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

$74.00 USD

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Part of Ideas in Context

  • Date Published: January 2005
  • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • format: Adobe eBook Reader
  • isbn: 9780511035296

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About the Authors
  • 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
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    Awards

    • Winner of the Runciman Award 2000

    Reviews & endorsements

    ' … 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

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    Product details

    • Date Published: January 2005
    • format: Adobe eBook Reader
    • isbn: 9780511035296
    • contains: 2 tables
    • availability: This ISBN is for an eBook version which is distributed on our behalf by a third party.
  • 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.

  • Author

    Reviel Netz, Stanford University, California

    Awards

    • Winner of the Runciman Award 2000

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