Euclidian heterogeneity
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Abstract
One can speak of expressive heterogeneity when a demonstration appeals (in its communication) to linguistic and visual resources. One can speak of inferential heterogeneity when such an appeal is essential (inferentially) for the demonstrative plot. A paradigmatic example of inferential heterogeneity is the Euclidean proof. This paper aims to draw attention to four ways of intervening the diagram in such argumentative structures: contributing to the application of inferential schemes or strategies, guiding the heterogeneous demonstrative sequence, intervening in the "decomposition of logical space" (Netz 1999), contributing to the reduction of alternatives to consider. In each of these modalities, the diagram participates in a singular way as an expressive resource and as an inferential device.
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References
DE RISI, V. (2020) “Euclid’s Common Notions and the Theory of Equivalence”, Foundations of Science, https://doi.org/10.1007/s10699-020-09694-w
DUBNOV, Ya. S. (2006) Mistakes in Geometric Proofs, (traducido por A. Henn y O. Titelbaum) en Fetisov, A. I. y Dubnov, Ya. S. (2006) Proof in Geometry (with Mistakes in Geometric Proofs), Dover: USA.
EUCLID (1956) The thirteen books of the Elements, (Traducción y comentario Thomas L. Heath). New York: Dover.
EUCLIDES (1991) Elementos (Libros I-IV), Traducción: M.L. Puertas Castaños, Introducción: L. Vega Reñón. Madrid: Editorial Gredos.
FERREIRÓS, J. (2016) Mathematical Knowledge and the Interplay of Practices, Princeton: Princeton University Press.
MANCOSU, P. 1996 Philosophy of Mathematics and Mathematical Practice in the Early Seventeenth Century, Oxford: Oxford University Press.
MANDERS, K. (1996) “Diagram Content and Representational Granular- ity.” Logic, Language, and Computation. Ed. by J. Seligman and D. Westerståhl. Vol. I. Stanford: CSLI Publications and Stanford University Press.
MANDERS, K. (2008) “The Euclidian Diagram (1995)”, en Mancosu, P. (ed.) (2008) The Philosophy of Mathematical Practice, 80-133. Oxford: Oxford University Press.
MAXWELL, E. (1963), Fallacies in Mathematics. Cambridge: Cambridge University Press.
NETZ, R. (1999) The Shaping of Deduction in Greek Mathematics, Cambridge: Cambridge University Press.
NORMAN, J. (2006), After Euclid. Stanford: CSLI.
LASSALLE CASANAVE & SEOANE, J. (2016) “Las demostraciones por absurdo y la Noción Común 5” en Caorsi, E., Sautter, F. y Navia, R. (Editores) Significado y Negación: escritos lógicos, semánticos y epistemológicos, 39-50. Montevideo: CAPES-UdelaR.
RODRÍGUEZ PÉREZ, D. y MANNACK, T. (2019) La cerámica ática y su historiografía, Coímbra: Impresa da Universidade de Coimbra.
SEOANE, J. (2016) “Demostraciones heterogéneas: repensando las preguntas”, Representaciones, Vol. XII, N° 2, 87-108. Córdoba: SIRCA Publicaciones Académicas.
SEOANE, J. (en prensa) “Demostración euclidiana y ambigüedad perceptual”, en Sautter, F., Seco, G., Esquisabel, O. (Organizadores) De Mathematicae atque philosophicae Elegantia Notas festivas para Abel Lassalle Casanave.