Kant on the Generality of Model-Based Reasoning in Geometry

Abstract

Kant can be seen as the philosophical ancestor of contemporary attempts to articulate the epistemological and practical significance of model-based reasoning. His recognition of the role of singular, immediate representations, or intuitions, in synthetic judgment–and thus in our ampliative claims about the world–is not only central to his philosophical program, but also grounded in many of the same insights that underwrite the contemporary MBR research program. Kant’s account of the necessary role of intuition in synthetic judgment is introduced by way of his philosophy of mathematics. Mathematics, and most significantly Euclidean geometry, is what first opens Kant’s eyes to the crucial role of what we would now call models in establishing contentful, novel claims about the world. Similarly, contemporary work in model-based reasoning in mathematics has also focused on Euclidean geometry (Giardino 2017). In this paper, I hope to bring out some of the ways that Kant’s reflections on geometry not only anticipate this contemporary work, but also rest on the very same features of Euclidean proof. Furthermore, some of the challenges faced by Kant’s model-based account of geometrical reasoning are still very much with us.