- P. Ebert and M. Rossberg “Cantor's Review of Frege's Grundlagen: Cantor's 1885 Review of Frege's Die Grundlagen der Arithmetik,” forthcoming in History of Philosophy of Logic
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 entered 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 vary and sometimes extend 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.
- P. Ebert and M. Rossberg “Neo-Logicism: A Friendly Letter of Complaint,” in H. Leitgeb and A. Hieke ed., Reduction – Abstraction – Analysis: Papers from the 31st International Wittgenstein Symposium, Austrian Wittgenstein Society, 2009
- Edward Zalta “Reply to Ebert and Rossberg,” n H. Leitgeb and A. Hieke ed., Reduction – Abstraction – Analysis: Papers from the 31st International Wittgenstein Symposium, Austrian Wittgenstein Society, 2009
1本目が一番興味深い。
確かに Frege の値域もしくは概念の外延には、疑念を呼び起こすものがあるのかもしれない。
Constructive でも iterative でもない Frege's conception of set に何か悪いところがあるのだろうか。
街中の道を歩きながら、今朝もぶつぶつ考えていました。
何も思い付きませんでしたが…。
3本目は2本目に対する応答です。
またそれぞれのんびり拝見させていただくことに致します。
おやすみなさい。
