¿“Natural” y “Euclidiana”? Reflexiones sobre la geometría práctica y sus raíces cognitivas

• Autores: José Ferreirós Domínguez , Manuel Jesús García Pérez
• Localización: Theoria: an international journal for theory, history and foundations of science, ISSN 0495-4548, Vol. 33, Nº 2, 2018, págs. 325-344
• Idioma: inglés
• DOI: 10.1387/theoria.17839
• Enlaces
  • Texto completo (pdf)
• Dialnet Métricas: 2 Citas
• Resumen
  • español

    Se discutirán críticamente algunas tesis recientes sobre cognición geométrica, específicamente la tesis de la universalidad planteada por Dehaene et al., y la idea de una “geometría natural” empleada por Spelke. Argumentaremos la necesidad de distinguir entre cognición visuo-espacial y conocimiento geométrico básico, y más aún, afirmaremos que este último no se puede identificar con la geometría euclidiana. El propósito principal del artículo es proponer una caracterización de la geometría básica, para lo cual se requiere una combinación de experimentos en cognición visuo-espacial con estudios en arqueología cognitiva e historia comparativa. Ofreceremos ejemplos de estos campos, con especial énfasis en la comparación de ideas y procedimientos geométricos de la antigua China y Grecia

  • English

    We discuss critically some recent theses about geometric cognition, namely claims of universality made by Dehaene et al., and the idea of a “natural geometry” employed by Spelke. We offer arguments for the need to distinguish visuo-spatial cognition from basic geometric knowledge; furthermore, we claim that the latter cannot be identified with Euclidean geometry. The main aim of this paper is to advance toward a characterization of basic geometry, which in our view requires a combination of experiments on visuo-spatial cognition with studies in cognitive archaeology and comparative history. Examples from these fields are given, with special emphasis on the comparison of ancient Chinese and ancient Greek geometric ideas and procedures

• Referencias bibliográficas
  • Campbell, Jamie I. D. (Ed.). 2005. Handbook of mathematical cognition. New York: Psychology Press.
  • Chemla, Karine y Shuchun Guo. 2004. Les Neuf Chapitres: Le Classique mathématique de la Chine ancienne et ses commentaires. Paris: Dunod.
  • Coolidge, Frederick L. y Thomas Wynn. 2016a. Epilogue, en T. Wynn & F. Coolidge, eds., Cognitive Models in Palaeolithic Archaeology, 215-219....
  • Coolidge, Frederick L. y Thomas Wynn. 2016b. An Introduction to Cognitive Archaeology. Current Directions in Psychological Science 25/6: 386-392.
  • Cullen, Christopher. 1996. Astronomy and Mathematics in Ancient China: The Zhou Bi Suan Jing. Cambridge, New York: Cambridge University Press.
  • Dehaene, Stanislas, Véronique Izard, Pierre Pica y Elizabeth Spelke. 2006. Core knowledge of geometry in an Amazonian indigene group. Science,...
  • Feigenson, Lisa, Stanislas Dehaene y Elizabeth Spelke. 2004. Core systems of number. Trends in Cognitive Sciences 8/7: 307-314.
  • Ferreirós, José. 2015. Mathematical knowledge and the interplay of practices. Princeton: Princeton University Press.
  • Giaquinto, Marcus. 2007. Visual thinking in mathematics: An epistemological study. Oxford: Orford University Press.
  • Giardino, Valeria. 2016. ¿Dónde situar los fundamentos cognitivos de las matemáticas?, en J. Ferreirós y A. Lassalle Casanave, eds., El árbol...
  • Gomila, Antoni. 2012. Verbal Minds: Language and the Architecture of Cognition. Amsterdam: Elsevier Science.
  • Gray, Jeremy. 1992. Ideas de espacio. Madrid: Mondadori.
  • Heath, Thomas L. 1956. The thirteen books of Euclid’s Elements (Vol. 1). New York: Dover.
  • Høyrup, Jens. 2002. Lengths, Widths, Surfaces: A portrait of Old Babylonian Algebra and its kin. Berlin: Springer.
  • Izard, Véronique y Elizabeth Spelke. 2009. Development of sensitivity to geometry in visual forms. Human Evolution 24/3: 213-248.
  • Keller, Olivier. 2004. Aux origines de la géométrie: Le Paléolithique et le Monde des chasseurs-cueilleurs. Paris: Vuibert.
  • Keller, Olivier. 2014. The figure of the world. An insight into the developments of geometry during the Neolithic. Documents for a workshop:...
  • Knorr, Wilbur R. 1996. The Method of Indivisibles in Ancient Geometry, en R. Calinger, ed., Vita Mathematica: Historical research and integration...
  • Laland, Kevin. 2017. Darwin’s unfinished symphony. How culture made the human mind. Princeton y Oxford: Princeton University Press.
  • Manders, Kenneth. 2008. The Euclidean diagram, en P. Mancosu, ed., The Philosophy of Mathematical Practice, 80-133. Oxford: Oxford University...
  • Núñez, Rafael. 2011. No Innate Number Line in the Human Brain. Journal of Cross-Cultural Psychology 42/4: 651-668.
  • Overmann, Karenleigh. 2013. Material Scaffolds in Numbers and Time. Cambridge Archaeological Journal 23/1, 19-39.
  • Overmann, Karenleigh. 2016. Materiality and Numerical Cognition: A Material Engagement Theory Perspective, en T. Wynn y F. Coolidge, Cognitive...
  • Poincaré, Henri. 2002. Ciencia e hipótesis. Madrid: Espasa Calpe.
  • Renfrew, Colin e Iain Morley. 2010. Introduction, en C. Renfrew e I. Morley, eds., The Archaeology of Measurement: Comprehending Heaven, Earth...
  • Sterelny, Kim. 2011. From hominins to humans: how sapiens became behaviourally modern. Philosophical Transactions of the Royal Society B:...
  • Stillwell, John. 2010. Mathematics and it history. New York: Springer-Verlag.
  • Spelke, Elizabeth, Sang Ah Lee y Verónique Izard. 2010. Beyond core knowledge: Natural geometry. Cognitive Science 34/5: 863-884.
  • Spelke, Elizabeth y Katherine D. Kinzler. 2007. Core knowledge. Developmental Science 10/1: 89-96.
  • Spelke, Elizabeth y Sang Ah Lee. 2012. Core systems of geometry in animal minds. Philosophical Transactions of the Royal Society B: Biological...
  • Teng, Shu-p’ing. 2000. The original significance of bi disks: insights based on Liangzhu jade bi with incised symbolic motifs. Journal of...
  • Tommasi, Luca, Cinzia Chiandetti, Tommaso Pecchia, Valeria Ana Sovrano y Giorgio Vallortigara. 2012. From natural geometry to spatial cognition....
  • Twyman, Alexandra D. y Nora S. Newcombe. 2010. Five Reasons to Doubt the Existence of a Geometric Module. Cognitive Science 34/7, 1315-1356.
  • Vallortigara, Giorgio. 2012. Core knowledge of object, number, and geometry: A comparative and neural approach. Cognitive Neuropsychology...