The Euclidean Programme

'The Euclidean Programme' is co-written by Professor of Mathematical Philosophy and Stuart Hampshire Fellow and Tutor in Philosophy, Alex Paseau and Dr Wesley Wrigley, a philosopher based in the Department of Philosophy, Logic, and Scientific Method at the London School of Economics. Dr Wrigley has also spent time at Wadham, lecturing in 2020-21.

Prof Paseau shares, "I’ve wanted to write about ‘the Euclidean Programme’ ever since I first read Imre Lakatos’s account of it. That was back in the late 1990s, when I was a postgraduate student.

Twenty years later, I started thinking about the topic again. Lakatos aside, very little has been written about Euclidean foundationalism in modern English-speaking philosophy. I wrote up some ideas and got talking to Wesley, then a lecturer at Wadham.

We came up with the idea of writing a book on the Euclidean Programme that covers the history of the idea and its philosophical aspects. It's now been published and I hope it lives up to our conception of a work that interestingly combines history and philosophy. It’s grown out of a wonderful Wadham collaboration."

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.