5 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 |
| 19691 | Unlike knowledge, you can achieve understanding through luck [Grimm] |
| Full Idea: It may be that understanding is compatible with luck, in a way that knowledge is not. | |
| From: Stephen R. Grimm (Understanding [2011], 3) | |
| A reaction: [He cites Kvanvig and Prichard] If so, then we cannot say that knowledge is a lesser type of understanding. If you ask a trusted person how a mechanism works, and they have a wild guess that is luckily right, you would then understand it. |
| 19690 | 'Grasping' a structure seems to be modal, because we must anticipate its behaviour [Grimm] |
| Full Idea: 'Graspng' a structure would seem to bring into play something like a modal sense or ability, not just to register how things are, but also to anticipate how certain elements of the system would behave. | |
| From: Stephen R. Grimm (Understanding [2011], 2) | |
| A reaction: In the case of the chronology of some historical events, talking of 'grasping' or 'understanding' seems wrong because the facts are static and invariant. That seems to support the present idea. But you might 'understand' a pattern if you can reproduce it. |
| 19692 | You may have 'weak' understanding, if by luck you can answer a set of 'why questions' [Grimm] |
| Full Idea: There may be a 'weak' sense of understanding, where all you need to do is to be able to answer 'why questions' successfully, where one might have come by this ability in a lucky way. | |
| From: Stephen R. Grimm (Understanding [2011], 3) | |
| A reaction: We can see this point (in Idea 19691), but the idea that one could come by true complex understanding of something by purely lucky means is a bit absurd. Surely you would get one or two why questions wrong? 100%, just by luck? |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |