Abstract
Diagrams are hybrid entities, which incorporate both linguistic and pictorial elements, and are crucial to any account of scientific and mathematical reasoning. Hence, they offer a rich source of examples to examine the relation between model-theoretic considerations (central to a model-based approach) and linguistic features (crucial to a language-based view of scientific and mathematical reasoning). Diagrams also play different roles in different fields. In scientific practice, their role tends not to be evidential in nature, and includes: (i) highlighting relevant relations in a micrograph (by making salient certain bits of information); (ii) sketching the plan for an experiment; and (iii) expressing expected visually salient information about the outcome of an experiment. None of these traits are evidential; rather they are all pragmatic. In contrast, in mathematical practice, diagrams are used as (i) heuristic tools in proof construction (including dynamic diagrams involved in computer visualization); (ii) notational devices; and (iii) full-blown proof procedures (Giaquinto 2005; and Brown in Philosophy of mathematics. Routledge, New York, 2008). Some of these traits are evidential. After assessing these different roles, I explain why diagrams are used in the way they are in these two fields. The result leads to an account of different styles of scientific reasoning within a broadly model-based conception.
