6 ideas
| 21558 | 'Predicative' norms are those which define a class [Russell] |
| Full Idea: Norms (containing one variable) which do not define classes I propose to call 'non-predicative'; those which do define classes I shall call 'predicative'. | |
| From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141) |
| 21559 | We need rules for deciding which norms are predicative (unless none of them are) [Russell] |
| Full Idea: We need rules for deciding what norms are predicative and what are not, unless we adopt the view (which has much to recommend it) that no norms are predicative. ...[146] A predative propositional function is one which determines a class. | |
| From: Bertrand Russell (Difficulties of Transfinite Numbers and Types [1905], p.141) | |
| A reaction: He is referring to his 'no class' theory, which he favoured at that time. |
| 13230 | Particular essence is often captured by generality [Steiner,M] |
| Full Idea: Generality is often necessary for capturing the essence of a particular. | |
| From: Mark Steiner (Mathematical Explanation [1978], p.36) | |
| A reaction: The most powerful features of an entity are probably those which are universal, like intelligence or physical strength in a human. Those characteristics are powerful because they compete with the same characteristic in others (perhaps?). |
| 13229 | Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M] |
| Full Idea: Maybe to deduce a theorem as an instance of a generalization is more explanatory than to deduce it correctly. | |
| From: Mark Steiner (Mathematical Explanation [1978], p.32) | |
| A reaction: Steiner eventually comes down against this proposal, on the grounds that some proofs are too general, and hence too far away from the thing they are meant to explain. |
| 13231 | Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M] |
| Full Idea: My proposal is that an explanatory proof makes reference to the 'characterizing property' of an entity or structure mentioned in the theorem, where the proof depends on the property. If we substitute a different object, the theory collapses. | |
| From: Mark Steiner (Mathematical Explanation [1978], p.34) | |
| A reaction: He prefers 'characterizing property' to 'essence', because he is not talking about necessary properties, since all properties are necessary in mathematics. He is, in fact, reverting to the older notion of an essence, as the core power of the thing. |
| 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'). |