Over the past forty years the visual system has been the most important battleground for competing general theories of brain function. In their most interesting form, theories of brain function are directed towards answering basic philosophical questions concerning the nature of mind. A large part of this monograph involves a presentation and analysis of David Marr’s computational theory of vision, focusing especially on his tripartition of computational, algorithmic and implementational levels of analysis. This historical analysis is intended to provide the motivation for a reevaluation of the central methodological presuppositions in the study of the visual system. Ultimately, this book demonstrates that the dream of being able to distinguish psychological functions without attending to neuroscientific detail has come to an end.