4 ideas
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
Full Idea: Zermelo realised that the Axiom of Choice (based on arbitrary functions) could be used to 'count', in the Cantorian sense, those collections that had given Cantor so much trouble, which restored a certain unity to set theory. | |
From: report of Ernst Zermelo (Proof that every set can be well-ordered [1904]) by Shaughan Lavine - Understanding the Infinite I |
16050 | The goodness of a picture supervenes on the picture; duplicates must be equally good [Hare] |
Full Idea: Characteristic of value-words is that they name 'supervenient' properties. If we are discussing whether a picture is a good picture, ..and there is another picture that is a replica of it, we cannot say 'they are alike, but one is good and the other not'. | |
From: Richard M. Hare (The Language of Morals [1952], 5.2) | |
A reaction: [compressed] Horgan says this is the passage which introduced 'supervenience' into contemporary discussions. I think the best simple word for it is that the goodness of the picture 'tracks' its physical characteristics. It also depend on them. |
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? |
2855 | In primary evaluative words like 'ought' prescription is constant but description can vary [Hare, by Hooker,B] |
Full Idea: Hare says words are secondarily evaluative (e.g. 'soft-hearted') if prescriptive meaning varies but description is constant; primarily evaluative words ('good', 'right', 'ought') are the opposite, with the descriptive content varying. | |
From: report of Richard M. Hare (The Language of Morals [1952]) by Brad W. Hooker - Prescriptivism p.640 | |
A reaction: I would have thought that the prescriptive meaning of the evaluative word could at least vary in strength. You really, really ought to do that. |