Un análisis comparativo del uso de diagramas en dos prácticas matemáticas de la antigüedad
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Abstract
In our article, we will analyze the differences and similarities that we can find in the use of diagrams between two mathematical practices of antiquity. We will show that there is no single possible use of these, but that they have to be considered as reasoning tools created and manipulated according to the purposes of each tradition. We will argue that the differences in the procedures and organizations of knowledge that both traditions present do not imply any kind of assessment of their greater or lesser “mathematicity”, since both traditions reached sufficiently general and precise mathematical results, a fact that is characteristic of mathematical research at a theoretical level.
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García-Pérez, M. J., & Dal Magro, T. (2019). Un análisis comparativo del uso de diagramas en dos prácticas matemáticas de la antigüedad. Crítica. Revista Hispanoamericana De Filosofía, 51(152), 5–31. https://doi.org/10.22201/iifs.18704905e.2019.07
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References
Artmann, B., 1999, Euclid —The Creation of Mathematics, Springer- Verlag, Nueva York.
Avigad, J., E. Dean, y J. Mumma, 2009, “A Formal System for Euclid’s Elements”, Review of Symbolic Logic, vol. 2, no. 4, pp. 700–768.
Bray, F., V. Dorofeeva-Lichtmann y G. Métailié (eds.), 2007, Graphics and Text in the Production of Technical Knowledge in China, Brill, Leiden, Boston.
Charette, F., 2012, “The Logical Greeks versus the Imaginative Oriental: on the Historiography of “Non–Western” Mathematics During the Period 1820–1920”, en Chemla 2012, pp. 274–293.
Chemla, K. (ed.), 2012, The History of Mathematical Proofs in Ancient Traditions, Cambridge University Press, Nueva York.
Chemla, K. (ed.), 2010, “Changes and Continuities in The Use of Diagrams tu in Chinese Mathematical Writings (3rd century–14th century)”, East Asian Science, Technology, and Society: An International Journal, vol. 4, no. 2, pp. 303–326.
Chemla, K. (ed.), 2009, “On Mathematical Problems as Historically Determined Artifacts: Reflections Inspired by Sources from Ancient China”, Historia Mathematica, vol. 36, no. 3, pp. 213–246.
Chemla, K. (ed.), 2003, “Generality above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China”, Science in Context, vol. 16, no. 3, pp. 413–458.
Chemla, K. y S. Guo, 2004, Les neuf chapitres: Le Classique mathématique de la Chine ancienne et ses commentaires, Dunod, París.
Cullen, C., 2009, “People And Numbers in Early Imperial China”, en Robson and Stedall 2009, pp. 591–618.
Cullen, C., 1996, Astronomy and Mathematics in Ancient China: The Zhou bi suan jing, Cambridge University Press, Cambridge.
Dauben, J.W., 2008, “Suan Shu Shu. A Book on Numbers And Compu- tation”, Archive for History of Exact Sciences, vol. 62, no. 2, pp. 91–178. De Regt, H.W. y D. Dieks, 2005, “A Contextual Approach to Scientific
Understanding”, Synthese, vol. 144, no. 1, pp. 137–170.
Ferreirós, J., 2016, Mathematical Knowledge and the Interplay of Prac-
tices, Princeton University Press, Princeton.
Giardino, V., 2017, “Diagrammatic Reasoning in Mathematics”, en Magnani
y Bertolotti 2017, pp. 499–522.
Giardino, V., 2013, “A Practice–Based Approach to Diagrams”, en Moktefi y Shin 2013, pp. 135–151.
Giardino, V. y R. Casati, 2013, “Public Representations and Indeterminacies of Perspectival Content”, en Kondor 2013, pp. 111–126.
Giardino, V. y G. Greenberg, 2014, “Introduction: Varieties of Iconicity”, Review of Philosophy and Psychology, vol. 6, no. 1, pp. 1–25.
Hardy, G.H., 1940/1992, A Mathematician’s Apology, Cambridge Univer- sity Press, Cambridge.
Heath, T., 1956, The Thirteen Books of the Elements, Vol. I Books I and II, Cambridge University Press, Cambridge.
Heath, T., 1921, A History of Greek Mathematics, Vol. 1: From Thales to Euclid, Dover.
Joseph, G.G., 2011, The Crest of The Peacock: Non-European Roots of Mathematics (3a. edición), Princeton University Press, Princeton, Oxford.
Kondor, Z. (ed.), 2013, Enacting Images – Representation Revisited, Her- bert von Halem Verlag, Köln.
Lloyd, G.E.R., 2009, “What Was Mathematics in The Ancient World? Greek and Chinese Perspectives”, en Robson y Stedall 2009, pp. 7–25.
Magnani, L. y T. Bertolotti (eds.), 2017, Springer Handbook of Model– Based Science, Springer Dordrecht, Heidelberg, Londres/Nueva York.
Mancosu, P., (ed.), 2008, The Philosophy of Mathematical Practice, Oxford University Press, Oxford, Nueva York.
Mancosu, P., (ed.), 1996, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford University Press, Nueva York, Oxford.
Manders, K., 2008a, “Diagram–Based Geometric Practice”, en Mancosu 2008, pp. 65–79.
Manders, K., 2008b, “The Euclidean Diagram”, en Mancosu 2008, pp. 80–133.
Martzloff, J.-C., 1997, A History of Chinese Mathematics, Springer, Heidelberg, Berlín.
Moktefi, A. y S.J. Shin (eds.), 2013, Visual Reasoning with Diagrams, Birkhäuser, Basel.
Netz, R., 1999, The Shaping of Deduction in Greek Mathematics: A Study of Cognitive History, Cambridge University Press, Cambridge.
Puertas Castaños, M.L. (trad.), 2000, Los Elementos de Euclides. Libros I–IV, Gredos, Madrid.
Robson, E. y J. Stedall (eds.), 2009, The Oxford Handbook of the History of Mathematics, Oxford University Press, Oxford, Nueva York.
Swetz, F., 1984, “The Introduction of Mathematics in Higher Education in China, 1865–1887”, Historia Mathematica, vol. 1, no. 2, pp. 167–179.
Volkov, A., 2007, “Geometrical Diagrams in Traditional Chinese Mathematics”, en F. Bray, V. Dorofeeva-Lichtmann y G. Métailié, pp. 425–459.
Wagner, R., 2017, Making and Breaking Mathematical Sense, Princeton University Press, Princeton, Oxford.
Xu, Y., 2005, “The First Chinese Translation of The Last Nine Books of Euclid’s Elements and Its Source”, Historia Mathematica, vol. 32, no. 1, pp. 4–32.
Avigad, J., E. Dean, y J. Mumma, 2009, “A Formal System for Euclid’s Elements”, Review of Symbolic Logic, vol. 2, no. 4, pp. 700–768.
Bray, F., V. Dorofeeva-Lichtmann y G. Métailié (eds.), 2007, Graphics and Text in the Production of Technical Knowledge in China, Brill, Leiden, Boston.
Charette, F., 2012, “The Logical Greeks versus the Imaginative Oriental: on the Historiography of “Non–Western” Mathematics During the Period 1820–1920”, en Chemla 2012, pp. 274–293.
Chemla, K. (ed.), 2012, The History of Mathematical Proofs in Ancient Traditions, Cambridge University Press, Nueva York.
Chemla, K. (ed.), 2010, “Changes and Continuities in The Use of Diagrams tu in Chinese Mathematical Writings (3rd century–14th century)”, East Asian Science, Technology, and Society: An International Journal, vol. 4, no. 2, pp. 303–326.
Chemla, K. (ed.), 2009, “On Mathematical Problems as Historically Determined Artifacts: Reflections Inspired by Sources from Ancient China”, Historia Mathematica, vol. 36, no. 3, pp. 213–246.
Chemla, K. (ed.), 2003, “Generality above Abstraction: The General Expressed in Terms of the Paradigmatic in Mathematics in Ancient China”, Science in Context, vol. 16, no. 3, pp. 413–458.
Chemla, K. y S. Guo, 2004, Les neuf chapitres: Le Classique mathématique de la Chine ancienne et ses commentaires, Dunod, París.
Cullen, C., 2009, “People And Numbers in Early Imperial China”, en Robson and Stedall 2009, pp. 591–618.
Cullen, C., 1996, Astronomy and Mathematics in Ancient China: The Zhou bi suan jing, Cambridge University Press, Cambridge.
Dauben, J.W., 2008, “Suan Shu Shu. A Book on Numbers And Compu- tation”, Archive for History of Exact Sciences, vol. 62, no. 2, pp. 91–178. De Regt, H.W. y D. Dieks, 2005, “A Contextual Approach to Scientific
Understanding”, Synthese, vol. 144, no. 1, pp. 137–170.
Ferreirós, J., 2016, Mathematical Knowledge and the Interplay of Prac-
tices, Princeton University Press, Princeton.
Giardino, V., 2017, “Diagrammatic Reasoning in Mathematics”, en Magnani
y Bertolotti 2017, pp. 499–522.
Giardino, V., 2013, “A Practice–Based Approach to Diagrams”, en Moktefi y Shin 2013, pp. 135–151.
Giardino, V. y R. Casati, 2013, “Public Representations and Indeterminacies of Perspectival Content”, en Kondor 2013, pp. 111–126.
Giardino, V. y G. Greenberg, 2014, “Introduction: Varieties of Iconicity”, Review of Philosophy and Psychology, vol. 6, no. 1, pp. 1–25.
Hardy, G.H., 1940/1992, A Mathematician’s Apology, Cambridge Univer- sity Press, Cambridge.
Heath, T., 1956, The Thirteen Books of the Elements, Vol. I Books I and II, Cambridge University Press, Cambridge.
Heath, T., 1921, A History of Greek Mathematics, Vol. 1: From Thales to Euclid, Dover.
Joseph, G.G., 2011, The Crest of The Peacock: Non-European Roots of Mathematics (3a. edición), Princeton University Press, Princeton, Oxford.
Kondor, Z. (ed.), 2013, Enacting Images – Representation Revisited, Her- bert von Halem Verlag, Köln.
Lloyd, G.E.R., 2009, “What Was Mathematics in The Ancient World? Greek and Chinese Perspectives”, en Robson y Stedall 2009, pp. 7–25.
Magnani, L. y T. Bertolotti (eds.), 2017, Springer Handbook of Model– Based Science, Springer Dordrecht, Heidelberg, Londres/Nueva York.
Mancosu, P., (ed.), 2008, The Philosophy of Mathematical Practice, Oxford University Press, Oxford, Nueva York.
Mancosu, P., (ed.), 1996, Philosophy of Mathematics and Mathematical Practice in the Seventeenth Century, Oxford University Press, Nueva York, Oxford.
Manders, K., 2008a, “Diagram–Based Geometric Practice”, en Mancosu 2008, pp. 65–79.
Manders, K., 2008b, “The Euclidean Diagram”, en Mancosu 2008, pp. 80–133.
Martzloff, J.-C., 1997, A History of Chinese Mathematics, Springer, Heidelberg, Berlín.
Moktefi, A. y S.J. Shin (eds.), 2013, Visual Reasoning with Diagrams, Birkhäuser, Basel.
Netz, R., 1999, The Shaping of Deduction in Greek Mathematics: A Study of Cognitive History, Cambridge University Press, Cambridge.
Puertas Castaños, M.L. (trad.), 2000, Los Elementos de Euclides. Libros I–IV, Gredos, Madrid.
Robson, E. y J. Stedall (eds.), 2009, The Oxford Handbook of the History of Mathematics, Oxford University Press, Oxford, Nueva York.
Swetz, F., 1984, “The Introduction of Mathematics in Higher Education in China, 1865–1887”, Historia Mathematica, vol. 1, no. 2, pp. 167–179.
Volkov, A., 2007, “Geometrical Diagrams in Traditional Chinese Mathematics”, en F. Bray, V. Dorofeeva-Lichtmann y G. Métailié, pp. 425–459.
Wagner, R., 2017, Making and Breaking Mathematical Sense, Princeton University Press, Princeton, Oxford.
Xu, Y., 2005, “The First Chinese Translation of The Last Nine Books of Euclid’s Elements and Its Source”, Historia Mathematica, vol. 32, no. 1, pp. 4–32.
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