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The forgotten individual: diagrammatic reasoning in mathematics

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Abstract

Parallelism has been drawn between modes of representation and problem-sloving processes: Diagrams are more useful for brainstorming while symbolic representation is more welcomed in a formal proof. The paper gets to the root of this clear-cut dualistic picture and argues that the strength of diagrammatic reasoning in the brainstorming process does not have to be abandoned at the stage of proof, but instead should be appreciated and could be preserved in mathematical proofs.

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References

  • Anderson, M., Cheng, P., Haarslev, V. (eds) (2000) Theory and application of diagrams. Springer, Berlin

    Google Scholar 

  • Barwise, J., Allwein, G. (eds) (1996) Logical reasoning with diagrams. Oxford University Press, New York

    Google Scholar 

  • Barwise J., Etchemendy J. (1989) Information, infons and inference. In: Cooper R., Mukai K., Perry J. (eds) Situation theory and its applications I. Center for the Study of Language and Information, Stanford, CA, pp 33–78

    Google Scholar 

  • Barwise J., Hammer E. (1994) Diagrams and the concept of logical system. In: Gabbay D. M. (eds) What is a logical system?. Oxford University Press, New York

    Google Scholar 

  • Berkeley, G. (1920). [1776]. A treatise concerning the principles of human knowledge. Chicago: Open Court.

  • Boolos, G., Jeffrey, R. (1989). [1974]. Computability and logic Cambridge, UK: Cambridge University Press.

  • Heath, T. (Ed.), (1956) The thirteen books of Euclid’s elements. Dover Publications, New York

    Google Scholar 

  • Hilbert, D. (1971). The foundations of geometry (L. Unger, Trans. and P. Bernays, Revised). Chicago: Open Court.

  • Kant, I. (1929). Critique of pure reason (N. K. Smith, Trans.). London: Macmillan Press.

  • Locke J. (1924). [1737]. Essay concerning human understanding. Oxford: Clarendon Press.

  • Mancosu, P., Jørgensen, K. F., Pedersen, S. A. (eds) (2005) Visualization, explanations and reasoning styles in mathematics. Springer, Dordrecht

    Google Scholar 

  • Peirce, C. S. (1933). In C. Hartshorne & P. Weiss (Eds.), Collected papers of Charles Sanders Peirce (Vol. 3). Cambridge, MA: Harvard University Press.

  • Polya, G. (1973). [1945]. How to solve it: A new aspect of mathematical method. Princeton, NJ: Princeton University Press.

  • Shimojima A. (1996) Operational constraints in diagrammatic reasoning. In: Barwise J., Allwein G. (eds) Logical reasoning with diagrams. Oxford University Press, New York, pp 27–48

    Google Scholar 

  • Shin S.-J. (1994) The logical status of diagrams. Cambridge University Press, New York

    Google Scholar 

  • Shin S.-J. (1997) Kant’s syntheticity revisited by Peirce. Synthese, 113: 1–41

    Article  Google Scholar 

  • Shin S.-J. (2002) The iconic logic of Peirce’s graphs. MIT Press (Bradford), Cambridge, MA

    Google Scholar 

  • Shin, S.-J. (2010). Peirce’s two ways of abstraction. In M. Moore (Ed.), Charles S. Peirce’s philosophy of mathematics (pp. 23–40). Chicago: Open Court (forthcoming).

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  1. Department of Philosophy, Yale University, New Haven, CT, USA

    Sun-Joo Shin

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  1. Sun-Joo Shin
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Correspondence to Sun-Joo Shin.

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Shin, SJ. The forgotten individual: diagrammatic reasoning in mathematics. Synthese 186, 149–168 (2012). https://doi.org/10.1007/s11229-012-0075-1

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  • DOI: https://doi.org/10.1007/s11229-012-0075-1

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