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

There has been a rising tide of interest among argumentation theorists in visual reasoning, most notably in the form of special editions of Argumentation and Advocacy in 1996 and 2007. In the hands of the leaders of this development, and particularly Birdsell and Groarke (1996, 2007), 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 (e.g. Dove, 2002; Manders, 1995; Netz, 2003). There have been efforts to bring the two together (see in particular Kulpa, 2009; Sherry, 2009; Inglis and Mejía-Ramos, 2009). 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.