The Euclidean Programme

This Element shows that Euclidean Programme (EP) embodies a traditional epistemological foundationalism about mathematics. Epistemologists have examined foundationalism more generally, but neglected its more specific, and historically dominant, instance--the EP. This Element is devoted to an examination of the EP. The authors propose a rational reconstruction of the EP's key principles, showing it to be more than the axiomatic method. The authors compare their reconstruction of the EP with some historical accounts: Euclid's Elements, Aristotle's discussion of scientific method in the Posterior Analytics, the 17th-century accounts in Descartes' Discourse on Method and Blaise Pascal's On the Geometric Mind, and 20th-century Descriptive Axiomatisation. Next, history is followed by philosophical assessment. The authors critically assess the EP, and sketch what it should be replaced with.