Geometrical Figures in Spinoza's Book of Nature

Emphasizing the abstractness of figures, recent scholarship has tended to reject the standard view that geometrical figures belong in Spinoza's "book of nature." In this paper, I outline an interpretation of Spinozan nature as geometrically tractable that both addresses the challenges facing the standard view and clarifies its basis. I argue that many of the problems that have been raised about figures are actually problems for bodies qua finite, not qua figural. To the extent that finite bodies exist in Spinozan nature, geometrical figures have a place as the determinations of finite bodies. Geometry, moreover, is relevant to the knowledge of the geometrical properties of finite bodies. The need for continuity between intellectual and imaginative conceptions of finite bodies implied by the role of experience in Spinoza's scientific method speaks in favor of the adequacy of geometrical conceptions of finite bodies. I suggest that Spinoza countenances the deployment of intellectual geometric conceptions as part of a hypothetico-deductive approach to natural science.