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

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.

‘ … 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