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. |
| 16766 | One thing needs a single thing to unite it; if there were two forms, something must unite them [Aquinas] |
| Full Idea: One thing simpliciter is produced out of many actually existing things only if there is something uniting and tying them to each other. If Socrates were animal and rational by different forms, then to be united they would need something to make them one. | |
| From: Thomas Aquinas (Quaestiones de anima [1269], 11c), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 25.2 | |
| A reaction: This is the reply to the idea that a single thing is just an interesting of many sortal essences. It presumes, of course, that a thing like a horse has something called 'unity'. |
| 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? |