The Netz-Works of Greek Deductions – A Review of Reviel Netz’s The Shaping of Deductions in Greek Mathematics

Netz’s book is, without question, the most important work in science studies since Shapin & Schaffer Leviathan and the Air Pump. By resorting to a very original semiotic and constructivist method, it manages to redescribe entirely the practice of deduction in the beginning of Greek geometry. It shows how this practice bears almost no connection with the various theories of abstraction and conviction that have been offered by philosophers from Plato onwards. It offers the first systematic non-formalist description of formalism at its early historical stage. In doing so it offers the best occasion to elaborate a metalangage to speak concretely of abstraction.