The Shaping of Deduction in Greek Mathematics
A Study in Cognitive History

An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics.

Reviel Netz (Author)

9780521622790, Cambridge University Press

Hardback, published 11 March 1999

352 pages, 2 tables
22.9 x 15.2 x 2.4 cm, 0.69 kg

' … 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

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.

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.

Subject Areas: History of science [PDX], Philosophy of science [PDA], History of ideas [JFCX], Western philosophy: Ancient, to c 500 [HPCA]