more from Gottlob Frege

Single Idea 9989

[catalogued under 6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / a. Units]

Full Idea

The fact that units are equal does not mean that they are identical. The units can be equal just in the sense that once can be substituted for any other without altering the name assigned, i.e. the number.

Gist of Idea

Units can be equal without being identical


comment on Gottlob Frege (Grundlagen der Arithmetik (Foundations) [1884], 54) by William W. Tait - Frege versus Cantor and Dedekind XI

Book Reference

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

A Reaction

[this is in reference to Thomae 1880] Presumably this might mean that units have type-identity, rather than token-dentity. 'This' unit might be a token, but 'a' unit would be a type. I am extremely reluctant to ditch the old concept of a unit.