A Practice-Based Approach to Diagrams
In this article, I propose an operational framework for diagrams. According to this framework, diagrams do not work like sentences, because we do not apply a set of explicit and linguistic rules in order to use them. Rather, we become able to manipulate diagrams in meaningful ways once we are familiar with some specific practice, and therefore we engage ourselves in a form of reasoning that is stable because it is shared. This reasoning constitutes at the same time discovery and justification for this discovery. I will make three claims, based on the consideration of diagrams in the practice of logic and mathematics. First, I will claim that diagrams are tools, following some of Peirce’s suggestions. Secondly, I will give reasons to drop a sharp distinction between vision and language and consider by contrast how the two are integrated in a specific manipulation practice, by means of a kind of manipulative imagination. Thirdly, I will defend the idea that an inherent feature of diagrams, given by their nature as images, is their ambiguity: when diagrams are ‘tamed’ by the reference to some system of explicit rules that fix their meaning and make their message univocal, they end up in being less powerful.
KeywordsDiagrammatic reasoning Practice-based philosophy of mathematics Peirce’s diagrams Manipulative imagination Productive ambiguity
Mathematics Subject Classification (2010)00A66 03A05 97C30
I want to thank Mario Piazza, Achille Varzi, Roberto Casati, and two anonymous referees who gave me very useful suggestions in order to improve this article. Many thanks to Christopher Whalin for having proof-read the final version. Special thanks to the editors, Amirouche Moktefi and Sun-Joo Shin, for their careful work.
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