3 ideas
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. |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |
7489 | Joshua said, Sun, stand thou still [Anon (Josh)] |
Full Idea: Then Joshua spake to the Lord, and he said in the sight of Israel, Sun, stand thou still upon Gibeon; and the Sun stood still. | |
From: Anon (Josh) (06: Book of Joshua [c.540 BCE], 10.12) | |
A reaction: This verse became highly significant during the controversies from Copernicus to Galileo about the heliocentric universe. |