The role of visual methods in geometry is puzzling. Though diagrams can make a geometric theorem immediately evident, current rules of proper inference suggest that diagrams are mere heuristics-simply aiding in the psychological digestibility of a proof. Securing a justificatory role for visual methods involves describing how inference from a diagram guarantees the universality and the a:priority of a geometric theorem. Such an analysis is provided in Kant's synthetic a priori account of geometry. In this paper, Kant's theory is explicated and subsequently defended from attacks related to modern advances in predicate logic, relativistic physics, non-Euclidean geometry and formalism.
McNulty, Michael, "The Geometry of Intuitions: Reconsidering Kantian Constructivism" (2008). Philosophy Honors Projects. 2.
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