Mendeley出力
＜図書＞
The philosophical status of diagrams
| 責任表示 | by Mark Greaves |
|---|---|
| シリーズ | CSLI lecture notes ; 116 |
| データ種別 | 図書 |
| 出版情報 | Stanford, Calif. : CSLI Publications , c2002 |
| 本文言語 | 英語 |
| 大きさ | vii, 214 p. : ill. ; 23 cm |
| 概要 | The use of diagrams in logic and geometry has encountered resistance in recent years. For a proof to be valid in geometry, it must not rely on the graphical properties of a diagram. In logic, the tea...hing of proofs depends on sentenial representations, ideas formed as natural language sentences such as "If A is true and B is true...." No serious formal proof system is based on diagrams. This book explores the reasons why structured graphics have been largely ignored in contemporary formal theories of axiomatic systems. In particular, it elucidates the systematic forces in the intellectual history of mathematics which have driven the adoption of sentential representational styles over diagrammatic ones. In this book, the effects of historical forces on the evolution of diagrammatically-based systems of inference in logic and geometry are traced from antiquity to the early twentieth-century work of David Hilbert. From this exploration emerges an understanding that the present negative attitudes towards the use of diagrams in logic and geometry owe more to implicit appeals to their history and philosophical background than to any technical incompatibility with modern theories of logical systems. 続きを見る |
| 目次 | Machine generated contents note: 1 Introduction 1 Part I: Geometry 13 2 Diagrams for Geometry 15 3 Euclidean Geometry 19 4 Descartes and the Rise of Analytic Geometry 35 5 Geometric Diagrams in the Nineteenth Century 43 5.1 Diagrams in the Geometry of Poncelet 43 5.2 Non-Euclidean Geometries and the Rejection of Kantianism 53 5.3 Pasch, Hilbert, and the Rise of Pure Geometry 65 6 Summary 77 Part II: Logic 83 7 Diagrams for Logic 85 8 The Logical Framework of the Syllogism 93 9 Diagrams for Syllogistic Logic 107 9.1 Introduction 107 9.2 The Linguistic Formulation of the Syllogism 110 9.3 Early Diagrams for Syllogistic Logic 115 9.4 Euler Diagrams and the Rise of Extensional Logic 121 10 Diagrams for Symbolic Logic 139 10.1 Introduction 139 10.2 Boole's Symbolic Logic 141 10.3 Boolean Logic and Venn Diagrams 146 10.4 Peirce's Extensional Graphs 162 10.5 Logic at the End of the Nineteenth Century 175 11 Summary 193 12 Conclusion 201.続きを見る |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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: pbk | 中央図 2A | 116/G 81 | 2002 |
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050212003003607 |
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書誌詳細
| 一般注記 | Bibliography: p. 207-[210] Includes index |
|---|---|
| 著者標目 | Greaves, Mark, 1965- |
| 書誌ID | 1000950856 |
| ISBN | 1575862948 |
| NCID | BA59617650 |
| 巻冊次 | : pbk ; ISBN:1575862948 |
| 登録日 | 2009.09.16 |
| 更新日 | 2009.09.16 |