From Peirce to Skolem (eBook)

Cover 1
Contents 10
Introduction 14
Chapter 1. The Early Work of Charles S. Peirce 22
1.1. Overview of the Mathematical Systems of Charles S. Peirce 22
1.2. Peirce’s Influence on the Development of Logic 24
1.3. Peirce’s Early Approaches to Logic 27
Chapter 2. Peirce’s Calculus of Relatives: 1870 36
2.1. Peirce’s Algebra of Relations 37
2.2. Quantification in the Calculus of Relatives in 1870 59
2.3. Summary 61
Chapter 3. Peirce on the Algebra of Logic: 1880 64
3.1. Overview of Peirces On the algebra of logicŽ 64
3.2. Discussion 67
3.3. Conclusion 86
Chapter 4. Mitchell on a New Algebra of Logic: 1883 88
4.1. Mitchell’s Rule of Inference 88
4.2. Single-Variable Monadic Logic 91
4.3. Two-Variable Monadic Logic 99
4.4. Three-Variable Monadic Logic 102
4.5. Peirce on Mitchell 103
Chapter 5. Peirce on the Algebra of Relatives: 1883 108
5.1. Background in Linear Associative Algebras 108
5.2. The Algebra of Relatives 111
5.3. Syllogistic in the Relative Calculus 117
5.4. Prenex Predicate Calculus 119
5.5. Summary of Peirce's Accomplishments in 1883 122
5.6. Peirce's Appraisal of His Algebra of Binary Relatives 124
Chapter 6. Peirce’s Logic of Quantifiers: 1885 126
6.1. On the Derivation of Logic from Algebra 126
6.2. Nonrelative Logic 129
6.3. First-Order Logic 140
6.4. Second-Order Logic 145
Chapter 7. Schröder’s Calculus of Relatives 156
7.1. Die Algebra der Logik: Volume 1 157
7.2. Die Algebra der Logik: Volume 2 160
7.3. Die Algebra der Logik: Volume 3 162
7.4. Norbert Wiener’s Ph.D. Thesis 178
Chapter 8. Löwenheim’s Contribution 182
8.1. Overview of Löwenheim’s 1915 Paper 184
8.2. Löwenheim’s Theorem 185
8.3. Conclusions 204
8.4. Impact of Löwenheim’s Paper 208
Chapter 9. Skolem’s Recasting 210
Appendices 220
Appendix 1. Schröder’s Lecture I 220
Appendix 2. Schröder’s Lecture II 236
Appendix 3. Schröder’s Lecture III 264
Appendix 4. Schröder’s Lecture V 270
Appendix 5. Schröder’s Lecture IX 308
Appendix 6. Schröder’s Lecture XI 352
Appendix 7. Schröder’s Lecture XII 392
Appendix 8. Norbert Wiener’s Thesis 442
Bibliography 458
Index 474