The development of logic

Epigraph ......Page 2
Title ......Page 3
Copyright ......Page 4
Preface ......Page 5
Contents ......Page 7
1. The Notion of Validity ......Page 9
2. Geometrical Demonstration ......Page 10
3. Dialectic and Metaphysical Argument ......Page 15
4. Eristic and Sophistry ......Page 20
5. Plato and the Philosophy of Logic ......Page 25
1. The Contents of the Organon ......Page 31
2. The Doctrine of the Categories and its Logical Consequences ......Page 33
3. The Topics ......Page 41
4. Aristotle's Theory of Meaning and Truth ......Page 53
5. The Four Forms of General Statement ......Page 62
6. The Doctrine of the Syllogism ......Page 75
7. Aristotle's Modal Logic ......Page 89
8. Non-syllogistic Logic in the Analytics ......Page 104
9. Aristotle's School: Theophrastus ......Page 108
1. The Megarian Philosophy and the Origins of Stoic Logic ......Page 121
2. Megarian and Stoic Theories of Modality ......Page 125
3. The Debate on the Nature of Conditionals ......Page 136
4. The Stoic Theory of Meaning and Truth ......Page 146
5. The Stoic System of Inference Schemata ......Page 166
1. From Cicero to Boethius ......Page 185
2. From Alcuin to Abelard ......Page 206
3. The Logic of the Universities ......Page 232
4. Proprietatis Terminorum ......Page 254
5. Consequential ......Page 282
1. Humanism and the Rise of Natural Science ......Page 306
2. The Interests of Leibniz ......Page 328
3. Leibniz's Calculus de Continentibus et Contentis ......Page 344
4. From Saccheri to Hamilton ......Page 353
5. Bolzano and Mill ......Page 366
1. Geometry and Axiomatics ......Page 387
2. Numbers and Functions ......Page 398
3. Boole and the Algebra of Logic ......Page 412
4. Later Developments of Boolean Algebra ......Page 428
5. The Theory of Relations. De Morgan and Peirce ......Page 435
1. Frege and his Contemporaries ......Page 443
2. Cantor's Theory of Sets ......Page 446
3. Frege on his Predecessors ......Page 451
4. Frege's Definitions of the Natural Numbers ......Page 463
5. The Number Series ......Page 475
1. The Begriffsschrift ......Page 486
2. Sense and Reference: Objects and Functions ......Page 501
3. The Logic of the Grundgesetze ......Page 511
4. Frege's Achievement ......Page 518
1. Varieties of Symbolism ......Page 521
2. Methods of Presentation: Axioms and Rules ......Page 532
3. Natural Deduction and Development ......Page 546
4. Modal Logic ......Page 556
5. Suggestions for Alternative Logics ......Page 576
1. Expression, Designation, and Truth ......Page 584
2. The Theory of Descriptions and the Variety of Designations ......Page 601
3. Problems of Intensionaliry ......Page 609
4. Identity, Functions, and Classes ......Page 626
5. Necessity and Language ......Page 636
1. The Paradoxes of the Theory of Sets ......Page 660
2. Russell's Theory of Logical Types ......Page 665
3. The Intuitionism of Brouwer ......Page 680
4. Hilbert's Programme of Metamathematics ......Page 689
1. The Metatheory of Primary Logic ......Page 697
2. The Metatheory of General Logic ......Page 709
3. The Incompletability of Foimal Arithmetic ......Page 720
4. The Decision Problem ......Page 732
5. The Place of Logic among the Sciences ......Page 745
APPENDIX ......Page 751
SELECTIVE BIBLIOGRAPHY ......Page 773
INDEX ......Page 783