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Single Idea 9973

[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 definition is that the number N F(x) of F's, where F is a concept, is the extension of the second level concept 'is equipollent with F'.

Clarification

'Equipollent' means they map one-to-one onto each other

Gist of Idea

The number of F's is the extension of the second level concept 'is equipollent with F'

Source

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

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.43


A Reaction

In trying to pin Frege down precisely, we must remember that an extension can be a collection of sets, as well as a collection of concrete particulars.