The Euclidean Programme

A. C. Paseau; Wesley Wrigley

doi:10.1017/9781009221955

Series: Elements in the Philosophy of Mathematics

The Euclidean Programme

Published online by Cambridge University Press: 31 January 2024

A. C. Paseau and

Wesley Wrigley

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A. C. Paseau: Affiliation:
University of Oxford
Wesley Wrigley: Affiliation:
LSE - Philosophy, Logic and Scientific Method

Summary

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.

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Euclideanism epistemological foundationalism Pascal mathematical knowledge axioms

Type: Element
Information: Series: Elements in the Philosophy of Mathematics

DOI: https://doi.org/10.1017/9781009221955 [Opens in a new window]

Online ISBN: 9781009221955

Publisher: Cambridge University Press

Print publication: 22 February 2024

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The Euclidean Programme

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