3 ideas
| 8920 | Equivalence relations are reflexive, symmetric and transitive, and classify similar objects [Lipschutz] |
| Full Idea: A relation R on a non-empty set S is an equivalence relation if it is reflexive (for each member a, aRa), symmetric (if aRb, then bRa), and transitive (aRb and bRc, so aRc). It tries to classify objects that are in some way 'alike'. | |
| From: Seymour Lipschutz (Set Theory and related topics (2nd ed) [1998], 3.9) | |
| A reaction: So this is an attempt to formalise the common sense notion of seeing that two things have something in common. Presumably a 'way' of being alike is going to be a property or a part |
| 22110 | Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump] |
| Full Idea: According to Aquinas, what demonstration provides is not so much knowledge as conceived by foundationalists as depth of understanding and explanatory insight. | |
| From: Kretzmann/Stump (Aquinas, Thomas [2005]), quoted by Kretzmann/Stump - Aquinas, Thomas 11 | |
| A reaction: It was noticeable that Aristotle didn't make clear what demonstration aims to achieve, and he didn't employ it elsewhere in his writings. We aim for understanding, not for well grounded propositions. Understanding needs implications and mechanisms. |
| 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? |