The Euclidean Programme

The Euclidean Programme is an epistemological foundationalism that derives mathematical knowledge from self-evident axioms or first principles, which is examined in detail in this book. It compares the reconstructed programme with historical sources and philosophically assesses it, concluding with a replacement for it.

Format: Paperback / softback
Length: 82 pages
Publication date: 22 February 2024
Publisher: Cambridge University Press

The Euclidean Programme represents a traditional form of epistemological foundationalism, which posits that knowledge, particularly mathematical knowledge, is derived through deduction from self-evident axioms or first principles. While epistemologists have extensively studied foundationalism, they have largely overlooked its dominant Euclidean manifestation. In contrast, this book provides a comprehensive exploration of Euclidean foundationalism, which the authors refer to as the Euclidean Programme. Through a rational reconstruction of the programme's key principles, the authors demonstrate how it interprets the axiomatic method epistemologically. The book then compares the reconstructed programme with selected historical sources, including 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.

In the second half of the book, the authors philosophically assess the programme, examining whether various areas of contemporary mathematics conform to it. The book concludes by proposing a replacement for the Euclidean Programme.

This comprehensive examination of Euclidean foundationalism offers valuable insights into the philosophical foundations of mathematics and its historical development. It sheds light on the epistemological principles underlying mathematical knowledge and the role of axiomatic methods in shaping our understanding of the discipline. By comparing the reconstructed programme with historical sources, the book provides a rich context for understanding the evolution of mathematical thought and the challenges faced by contemporary mathematicians. The philosophical assessment of the programme further deepens our understanding of the strengths and limitations of foundationalism and its potential for addressing contemporary epistemological concerns. Overall, this book is a valuable resource for scholars and students interested in the philosophy of mathematics, epistemology, and the history of mathematics.

Weight: 133g
ISBN-13: 9781009221986