Combining Texts

Ideas for 'works', 'Letter to Weber' and 'Steps Towards a Constructive Nominalism'

unexpand these ideas     |    start again     |     choose another area for these texts

display all the ideas for this combination of texts

---

1 idea

6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / i. Reals from cuts

18244	I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind]
	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.