4 ideas
| 9616 | A set is a collection into a whole of distinct objects of our intuition or thought [Cantor] |
| Full Idea: A set is any collection into a whole M of definite, distinct objects m ... of our intuition or thought. | |
| From: George Cantor (The Theory of Transfinite Numbers [1897], p.85), quoted by James Robert Brown - Philosophy of Mathematics Ch.2 | |
| A reaction: This is the original conception of a set, which hit trouble with Russell's Paradox. Cantor's original definition immediately invites thoughts about the status of vague objects. |
| 15896 | Cantor needed Power Set for the reals, but then couldn't count the new collections [Cantor, by Lavine] |
| Full Idea: Cantor grafted the Power Set axiom onto his theory when he needed it to incorporate the real numbers, ...but his theory was supposed to be theory of collections that can be counted, but he didn't know how to count the new collections. | |
| From: report of George Cantor (The Theory of Transfinite Numbers [1897]) by Shaughan Lavine - Understanding the Infinite I | |
| A reaction: I take this to refer to the countability of the sets, rather than the members of the sets. Lavine notes that counting was Cantor's key principle, but he now had to abandon it. Zermelo came to the rescue. |
| 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'). |
| 21006 | If women share rights with men, they will exhibit similar virtues [Wollstonecraft] |
| Full Idea: Let woman share the rights and she will emulate the virtues of man; for she must grow more perfect when emancipated, or justify that authority that chains such a weak being to her duty. | |
| From: Mary Wollstonecraft (Vindication of the Rights of Women [1792], p.294), quoted by Amartya Sen - The Idea of Justice 18 'Wrath' | |
| A reaction: Presumably this implies that if emancipation led to women exceeding men in such virtues, there would be some justification for imposing the chains on the men rather than the women. Consider wars. Probably best to just abandon chains. |