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E-raamat: Shaping of Deduction in Greek Mathematics: A Study in Cognitive History

(Stanford University, California)
  • Formaat: PDF+DRM
  • Sari: Ideas in Context
  • Ilmumisaeg: 11-Mar-1999
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9780511035296
  • Formaat - PDF+DRM
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  • Formaat: PDF+DRM
  • Sari: Ideas in Context
  • Ilmumisaeg: 11-Mar-1999
  • Kirjastus: Cambridge University Press
  • Keel: eng
  • ISBN-13: 9780511035296

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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.

Arvustused

' 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 Logica

Muu info

Winner of Runciman Award 2000.An examination of the emergence of the phenomenon of deductive argument in classical Greek mathematics.
Preface xi
List of abbreviations
xiii
The Greek alphabet xvi
Note on the figures xvii
Introduction 1(8)
A specimen of Greek mathematics 9(304)
The lettered diagram
12(56)
The pragmatics of letters
68(21)
The mathematical lexicon
89(38)
Formulae
127(41)
The shaping of necessity
168(72)
The shaping of generality
240(31)
The historical setting
271(42)
Appendix: The main Greek mathematicians cited in the book 313(3)
Bibliography 316(7)
Index 323