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The Euclidean Programme
Hardcover
Series: Elements in the Philosophy of Mathematics
History & Philosophy of Science
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ISBN10: 1009494406
ISBN13: 9781009494403
Publisher: Cambridge University Press
Published: Feb 22 2024
Pages: 82
Weight: 0.62
Height: 0.25 Width: 6.00 Depth: 9.00
Language: English
ISBN13: 9781009494403
Publisher: Cambridge University Press
Published: Feb 22 2024
Pages: 82
Weight: 0.62
Height: 0.25 Width: 6.00 Depth: 9.00
Language: English
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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