What Philosophy of Mathematical Practice Can Teach Argumentation Theory About Diagrams and Pictures

  • Brendan Larvor
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 30)


There has been a rising tide of interest among argumentation theorists in visual reasoning. In the hands of the leaders of this development the effort has been to assimilate visual reasoning to verbal argumentation. At the same time, there is a more mature but still advancing literature on the use of diagrams in mathematical reasoning. There have been efforts to bring the two together. In this paper, I wish to use the philosophy of mathematical practice to identify a severe limitation in the attempt to assimilate visual reasoning to verbal reasoning, and by extension to criticise the approach to reasoning that treats all reasoning as if it were verbal reasoning.


Diagram Icon Inferential action Notation Speech-act Verbal reasoning. 



I am grateful to the members of the Open University philosophy department for the opportunity they gave me to test this paper on them and to Valeria Giardino for the inspiration of her (2010).


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Philosophy, School of HumanitiesUniversity of HertfordshireHatfieldUK

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