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 |
| 13479 | Given that thinking aims at truth, logic gives universal rules for how to do it [Burge] |
| Full Idea: The laws of logic - which are constituted by atemporal thoughts and atemporal subject matter - provide universal prescriptions of how one ought to think, given that one's thinking has the function of attaining truth. | |
| From: Tyler Burge (Frege on Knowing the Third Realm [1992], p.316) | |
| A reaction: Burge is giving, and endorsing, Frege's view. Burge is fighting a rearguard action, when logical systems keep proliferating. See Idea 10282. I sympathise with the dream of Burge and Frege. |
| 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? |