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Single Idea 18244

[from 'Letter to Weber' by Richard Dedekind, in 6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts ]

Full Idea

Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power.

Gist of Idea

I say the irrational is not the cut itself, but a new creation which corresponds to the cut

Source

Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4

Book Reference

Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.173


A Reaction

Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects.