and Geometric Entanglements: British Algebra Through the Commentaries on Newton’s Universal Arithmetick. New York: Cambridge University Press.
Roux, S. (2010). Forms of Mathematization (14th-17th Centuries). Early Science and Medicine, 15(4-5), 319-337. doi: 10.1163/157338210X516242
Scheiner, C. (1614). Disquisitiones mathematicae
de controuersii set nouitatibus astronomicis. Ingolstadii: Elisabetham Angermariam.
Smiglecki, M. (1618). Logica Martini Smiglecii:
Selectis disputationi bus et quaestioni bus illustrata. Ingolstadii: Eder.
Smolarski, D. C. (2002a). Historical Documents,
Part II.Two Documents on Mathematics. Science in Context, 15(3), 465- 470. doi:10.1017/S0269889702000583
Smolarski, D.C. (2002b). Historical Documents,
Part I. Sections on mathematics from the various editions of the Ratio Studiorum. Science in context, 15(3), 459-464.doi: 10.1017/S0269889702000571
Sorell, T. (1993).The Rise of Modern Philosophy: The Tension between the new and traditional philosophies from Machiavelli to Leibniz. Oxford: Clarendon Press.
Vickers, B. (1984). Occult and Scientific Mentalities in the Renaissance. Cambridge: Cambridge University Press.
Wallis, J. (1693-1699). Johannis Wallis Oxoniensi Opera mathematica: tribus volumini buscontenta. Oxford: Theatro Sheldoniano.
Yolder, J. G. (1988). Unrolling time: Christiaan Huygens and the Mathematization of Nature. Cambridge: Cambridge University Press.
Una vez publicado, los derechos de impresión y reproducción son del Universidad Sergio Arboleda. Es potestativo del editor permitir la reproducción del artículo.