What is perception doing in mathematical reasoning? To address this question, I discuss the role of perception in geometric reasoning. Perception of the shape properties of concrete diagrams provides, I argue, a surrogate consciousness of the shape properties of the abstract geometric objects depicted in the diagrams. Some of what perception is not doing in mathematical reasoning is also discussed. I take issue with both Parsons and Maddy. Parsons claims that we perceive a certain type of abstract object. Maddy claims (...) (at least at one time claimed) that perception provides the basis for intuition of mathematical sets. 1 Mathematical reasoning with diagrams 2 Do we perceive abstract objects? 3 Do we perceive mathematical sets? (shrink)

Shepard claims that “evolutionary internalization of universal regularities in the world” takes place. His position is interesting and seems plausible with regard to “default” motion detection and aspects of colour constancy which he addresses. However, his claim is not convincing with regard to object recognition. [Shepard].

Representationalism emerges unscathed from Pessoa et al.'s attack. They fail to undermine a key reason for its influence: it has the theoretical resources to explain many illusory visual experiences such as illusory contours and features. Furthermore, in attempting to undermine representationalism, the authors seem to erect an unduly inflated distinction between neural accounts of perception and personal-level accounts of perception.