On the Preeminence of Euclidean Geometry: Nash’s Embedding Theorems

Abstract

AbstractAccording to Kant’s philosophy of geometry, Euclidean geometry is synthetic a priori. The advent of non-Euclidean geometries proved this position at least problematic, if not obsolete. However, based on Nash’s embedding theorems we show that a weaker notion of preeminence supports the view that Euclidean geometry, even though not strictly a priori, enjoys a more fundamental status than non-Euclidean geometries.