Skip to main content
eScholarship
Open Access Publications from the University of California

Representing Geometry: Perception, Concepts, and Knowledge

  • Author(s): Galebach, John Ethan
  • Advisor(s): Heis, Jeremy
  • et al.
No data is associated with this publication.
Abstract

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.

Main Content

This item is under embargo until March 11, 2020.