The Finite and the Infinite in Frege's Grundgesetze der Arithmetik
In M. Schirn (ed.), Philosophy of Mathematics Today. OUP (1998)
| Abstract | Discusses Frege's formal definitions and characterizations of infinite and finite sets. Speculates that Frege might have discovered the "oddity" in Dedekind's famous proof that all infinite sets are Dedekind infinite and, in doing so, stumbled across an axiom of countable choice. | |||||||||
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Richard Heck (1993). The Development of Arithmetic in Frege's Grundgesetze der Arithmetik. Journal of Symbolic Logic 58 (2):579-601.
Fernando Ferreira (2005). Amending Frege's Grundgesetze der Arithmetik. Synthese 147 (1).
Richard Heck (1995). Definition by Induction in Frege's Grundgesetze der Arithmetik. In W. Demopoulos (ed.), Frege's Philosophy of Mathematics. OUP.
Fernando Ferreira (2005). Amending Frege's "Grundgesetze der Arithmetik" to the Memory of Nhê (1925-2001). Synthese 147 (1):3 - 19.
Richard Heck & George Boolos (1998). Die Grundlagen der Arithmetik §§82-83. In M. Schirn (ed.), Philosophy of Mathematics Today. OUP.
Richard Heck (1996). The Consistency of Predicative Fragments of Frege's Grundgesetze der Arithmetik. History and Philosophy of Logic 17 (1):209-220.
Kai F. Wehmeier (2004). Russell's Paradox in Consistent Fragments of Frege's Grundgesetze der Arithmetik. In Godehard Link (ed.), One Hundred Years of Russell’s Paradox. de Gruyter.
Yaroslav D. Sergeyev (2008). A New Applied Approach for Executing Computations with Infinite and Infinitesimal Quantities. Informatica 19 (4):567-596.
G. Frege (1960). Grundgesetze der Arithmetik. Section 56ff. In P. Geach & M. Black (eds.), Translations From the Philosophical Writings of Gottlob Frege. Blackwell.
Gottlob Frege (1950). Frege Against the Formalists (II): A Translation of Part of Grundgesetze der Arithmetik. Philosophical Review 59 (2):202-220.
Gottlob Frege (1950). Frege Against the Formalists. III: A Translation of Part of Grundgesetze der Arithmetik. Philosophical Review 59 (3):332-345.
Richard Heck (1997). Grundgesetze der Arithmetik I §§29‒32. Notre Dame Journal of Formal Logic 38 (3):437-474.
Fernando Ferreira & Kai F. Wehmeier (2002). On the Consistency of the Δ11-CA Fragment of Frege's Grundgesetze. Journal of Philosophical Logic 31 (4):301-311.
A. C. Walczak-Typke (2005). The First-Order Structure of Weakly Dedekind-Finite Sets. Journal of Symbolic Logic 70 (4):1161 - 1170.
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