4 ideas
| 9141 | Abstraction theories build mathematics out of second-order equivalence principles [Cook/Ebert] |
| Full Idea: A theory of abstraction is any account that reconstructs mathematical theories using second-order abstraction principles of the form: §xFx = §xGx iff E(F,G). We ignore first-order abstraction principles such as Frege's direction abstraction. | |
| From: R Cook / P Ebert (Notice of Fine's 'Limits of Abstraction' [2004], 1) | |
| A reaction: Presumably part of the neo-logicist programme, which also uses such principles. The function § (extension operator) 'provides objects corresponding to the argument concepts'. The aim is to build mathematics, rather than the concept of a 'rabbit'. |
| 18552 | Forget about beauty; just concentrate on the virtues of delicacy and discernment admired in critics [Hume, by Scruton] |
| Full Idea: Hume suggest we get away from the fruitless discussion of beauty, and simply concentrate on the qualities we admire, and ought to admire, in a critic - qualities such as delicacy and discernment. | |
| From: report of David Hume (Of the standard of taste [1757]) by Roger Scruton - Beauty: a very short introduction 6 | |
| A reaction: We might wonder how you can admire 'discernment' without some view of the thing being discern, which is in danger of being beauty. How do you judge delicacy and discernment without judging the objects of the critic's taste? Mere authority? |
| 6608 | Strong sense, delicate sentiment, practice, comparisons, and lack of prejudice, are all needed for good taste [Hume] |
| Full Idea: Strong sense, united to delicate sentiment, improved by practice, perfected by comparison, and cleared of all prejudice, can alone entitle critics to the valuable character of having 'taste'. | |
| From: David Hume (Of the standard of taste [1757]), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.6 | |
| A reaction: I agree entirely with this, but then I am a very politically incorrect elitist when it comes to taste. It just seems screamingly obvious that professional wine-tasters have a better appreciation of wine than me, and so on for the rest of the arts. |
| 6017 | Nomos is king [Pindar] |
| Full Idea: Nomos is king. | |
| From: Pindar (poems [c.478 BCE], S 169), quoted by Thomas Nagel - The Philosophical Culture | |
| A reaction: This seems to be the earliest recorded shot in the nomos-physis wars (the debate among sophists about moral relativism). It sounds as if it carries the full relativist burden - that all that matters is what has been locally decreed. |