Visual reasoning in science and mathematics

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.