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Kairos. Journal of Philosophy & Science

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The Epistemological Import of Euclidean Diagrams (in a non-Euclidean world)

Daniele Molinini
Published Online: 2016-11-08 | DOI: https://doi.org/10.1515/kjps-2016-0012


In this paper I concentrate on Euclidean diagrams, namely on those diagrams that are licensed by the rules of Euclid’s plane geometry. I shall overview some philosophical stances that have recently been proposed in philosophy of mathematics to account for the role of such diagrams in mathematics, and more particularly in Euclid’s Elements. Furthermore, I shall provide an original analysis of the epistemic role that Euclidean diagrams may (and, indeed) have in empirical sciences, more specifically in physics. I shall claim that, although the world we live in is not Euclidean, Euclidean diagrams permit to obtain knowledge of the world through a specific mechanism of inference I shall call inheritance.


  • Avigad, J., Dean, E., and Mumma, J., 2009, A formal system for Euclid’s elements. Review of Symbolic Logic, 2 (4):700-768.Google Scholar

  • Barwise, J. and Etchemendy, J., 1996, Visual information and valid reasoning. In Allwein, G. and Barwise, J. (eds.), Logical Reasoning with Diagrams, New York (USA): Oxford University Press, pp. 3-25.Google Scholar

  • Brown, J. R., 1999, Philosophy of Mathematics: an Introduction to the World of Proofs and Pictures. London: Routledge.Google Scholar

  • Bueno, O. and Colyvan, M., 2011, An inferential conception of the application of mathematics. Noûs, 45 (2): 345-374.Web of ScienceGoogle Scholar

  • De Risi, V., 2016, Leibniz on the Parallel Postulate and the Foundations of Geometry. Basel: Birkhäuser.Google Scholar

  • Feynman, R., 1965, The Character of Physical Law. Cambridge, Mass.: MIT Press.Google Scholar

  • Giaquinto, M., 2007, Visual Thinking in Mathematics. Oxford: Oxford University Press.Google Scholar

  • Giaquinto, M., 2008, Visualizing in mathematics. In: Mancosu, P. (ed.), The Philosophy of Mathematical Practice, Oxford: Oxford University Press, pp. 22-42.Google Scholar

  • Gray, J., 1989, Ideas of Space: Euclidean, Non-Euclidean and Relativistic. Oxford: Clarendon Press.Google Scholar

  • Kosslyn, S., 1994, Image and Brain. Cambridge, Mass.: MIT Press.Google Scholar

  • Leibniz, G., 1949, New Essays Concerning Human Understanding. La Salle, IL: Open Court Publishing.Google Scholar

  • Mancosu, P., 2005, Visualization in logic and mathematics. In Mancosu, P., Jørgensen, K. F., and Pedersen, S. A. (eds.), Visualization, Explanation and Reasoning Styles in Mathematics, Dordrecht: Springer, pp. 13-30.Google Scholar

  • Mancosu, P., Jørgensen, K. F., and Pedersen, S. A., 2005, Visualization, Explanation and Reasoning Styles in Mathematics, Dordrecht: Springer, vol. 327.Google Scholar

  • Manders, K., 2008a, Diagram-based geometric practice. In: Mancosu, P. (ed.), The Philosophy of Mathematical Practice, Oxford: Clarendon Press, pp. 65-79.Google Scholar

  • Manders, K., 2008b, The Euclidean diagram (1995). In: Mancosu, P. (ed.), The Philosophy of Mathematical Practice, Oxford: Clarendon Press, pp. 80-133.Google Scholar

  • Miller, N., 2008, Euclid and his Twentieth Century Rivals: Diagrams in the Logic of Euclidean Geometry, Stanford, CA: CSLI.Google Scholar

  • Molinini, D. and Panza, M., 2014, Sull’applicabilità della matematica. In: Varzi, A. and Fontanari, C. (eds.), La matematica nella società e nella cultura - Rivista della Unione Matematica Italiana, vol. VII, Serie I, pp. 367-395.Google Scholar

  • Mumma, J., 2006, Intuition formalized: Ancient and modern methods of proof in elementary geometry. PhD thesis, Carnegie Mellon University.Google Scholar

  • Mumma, J., 2010, Proofs, pictures, and Euclid. Synthese, 175: 255-287.Web of ScienceGoogle Scholar

  • Netz, R., 1998, Greek mathematical diagrams: Their use and their meaning. For the Learning of Mathematics, 18 (3): 33-39.Google Scholar

  • Netz, R., 1999, The shaping of deduction in Greek mathematics: a study in cognitive history. Cambridge: Cambridge University Press.Google Scholar

  • Norman, J., 2006, After Euclid: Visual Reasoning and the Epistemology of Diagrams. Stanford: CSLI Publications.Google Scholar

  • Panza, M., 2012, The twofold role of diagrams in Euclid’s plane geometry. Synthese, 186: 55-102.Web of ScienceGoogle Scholar

  • Shepard, R. N. and Cooper, L. A., 1982, Mental images and their transformations. Cambridge (Mass): MIT Press.Google Scholar

  • Sheredos, B., Burston, D. C., Abrahamsen, A., and Bechtel, W., 2013, Why do biologists use so many diagrams? Philosophy of Science, 80: 931-944.Google Scholar

  • Smadja, I., 2012, Local axioms in disguise: Hilbert on Minkowski diagrams. Synthese, 186 (1): 315-370.Web of ScienceGoogle Scholar

  • Tennant, N., 1986, The withering away of formal semantics? Mind & Language, 1 (4): 302-318.Google Scholar

  • Thagard, P., 2005, Mind: Introduction to Cognitive Sciences. The MIT Press, 2nd ed.Google Scholar

About the article

Published Online: 2016-11-08

Published in Print: 2016-10-01

Citation Information: Kairos. Journal of Philosophy & Science, ISSN (Online) 1647-659X, DOI: https://doi.org/10.1515/kjps-2016-0012.

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© 2016. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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