《The Development of Logic》

Ⅰ．THE BEGINNINGS1

1．The Notion of Validity1

2．Geometrical Demonstration2

3．Dialectic and Metaphysical Argument7

4．Eristic and Sophistry12

5．Plato and the Philosophy of Logic17

Ⅱ．ARISTOTLE＇S ORGANON23

1．The Contents of the Organon23

2．The Doctrine of the Categories and its Logical Consequences25

3．The Topics33

4．Aristotle＇s Theory of Meaning and Truth45

5．The Four Forms of General Statement54

6．The Doctrine of the Syllogism67

7．Aristotle＇s Modal Logic81

8．Non-sysllogistic Logic in the Analytics96

9．Aristotle＇s School：Theophrastus100

Ⅲ．THE MEGARIANS AND THE STOICS113

1．The Megarian Philosophy and the Origins of Stoic Logic113

2．Megarian and Stoic Theories of Modality117

3．The Debate on the Nature of Conditionals128

4．The Stoic Theory of Meaning and Truth138

5．The Stoic System of Inference Schemata158

Ⅳ．ROMAN AND MEDIEVAL LOGIC177

1．From Cicero to Boethius177

2．From Alcuin to Abelard198

3．The Logic of the Universities224

4．Proprietates Terminorum246

5．Consequentiae274

Ⅴ．LOGIC AFTER THE RENAISSANCE298

1．Humanism and the Rise of Natural Science298

2．The Interests of Leibniz320

3．Leibniz＇s Calculus de Continentibus et Contentis336

4．From Saccheri to Hamilton345

5．Bolzano and Mill358

Ⅵ．MATHEMATICAL ABSTRACTION379

1．Geometry and Axiomatics379

2．Numbers and Functions390

3．Boole and the Algebra of Logic404

4．Later Developments of Boolean Algebra420

5．The Theory of Relations：De Morgan and Peirce427

Ⅶ．NUMBERS，SETS，AND SERIES435

1．Frege and his Contemporaries435

2．Cantor＇s Theory of Sets438

3．Frege on his Predencessors443

4．Frege＇s Definitions of the Natural Numbers455

5．The Number Series467

Ⅷ．FREGE＇S GENERAL LOGIC478

1．The Begriffsschri@t478

2．Sense and Referemce：Objects and Functions493

3．The Logic of the Grundgesetze503

4．Frege＇s Achievement510

Ⅸ．FORMAL DEVELOPMENTS AFTER FREGE513

1．Varieties of Symbolism513

2．Methods of Presentation：Axioms and Rules524

3．Natural Deduction and Development538

4．Modal Logic548

5．Suggestions for Alternative Logics568

Ⅹ．THE PHILOSOPHY OF LOGIC AFTER FREGE576

1．Expression，Designation，and Truth576

2．The Theory of Descriptions and the Variety of Designations593

3．Problems of Intensionality601

4．Identity，Functions，and Classes618

5．Necessity and Language628

Ⅺ．THE PHILOSOPHY OF MATHEMATICS AFTER FREGE652

1．The Paradoxes of the Theory of Sets652

2．Russell＇s Theory of Logical Types657

3．The Intuitionism of Brouwer672

4．Hilbert＇s Programme of Metamathematics681

Ⅻ．THE THEORY OF DEDUCTIVE SYSTEMS689

1．The Metatheory of Primary Logic689

2．The Metatheory of General Logic701

3．The Incompletability of Formal Arithmetic712

4．The Decision Problem724

5．The Place of Logic among the Sciences737

APPENDIX743

SELECTIVE BIBLIOGRAPHY765

INDEX775