3 ideas
| 15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
| Full Idea: Zermelo realised that the Axiom of Choice (based on arbitrary functions) could be used to 'count', in the Cantorian sense, those collections that had given Cantor so much trouble, which restored a certain unity to set theory. | |
| From: report of Ernst Zermelo (Proof that every set can be well-ordered [1904]) by Shaughan Lavine - Understanding the Infinite I |
| 5958 | The sun is always bright; it doesn't become bright when it emerges [Plutarch] |
| Full Idea: The sun doesn't become bright when it emerges from the clouds; it always is bright. | |
| From: Plutarch (26: Oracles in Decline [c.85], §39) | |
| A reaction: Not an argument, but a nice appeal to common sense, like Russell's example of the cat that disappears behind the furniture and then reappears. To disagree with Plutarch here strikes me as the road to philosophical absurdity. |
| 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? |