The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History: 51 (Ideas in Context, Series Number 51) - Hardcover

Netz, Reviel

Hardcover

ISBN 10: 0521622794 ISBN 13: 9780521622790

Publisher: Cambridge University Press, 1999

Synopsis

The aim of this book is to explain the shape of Greek mathematical thinking. It can be read on three levels: as a description of the practices of Greek mathematics; as a theory of the emergence of the deductive method; and as a case-study for a general view on the history of science. The starting point for the enquiry is geometry and the lettered diagram. Reviel Netz exploits the mathematicians' practices in the construction and lettering of their diagrams, and the continuing interaction between text and diagram in their proofs, to illuminate the underlying cognitive processes. A close examination of the mathematical use of language follows, especially mathematicians' use of repeated formulae. Two crucial chapters set out to show how mathematical proofs are structured and explain why Greek mathematical practice manages to be so satisfactory. A final chapter looks into the broader historical setting of Greek mathematical practice.

About this title

Review

' ... a necessary read for anyone interested in the history of Greek mathematics but will also be interesting to a wider audience, particularly philosophers of science and intellectual historians ... Netz has made an important contribution to intellectual history and has asked a diverse set of questions whose answers, while difficult, will broaden our understanding of the development of deductive practices.' Bryn Mawr Classical Review

'This is a fascinating and stimulating book ...'. Journal of Hellenic Studies

'... his views are sure not only to stimulate some interesting debates outside the philosophical community ... but also to give philosophers of science an exotic fruit to sink their teeth into.' Philosophical Writings

' ... very well written ... almost every sentence, indeed next to every clause, carries a message that asks for the reader's active thought. It can safely be recommended as s must to anybody who is genuinely interested in the relation between Greek mathematics and logic ...' Studia Logica

Book Description

This book provides a way into understanding a momentous development in human intellectual history: the phenomenon of deductive argument in classical Greek mathematics. The argument rests upon a close description of the practices of Greek mathematics, principally the use of lettered diagrams and the regulated, formulaic use of language.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1999
• Language: English
• ISBN 10: 0521622794
• ISBN 13: 9780521622790
• Binding: Hardcover
• Number of pages: 352