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.

List of contents

1. Introduction; 2. The Euclidean programme; 3. Before the EP: Euclid; 4. Before the EP: Aristotle; 5. The EP's 17th-century apogee; 6. Descriptive Axiomatisation and the EP; 7. The EP assessed: core principles; 8. The EP assessed: subsidiary principles; 9. What should replace the EP?; 10. Summary; References.

Summary

This Element shows that Euclidean Programme (EP) embodies a traditional sort of epistemological foundationalism about mathematics. This Element is devoted to an examination of the EP. The authors propose a rational reconstruction of the EP's key principles, superior to the axiomatic method.

Foreword

This Element shows Euclidean foundationalism as a dominant historical paradigm along with its tenets, advocates, and accuracy.

Product details

• Authors: A. C. Paseau, A. C. (University of Oxford) Wrigley Paseau, Paseau A. C., Wesley Wrigley
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 29.02.2024
• EAN: 9781009494403
• ISBN: 978-1-0-0949440-3
• No. of pages: 82
• Series: Elements in the Philosophy of Mathematics
• Subjects: Humanities, art, music > Philosophy > General, dictionaries; Natural sciences, medicine, IT, technology > Natural sciences (general); SCIENCE / Philosophy & Social Aspects, Philosophy of Mathematics, Philosophy: epistemology & theory of knowledge, Ancient Greek and Roman philosophy, Western philosophy: Ancient, to c 500, Philosophy: epistemology and theory of knowledge, Euclidean geometry