The Euclidean Programme

The Euclidean Programme embodies a traditional sort of epistemological foundationalism according to which knowledge especially mathematical knowledge is obtained by deduction from self-evident axioms or first principles. Epistemologists have examined foundationalism extensively but neglected its historically dominant Euclidean form. By contrast this book offers a detailed examination of Euclidean foundationalism which following Lakatos the authors call the Euclidean Programme. The book rationally reconstructs the programme''s key principles showing it to be an epistemological interpretation of the axiomatic method. It then compares the reconstructed programme with select historical sources: Euclid''s Elements Aristotle''s Posterior Analytics Descartes''s Discourse on Method Pascal''s On the Geometric Mind and a twentieth-century account of axiomatisation. The second half of the book philosophically assesses the programme exploring whether various areas of contemporary mathematics conform to it. The book concludes by outlining a replacement for the Euclidean Programme.