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Single Idea 9990

[from 'Grundlagen der Arithmetik (Foundations)' by Gottlob Frege, in 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers ]

Full Idea

Frege's contribution with respect to the definition of equinumerosity was to replace Cantor's sets as the objects of number attributions by concepts.

Gist of Idea

Frege replaced Cantor's sets as the objects of equinumerosity attributions with concepts

Source

report of Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884]) by William W. Tait - Frege versus Cantor and Dedekind XII

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.59


A Reaction

This pinpoints Frege's big idea, which is a powerful one, and may be right. The difficulty seems to be that the extension is ultimately what counts (because that is where plurality resides), and it is tricky getting the concept to determine the extension.