The Shaping of Deduction in Greek Mathematics
A Study in Cognitive History
Published on 18. September 2003
Book
Paperback/Softback
352 pages
978-0-521-54120-6 (ISBN)
Description
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.
Reviews / Votes
' ... 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 LogicaMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Target group
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
Worked examples or Exercises; 2 Tables, unspecified; 2 Plates, unspecified
Dimensions
Height: 229 mm
Width: 152 mm
Thickness: 21 mm
Weight
572 gr
ISBN-13
978-0-521-54120-6 (9780521541206)
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Schweitzer Classification
Other editions
Additional editions
E-Book
01/2005
1st Edition
Cambridge University Press
€67.99
Available for download
Person
Content
Introduction: a specimen of Greek mathematics; 1. The lettered diagram; 2. The pragmatics of letters; 3. The mathematical lexicon; 4. Formulae; 5. The shaping of necessity; 6. The shaping of generality; 7. The historical setting; Appendix: the main Greek mathematicians cited in the book.