The Shaping of Deduction in Greek Mathematics
The Shaping of Deduction in Greek Mathematics
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.
- Brilliant investigation of a crucial and unexplored process
- As interesting for students of cognitive science as for those of Greek mathematics
- Should become the classic and definitive treatment of this phenomenon
Reviews & endorsements
"Reviel Netz has written a stimulating book about diagrams and mathematics, telling us facts that we all know, but hardly ever thought of." MAA Online
"...a novel work...Greek intellectual culture will be of interest to many classicists...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." Daryn Lehoux, University of Toronto
"Netz's book has made this reviewer look at Greek mathematics with new eyes, and it will certainly provoke further thought and discussion. Netz is to be thanked for a stimulating contribution to an important topic." Isis
"It's a first-contribution to intellectual history... also an enjoyable book....The Shaping of Deduction in Greek Mathematics will be of interest, not just to historians of mathematics, but to mathematicians and philosophers seeking to understand the aims and achievements of mathematics today." Philosophia Mathematica
Product details
September 2003Paperback
9780521541206
352 pages
229 × 152 × 23 mm
0.54kg
2 tables
Available
Table of Contents
- 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.
