Essays on Frege's Foundations of Arithmetic

by Ebert, Philip A.; Rossberg, Marcus

• ISBN13: 9780198712084
• ISBN10: 0198712081
• Format: Hardcover
• Copyright: 2019-11-11
• Publisher: Oxford University Press

Summary

The volume is the first collection of essays that focuses on Gottlob Frege's Basic Laws of Arithmetic (1893/1903), highlighting both the technical and the philosophical richness of Frege's magnum opus. It brings together twenty-two renowned Frege scholars whose contributions discuss a wide range of topics arising from both volumes of Basic Laws of Arithmetic. The original chapters in this volume make vivid the importance and originality of Frege's masterpiece, not just for Frege scholars but for the study of the history of logic, mathematics, and philosophy.

Author Biography

Philip A. Ebert, Senior Lecturer, University of Stirling, Marcus Rossberg, Associate Professor, University of Connecticut

Philip A. Ebert is Senior Lecturer in Philosophy at the University of Stirling. He received his PhD in Philosophy from the University of St Andrews in 2006 and was a Postdoctoral Research Fellow at the Arch? Research Centre from 2005 to 2007.

Marcus Rossberg is Associate Professor of Philosophy at the University of Connecticut. He received his PhD in Philosophy from the University of St Andrews in 2006 and was a Postdoctoral Research Fellow at the Arch? Research Centre from 2005 to 2008.

Table of Contents

Foreword, Philip A. Ebert and Marcus Rossberg
1. The Basic Laws of Cardinal Number, Richard Kimberly Heck
2. Axioms in Frege, Patricia Blanchette
3. When Logic Gives Out: Frege on Basic Logical Laws, Walter B. Pedriali
4. The Context Principle in Frege's Grundgesetze, Oystein Linnebo
5. Why Does Frege Care Whether Julius Caesar is a Numbera Section 10 of Basic Laws and the Context Principle, Joan Weiner
6. Grundgesetze and the Sense/Reference Distinction, Kevin C. Klement
7. Double Value-Ranges, Peter Simons
8. The Proof of Hume's Principle, Robert C. May and Kai F. Wehmeier
9. Frege's Theorems on Simple Series, William Stirton
10. Infinitesimals, Magnitudes, and Definition in Frege, Jamie Tappenden
11. Frege's Relation to Dedekind: Basic Laws and Beyond, Erich H. Reck
12. Frege on Creation, Michael Hallett
13. Mathematical Creation in Frege's Grundgesetze, Philip A. Ebert and Marcus Rossberg
14. Frege on the Real Numbers, Eric Snyder and Stewart Shapiro
15. Frege's Little Theorem and Frege's Way Out, Roy T. Cook
16. How did the serpent of inconsistency enter Frege's paradise?, Crispin Wright
17. Second-Order Abstraction Before and After Russell's Paradox, Matthias Schirn
18. Formal Arithmetic Before Grundgesetze, Richard Kimberly Heck
19. Definitions in Begriffsschrift and Grundgesetze, Michael Kremer
20. A Brief History of English Translations of Frege's Writings, Michael Beaney
21. Translating 'Bedeutung' in Frege's Writings: A Case Study and Cautionary Tale in the History and Philosophy of Translation, Michael Beaney
22. Contemporary Reviews of Frege's Grundgesetze, Philip A. Ebert and Marcus Rossberg