, Volume 186, Issue 1, pp 121–148 | Cite as

Human diagrammatic reasoning and seeing-as

  • Annalisa ColivaEmail author


The paper addresses the issue of human diagrammatic reasoning in the context of Euclidean geometry. It develops several philosophical categories which are useful for a description and an analysis of our experience while reasoning with diagrams. In particular, it draws the attention to the role of seeing-as; it analyzes its implications for proofs in Euclidean geometry and ventures the hypothesis that geometrical judgments are analytic and a priori, after all.


Diagrammatic reasoning Seeing-as Geometrical concepts Euclidean geometry A priori Analytic 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Audi R.: Reasons/causes. In: Dancy, J., Sosa, E. (eds) A companion to epistemology, pp. 424–426. Blackwell, Oxford (1992)Google Scholar
  2. Avigad, J., Dean, E., & Mumma J. (2008). A formal system for Euclid’s Elements. Review of Symbolic Logic, forthcoming.Google Scholar
  3. Boghossian P.: Epistemic rules. Journal of Philosophy 105(9), 472–500 (2008)Google Scholar
  4. Byrne O.: The first six books of the elements of Euclid. William Pickering, London (1847)Google Scholar
  5. Coliva A.: Wright and McDowell on the content of experience and the justification of empirical beliefs. Lingua e Stile 36(1), 3–23 (2001)Google Scholar
  6. Coliva A.: In difesa del contenuto non concettuale della percezione. In: Parrini, P. (eds) Conoscenza e cognizione, pp. 147–161. Guerini, Milano (2002)Google Scholar
  7. Coliva A.: The finer-grained content of experience. A redefinition of its role within the debate between McDowell and nonconceptual theorists. Dialectica 57(1), 57–70 (2003)CrossRefGoogle Scholar
  8. Coliva, A. (2004/2006). I concetti. Roma: Carocci.Google Scholar
  9. Euclid. (1959). Elements, published as Euclid’s Elements: All thirteen books complete in one volume (T. Heath, Trans., D. Densmore, Ed.). New York: Dover Books.Google Scholar
  10. Giaquinto, M. (2007a). Visual thinking in mathematics. An epistemological study (esp. Chaps. 1–5). Oxford, OUPGoogle Scholar
  11. Giaquinto M.: Visualizing in mathematics: An introduction. In: Mancosu, P. (eds) The philosophy of mathematical practice, pp. 32–58. Clarendon Press, Oxford (2007b)Google Scholar
  12. Giardino, V. (ms.). Diagrams and manipulation practices: The margins for an empirical research.Google Scholar
  13. Glasgow, J., Narayanan, N. H., Chandrasekaran, B. (eds): Diagrammatic reasoning: Cognitive and computational perspectives. MIT Press, Cambridge, MA (1995)Google Scholar
  14. Macbeth D.: Diagrammatic reasoning in Euclid’s Elements”. In: Van Kerkhove, B., De Vuyst, J., Van Bendegem, J.-P. (eds) Philosophical perspectives on mathematical practice, pp. 235–267. College Publications, London (2010)Google Scholar
  15. Macbeth, D. (2011). Diagrammatic reasoning in Frege’s Begriffßchrift. this issue, Vol. 2.Google Scholar
  16. Malone M. E.: Kuhn reconstructed: Incommensurability without relativism. Studies in History and Philosophy of Science 24(1), 66–93 (1993)CrossRefGoogle Scholar
  17. Manders K.: Diagram-based geometric practice. In: Mancosu, P. (eds) The philosophy of mathematical practice, pp. 88–111. Clarendon Press, Oxford (2007a)Google Scholar
  18. Manders K.: The Euclidean diagram. In: Mancosu, P. (eds) The philosophy of mathematical practice, pp. 112–183. Clarendon Press, Oxford (2007b)Google Scholar
  19. McDowell J.: Mind and world. Harvard University Press, Cambridge, MA (1994)Google Scholar
  20. Netz R.: The shaping of deduction in Greek mathematics. Cambridge University Press, Cambridge (1999)CrossRefGoogle Scholar
  21. Owens K., Outhred L.: The complexity of learning geometry and measurement. In: Gutiérrez, A., Boero, P. (eds) Handbook of research on the psychology of mathematics education, pp. 83–115. Sense Publishers, Rotterdam (2006)Google Scholar
  22. Panza, M. (2011). The two-fold role of diagrams in Euclid’s plain geometry. this issue, Vol. 2.Google Scholar
  23. Peacocke C.: A study of concepts. MIT Press, Cambridge, MA (1992)Google Scholar
  24. Saito K.: A preliminary study in the critical assessment of diagrams in Greek mathematical works. Sciamus 7, 81–144 (2006)Google Scholar
  25. Shin, S. J. (2008). Review of Giaquinto 2007a. Notre Dame Philosophical Reviews. Accessed July 29, 2008, from
  26. Shin, S. J. (2011). The forgotten individual: Diagrammatic reasoning in mathematics. this issue, Vol. 2.Google Scholar
  27. Wittgenstein L.: Philosophical investigations. Blackwell, Oxford (1953)Google Scholar
  28. Wittgenstein L.: Remarks on the philosophy of psychology (Vols. 1, 2). Chicago University Press, Chicago (1980)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Università degli Studi di Modena e Reggio EmiliaModenaItaly

Personalised recommendations