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? |
| 6231 | There is a self-determing power in each person, which makes them what they are [Cudworth] |
| Full Idea: This hegemonicon (self-power) always determines the passive capability of men's nature one way or other, either for better or for worse; and has a self-forming and self-framing power by which every man is self-made into what he is. | |
| From: Ralph Cudworth (Treatise of Freewill [1688], §X) | |
| A reaction: The idea that we can somehow create our own selves seems to me the core of existentialism, and the opposite of the Aristotelian belief in a fairly fixed human nature. See Stephen Pinker's 'The Blank Slate' for a revival of the old view. |