Space and Geometry in Kant's Critical Epistemology

Ohio State University Research Foundation -Do Not Use, Columbus OH

Investigators

Abstract

Project Abstract SES Proposal 0135441 Space and Geometry in Kant's Critical Epistemology Lisa Shabel, Ohio State University This project has two interdependent aims: 1) to examine Kant's philosophy of mathematics in its eighteenth-century historical context; and 2) to determine the role that Kant's philosophy of mathematics plays in the epistemological view he defends in the "Critique of Pure Reason." The project is motivated, at least in part, by the weakness of traditional interpretations of Kant's philosophy of mathematics. Most recent commentary on Kant's philosophy of mathematics falls victim to one or another sort of isolationism: commentators interpret Kant's philosophy of mathematics in isolation either from the eighteenth-century mathematical milieu that was familiar to him and his contemporaries, or from the epistemological arguments and results that his own philosophy of mathematics was deployed to serve, or both. This project aims to provide an account of Kant's philosophy of mathematics that situates it with respect to both the mathematical results that inspired it and the epistemological results that it inspired. The project uses textual research to show that in the eighteenth-century both symbolic and non-symbolic mathematical methods were dependent on constructive geometric procedures; in particular, early modern editions of Euclid's Elements show that modern geometric methods depend on diagrammatic reasoning. This textual research will support a defense of Kant's philosophy of geometry as a rich and compelling account of eighteenth-century mathematical practice. The project also shows that Kant's epistemological arguments regarding the nature of space serve to provide a foundation for constructive geometric procedures by establishing the pure cognitive faculty of spatial intuition as the source of geometric reasoning. It follows that, for Kant, the a priori representation of space is both the object of geometry and the medium in which we perceive spatial objects. In defending this interpretation of Kant, the project also provides a new explanation of Kant's defense of the applicability of pure geometry.