Inducing visibility and visual deduction

Scientists use diagrams not just to visualize objects and relations in their fields, both empirical and theoretical, but to reason with them as tools of their science. While the two dimensional space of diagrams might seem restrictive, scientific diagrams can depict many more than two elements, can be used to visualise the same materials in myriad different ways, and can be constructed in a considerable variety of forms. This paper takes up two generic puzzles about 2D visualizations. First: How do scientists in different communities use 2D spaces to depict materials which are not fundamentally spatial? This prompts the distinction between diagrams that operate in different kinds of spaces: ‘real’, ‘ideal’, and ‘artificial’. And second: How do diagrams, in these different usages of 2D space, support various kinds of visual reasoning that cross over between inductive and deductive? The argument links the representational form and content of a diagram (its vocabulary and grammar) with the kinds of inferential and manipulative reasoning that are afforded, and constrained, by scientists’ different usages of 2D space.