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 |
| 10994 | Conditionals are true if minimal revision of the antecedent verifies the consequent [Stalnaker, by Read] |
| Full Idea: Stalnaker proposes that a conditional is true if its consequent is true in the minimal revision in which the antecedent is true, that is, in the most similar possible world in which the antecedent is true. | |
| From: report of Robert C. Stalnaker (works [1970]) by Stephen Read - Thinking About Logic Ch.3 | |
| A reaction: A similar account of counterfactuals was taken up by Lewis to give a (rather dubious) account of causation. |
| 23053 | The great interest of the human race is cordial unity and unlimited mutual aid [Owen] |
| Full Idea: It is the one great and universal interest of the human race to be cordially united, and to aid each other to the full extent of their capacities. | |
| From: Robert Owen (works [1830]), quoted by John H. Muirhead - The Service of the State IV | |
| A reaction: [Inscribed on his tomb in Newport, Shropshire] In the middle of the early industrial revolution, Owen worked hard for the rights of the people who worked in his factory. |