Imagine a Place

Abstract Proclus conceived of complex kinematic constructions in geometry as involving motions of points and lines that produced figures like conic sections within the phantasia (imagination) of the reasoner. He contended that in such constructions, the geometer projects various figures in three-dimensional space and not on a two-dimensional screen, as many commentators believe. Hence Proclus believes in what one might call the three-dimensionality of imagination. He also presents the remarkable argument that space should be understood as a kind of intelligible matter, where the latter is understood to be three-dimensional (not merely two-dimensional). Finally, the chapter discusses the extent to which Proclus foresees various early modern conceptions of space.