Essays on Frege's Foundations of Arithmetic

ISBN : 9780198712084

Philip A. Ebert; Marcus Rossberg
672 Pages
153 x 234 mm
Pub date
Aug 2019
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This volume is the first collective study of a foundational text in modern philosophy and logic, Gottlob Frege's Basic Laws of Arithmetic
which appeared in two volumes in 1893 and 1903. Twenty-two Frege scholars discuss a wide range of philosophical and logical topics arising from Basic Laws of Arithmetic, and demonstrate the technical and philosophical richness of the work. Their original contributions make vivid the importance of this magnum opus not just for Frege scholars but for the study of the history of logic, mathematics, and philosophy.


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

About the author: 

Philip A. Ebert received his PhD from the University of St Andrews in 2006 and was a Post Doctoral Fellow at the Arche Centre from 2005-2007. Since 2007 he has worked at the University of Stirling.
Marcus Rossberg received his PhD from the University of St Andrews in 2006 and was a Post Doctoral Fellow at the Arche Centre from 2005-2008. Since 2008 he has worked at the University of Connecticut.

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