more from George Cantor

### Single Idea 9992

#### [catalogued under 6. Mathematics / B. Foundations for Mathematics / 5. Definitions of Number / c. Fregean numbers]

Full Idea

The author entirely overlooks the fact that the 'extension of a concept' in general may be quantitatively completely indeterminate. Only in certain cases is the 'extension of a concept' quantitatively determinate.

Gist of Idea

The 'extension of a concept' in general may be quantitatively completely indeterminate

Source

George Cantor (Review of Frege's 'Grundlagen' [1885], 1932:440), quoted by William W. Tait - Frege versus Cantor and Dedekind

Book Reference

'Philosophy of Mathematics: anthology', ed/tr. Jacquette,Dale [Blackwell 2002], p.60

A Reaction

Cantor presumably has in mind various infinite sets. Tait is drawing our attention to the fact that this objection long precedes Russell's paradox, which made the objection more formal (a language Frege could understand!).