Elsevier S & T

From Peirce to Skolem: A Neglected Chapter in the History of Logic

Brady, Geraldine

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Table of contents
  • Cover
  • Contentsix
  • Introduction1
  • Chapter 1. The Early Work of Charles S. Peirce9
  • 1.1. Overview of the Mathematical Systems of Charles S. Peirce9
  • 1.2. Peirce’s Influence on the Development of Logic11
  • 1.3. Peirce’s Early Approaches to Logic14
  • Chapter 2. Peirce’s Calculus of Relatives: 187023
  • 2.1. Peirce’s Algebra of Relations24
  • 2.2. Quantification in the Calculus of Relatives in 187046
  • 2.3. Summary48
  • Chapter 3. Peirce on the Algebra of Logic: 188051
  • 3.1. Overview of Peirces On the algebra of logicŽ51
  • 3.2. Discussion54
  • 3.3. Conclusion73
  • Chapter 4. Mitchell on a New Algebra of Logic: 188375
  • 4.1. Mitchell’s Rule of Inference75
  • 4.2. Single-Variable Monadic Logic78
  • 4.3. Two-Variable Monadic Logic86
  • 4.4. Three-Variable Monadic Logic89
  • 4.5. Peirce on Mitchell90
  • Chapter 5. Peirce on the Algebra of Relatives: 188395
  • 5.1. Background in Linear Associative Algebras95
  • 5.2. The Algebra of Relatives98
  • 5.3. Syllogistic in the Relative Calculus104
  • 5.4. Prenex Predicate Calculus106
  • 5.5. Summary of Peirce's Accomplishments in 1883109
  • 5.6. Peirce's Appraisal of His Algebra of Binary Relatives111
  • Chapter 6. Peirce’s Logic of Quantifiers: 1885113
  • 6.1. On the Derivation of Logic from Algebra113
  • 6.2. Nonrelative Logic116
  • 6.3. First-Order Logic127
  • 6.4. Second-Order Logic132
  • Chapter 7. Schröder’s Calculus of Relatives143
  • 7.1. Die Algebra der Logik: Volume 1144
  • 7.2. Die Algebra der Logik: Volume 2147
  • 7.3. Die Algebra der Logik: Volume 3149
  • 7.4. Norbert Wiener’s Ph.D. Thesis165
  • Chapter 8. Löwenheim’s Contribution169
  • 8.1. Overview of Löwenheim’s 1915 Paper171
  • 8.2. Löwenheim’s Theorem172
  • 8.3. Conclusions191
  • 8.4. Impact of Löwenheim’s Paper195
  • Chapter 9. Skolem’s Recasting197
  • Appendices207
  • Appendix 1. Schröder’s Lecture I207
  • Appendix 2. Schröder’s Lecture II223
  • Appendix 3. Schröder’s Lecture III251
  • Appendix 4. Schröder’s Lecture V257
  • Appendix 5. Schröder’s Lecture IX295
  • Appendix 6. Schröder’s Lecture XI339
  • Appendix 7. Schröder’s Lecture XII379
  • Appendix 8. Norbert Wiener’s Thesis429
  • Bibliography445
  • Index461
Book details
  • Vendor Elsevier S & T
  • SKU 9780444503343
  • ISBN-13 9780080532028
  • Author Brady, Geraldine
  • Category Mathematics
  • Subject Logic

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This book is an account of the important influence on the development of mathematical logic of Charles S. Peirce and his student O.H. Mitchell, through the work of Ernst Schröder, Leopold Löwenheim, and Thoralf Skolem. As far as we know, this book is the first work delineating this line of influence on modern mathematical logic.