The Nature of Diagrammatic Reasoning

We tend to think of mathematical proofs as written texts, mixtures of ordinary language (using expressions, such as “Therefore”, “Let this or that be given”, …) and mathematical symbols. In the ideal situation all use of ordinary language can be eliminated. This view is contradicted by actual mathematical practice where drawings, figures, diagrams, …, play a fundamentally important role. Hence it is important to understand how these diagrams function. As said, work has been done (see, e.g., Carter (2010)), but a lot of bottom-up work will be necessary, so in the first phase materials have to be collected to come to a theory of diagrams in the second phase. It must be mentioned here that there are logical approaches to the problem, see, e.g., Shin (1995) and Mumma (2010), which establishes a relation with the FP subprojects.