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 |
| 18779 | 'The' is a quantifier, like 'every' and 'a', and does not result in denotation [Montague] |
| Full Idea: The expression 'The' turns out to play the role of a quantifier, in complete analogy with 'every' and 'a', and does not generate (in common with common noun phrases) denoting expressions | |
| From: Richard Montague (English as a Formal Language [1970], p.216), quoted by Bernard Linsky - Quantification and Descriptions 4 | |
| A reaction: Linsky says that it is now standard to interpret definite descriptions as quantifiers |
| 22200 | If you eliminate the impossible, the truth will remain, even if it is weird [Conan Doyle] |
| Full Idea: When you have eliminated the impossible, whatever remains, however improbable, must be the truth. | |
| From: Arthur Conan Doyle (The Sign of Four [1890], Ch. 6) | |
| A reaction: A beautiful statement, by Sherlock Holmes, of Eliminative Induction. It is obviously not true, of course. Many options may still face you after you have eliminated what is actually impossible. |