Mathematical Pictures

There is still debate as to whether Euclidean diagrams are symbols, indexes or icons, and of what sort. I hold them to be pictorial icons that reproduce at least some visual features of their objects. This hypothesis has been directly challenged by Sherry [36] and Panza [29] among others. My aim on this paper is defending this thesis against Macbeth's [24-26] claim that if diagrams were pictures their content could not shift the way it does in Euclidean proof. To this goal I will present a broadly Gricean account of pictorial representation, where visual resemblance constraints but no fully determines reference, and then show how this account ratifies Macbeth's insights about the importance of the author's intentions in determining a diagram's content, in a way that allows for the sort of content-shifting that she has identified as key to understanding the role of diagrams in Euclidean proof.