The shaping of deduction in Greek mathematics : a study in cognitive history
著者
書誌事項
The shaping of deduction in Greek mathematics : a study in cognitive history
（Ideas in context / edited by Quentin Skinner (general editor) ... [et al.], 51）
Cambridge University Press, 1999
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注記
Includes bibliographical references (p. 316-322) and index
内容説明・目次
内容説明
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.
目次
- 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.
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