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

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The Argument of Mathematics

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

Abstract

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.

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Notes

  1. 1.

    “Functionalisation of the research object in pragma-dialectics is achieved by regarding the verbal expressions used in argumentative discourse and texts as speech acts…” (Van Eemeren and Grootendorst, 2004, 54).

  2. 2.

    See Lunsford and Ruszkiewicz (2001) and Gilbert (1997) for attempts to do justice to this variety.

  3. 3.

    The earliest algebraic notations did not use brackets quite as we have them now but this does not affect the present point.

  4. 4.

    For a brief account of this development, see Larvor (2005). For exhaustive detail, see Serfati (2005).

  5. 5.

    The emphasis on gesture in this section takes inspiration from (Marghetis and Núñez, 2010) and (Hacking, 2010).

  6. 6.

    Clearly, the hard case for this claim is the spoken argument in ordinary language that the pragma-dialectical school takes as paradigmatic of argument generally. On the other hand, note that the analysis of ordinary prose arguments by argumentation theorists (from Toulmin onwards) often results in a diagram with labelled parts (‘warrant’, ‘backing’, etc.). In connection with the diagrammatic quality of algebraic notation, taking the sign for the thing itself is a feature of syntactic reasoning.

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Acknowledgements

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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Authors and Affiliations

  1. Department of Philosophy, School of Humanities, University of Hertfordshire, de Havilland Campus, Hatfield, Hertfordshire, AL10 9AB, UK

    Brendan Larvor

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  1. Brendan Larvor
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Correspondence to Brendan Larvor .

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  1. , Dept. Humanities & Communication, Florida Institute of Technology, W. University Blvd. 150, Melbourne, 32901-6975, Florida, USA

    Andrew Aberdein

  2. , Department of Philosophy, University of Nevada, Maryland Parkway 4505, Las Vegas, 89154, Nevada, USA

    Ian J Dove

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Larvor, B. (2013). What Philosophy of Mathematical Practice Can Teach Argumentation Theory About Diagrams and Pictures. In: Aberdein, A., Dove, I. (eds) The Argument of Mathematics. Logic, Epistemology, and the Unity of Science, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6534-4_13

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