more from Richard Dedekind

### Single Idea 18094

#### [catalogued under 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts]

Full Idea

One view, favoured by Dedekind, is that the cut postulates a real number for each cut in the rationals; it does not identify real numbers with cuts. ....A view favoured by later logicists is simply to identify a real number with a cut.

Gist of Idea

Dedekind says each cut matches a real; logicists say the cuts are the reals

Source

report of Richard Dedekind (Nature and Meaning of Numbers [1888]) by David Bostock - Philosophy of Mathematics 4.4

Book Reference

Bostock,David: 'Philosophy of Mathematics: An Introduction' [Wiley-Blackwell 2009], p.99

A Reaction

Dedekind is the patriarch of structuralism about mathematics, so he has little interest in the existenc of 'objects'.