History and Philosophy of Logic 30 (4):341-348 (2009)
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Abstract |
In 1885, Georg Cantor published his review of Gottlob Frege's Grundlagen der Arithmetik . In this essay, we provide its first English translation together with an introductory note. We also provide a translation of a note by Ernst Zermelo on Cantor's review, and a new translation of Frege's brief response to Cantor. In recent years, it has become philosophical folklore that Cantor's 1885 review of Frege's Grundlagen already contained a warning to Frege. This warning is said to concern the defectiveness of Frege's notion of extension. The exact scope of such speculations varies and sometimes extends as far as crediting Cantor with an early hunch of the paradoxical nature of Frege's notion of extension. William Tait goes even further and deems Frege 'reckless' for having missed Cantor's explicit warning regarding the notion of extension. As such, Cantor's purported inkling would have predated the discovery of the Russell-Zermelo paradox by almost two decades. In our introductory essay, we discuss this alleged implicit (or even explicit) warning, separating two issues: first, whether the most natural reading of Cantor's criticism provides an indication that the notion of extension is defective; second, whether there are other ways of understanding Cantor that support such an interpretation and can serve as a precisification of Cantor's presumed warning
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Keywords | Gottlob Frege Georg Cantor Philosophy of Mathematics Set-theoretic paradoxes |
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Reprint years | 2009 |
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DOI | 10.1080/01445340903102813 |
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References found in this work BETA
Die Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl.Gottlob Frege - 1996 - Wittgenstein-Studien 3 (2):993-999.
Die Grundlagen der Arithmetik. Eine Logisch Mathematische Untersuchung Über den Begriff der Zahl.Gottlob Frege & Christian Thiel - 1988 - Journal of Symbolic Logic 53 (3):993-999.
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Citations of this work BETA
The Convenience of the Typesetter; Notation and Typography in Frege’s Grundgesetze der Arithmetik.Jim J. Green, Marcus Rossberg & A. Ebert Philip - 2015 - Bulletin of Symbolic Logic 21 (1):15-30.
Counting by Identity: A Reply to Liebesman.Oliver R. Marshall - 2017 - Australasian Journal of Philosophy 95 (2):385-390.
The Psychology and Philosophy of Natural Numbers.Oliver R. Marshall - 2017 - Philosophia Mathematica (1):nkx002.
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