Do geometrical diagrams resemble geometrical objects?

Abstract

Geometrical diagrams represent their subjects partially through visual resemblance. I defend this hypothesis against a critique by Panza, who argues that historical evidence indicates that the objects of Euclidean Geometry derive at least some of their spatial features from Euclidean diagrams. However, it is a widespread intuition that resemblance-based depictions reproduce the visual features of their subjects. Therefore, according to Panza, Euclidean diagrams cannot be resemblance-based. I will argue that this common intuition is misguided. As long as the depiction and its subject resemble each other visually, it does not matter which one comes first. Thus, for Euclidean diagrams to be resemblance-based, it is irrelevant whether they reproduce the visual features of geometrical objects, or vice versa, as long as they resemble each other. To support my argument, I will outline a resemblance-based account of depiction that does not assume that the visual appearance of depictions is derived from the visual appearance of their subjects.