Representing Geometry: Perception, Concepts, and Knowledge

In this dissertation, I investigate how humans represent space and other geometric entities. The topics of my three chapters are delimited by three kinds of spatial representation: perception, conception, and propositional knowledge. In chapter 1, argue against the widely-held philosophical view that the content of visual perception includes a “geometry,” or more precisely, a metric space. I appeal to behavioral and neural evidence to argue that the spatial contents of visual perception exhibit a disunity that most philosophers since Kant would find surprising. In chapter 2, I evaluate a theory of geometric concept acquisition known as “core geometric cognition,” and I use behavioral and neural evidence to argue that the most general assumptions of this approach are likely false. In chapter 3, I defend the view that, despite the geometric disunity exhibited by perception, it is still plausible to believe that some propositional knowledge of advanced mathematical theorems is grounded in visual imagination