green numbers give full details | back to texts | unexpand this idea
18244 | I say the irrational is not the cut itself, but a new creation which corresponds to the cut |
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. | |||
From: Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4 | |||
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. |