Mathematical Pictures (original) (raw)

In this text I develop the thesis that geometrical diagrams are depictions, not symbols; they depict geometrical objects, concepts or states of affairs. Besides developing this claim, I will defend it against three recent challenges from (Sherry 2009), Macbeth (2009, 2010, 2014) and (Panza 2012). First, according to Sherry, diagrams are not depictions, because no single depict can depict more than one thing, yet a single geometrical diagram can represent different geometrical figures in different contexts. I will argue that, once we recognize that resemblance underdetermines depiction, we can see that pictures can indeed depict different thing in different contexts and, consequently, there is nothing surprising about a single diagram depicting different geometrical figures. Next, I will defend it against a similar argument by Macbeth, according to which diagrams can represent different geometrical figures, even within the context of a single geometrical proof. Finally, I will defend it against Panza’s argument that there are essentially spatial features that geometrical objects have only insofar as they inherit them from the diagrams that represent them, and this is incompatible with the hypothesis that geometrical diagrams are depictions for depictions inherit their visual and spatial properties from the objects they represent, and not the other way around. In response, I will argue that once we understand the sense in which subjects are metaphysically prior to their depiction, we will see that my claim that Euclidean diagrams are depictions is not incompatible with Panza’s thesis.