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Ⅰ．THE BEGINNINGS 1

1．The Notion of Validity 1

2．Geometrical Demonstration 2

3．Dialectic and Metaphysical Argument 7

4．Eristic and Sophistry 12

5．Plato and the Philosophy of Logic 17

Ⅱ．ARISTOTLE＇S ORGANON 23

1．The Contents of the Organon 23

2．The Doctrine of the Categories and its Logical Consequences 25

3．The Topics 33

4．Aristotle＇s Theory of Meaning and Truth 45

5．The Four Forms of General Statement 54

6．The Doctrine of the Syllogism 67

7．Aristotle＇s Modal Logic 81

8．Non-sysllogistic Logic in the Analytics 96

9．Aristotle＇s School：Theophrastus 100

Ⅲ．THE MEGARIANS AND THE STOICS 113

1．The Megarian Philosophy and the Origins of Stoic Logic 113

2．Megarian and Stoic Theories of Modality 117

3．The Debate on the Nature of Conditionals 128

4．The Stoic Theory of Meaning and Truth 138

5．The Stoic System of Inference Schemata 158

Ⅳ．ROMAN AND MEDIEVAL LOGIC 177

1．From Cicero to Boethius 177

2．From Alcuin to Abelard 198

3．The Logic of the Universities 224

4．Proprietates Terminorum 246

5．Consequentiae 274

Ⅴ．LOGIC AFTER THE RENAISSANCE 298

1．Humanism and the Rise of Natural Science 298

2．The Interests of Leibniz 320

3．Leibniz＇s Calculus de Continentibus et Contentis 336

4．From Saccheri to Hamilton 345

5．Bolzano and Mill 358

Ⅵ．MATHEMATICAL ABSTRACTION 379

1．Geometry and Axiomatics 379

2．Numbers and Functions 390

3．Boole and the Algebra of Logic 404

4．Later Developments of Boolean Algebra 420

5．The Theory of Relations：De Morgan and Peirce 427

Ⅶ．NUMBERS，SETS，AND SERIES 435

1．Frege and his Contemporaries 435

2．Cantor＇s Theory of Sets 438

3．Frege on his Predencessors 443

4．Frege＇s Definitions of the Natural Numbers 455

5．The Number Series 467

Ⅷ．FREGE＇S GENERAL LOGIC 478

1．The Begriffsschri@t 478

2．Sense and Referemce：Objects and Functions 493

3．The Logic of the Grundgesetze 503

4．Frege＇s Achievement 510

Ⅸ．FORMAL DEVELOPMENTS AFTER FREGE 513

1．Varieties of Symbolism 513

2．Methods of Presentation：Axioms and Rules 524

3．Natural Deduction and Development 538

4．Modal Logic 548

5．Suggestions for Alternative Logics 568

Ⅹ．THE PHILOSOPHY OF LOGIC AFTER FREGE 576

1．Expression，Designation，and Truth 576

2．The Theory of Descriptions and the Variety of Designations 593

3．Problems of Intensionality 601

4．Identity，Functions，and Classes 618

5．Necessity and Language 628

Ⅺ．THE PHILOSOPHY OF MATHEMATICS AFTER FREGE 652

1．The Paradoxes of the Theory of Sets 652

2．Russell＇s Theory of Logical Types 657

3．The Intuitionism of Brouwer 672

4．Hilbert＇s Programme of Metamathematics 681

Ⅻ．THE THEORY OF DEDUCTIVE SYSTEMS 689

1．The Metatheory of Primary Logic 689

2．The Metatheory of General Logic 701

3．The Incompletability of Formal Arithmetic 712

4．The Decision Problem 724

5．The Place of Logic among the Sciences 737

APPENDIX 743

SELECTIVE BIBLIOGRAPHY 765

INDEX 775