6 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. |
| 16383 | Puzzled Pierre has two mental files about the same object [Recanati on Kripke] |
| Full Idea: In Kripke's puzzle about belief, the subject has two distinct mental files about one and the same object. | |
| From: comment on Saul A. Kripke (A Puzzle about Belief [1979]) by François Recanati - Mental Files 17.1 | |
| A reaction: [Pierre distinguishes 'London' from 'Londres'] The Kripkean puzzle is presented as very deep, but I have always felt there was a simple explanation, and I suspect that this is it (though I will leave the reader to think it through, as I'm very busy…). |
| 23829 | National leaders want to preserve necessary order - but always the existing order [Weil] |
| Full Idea: Those in command see their duty as defending order, without which no social life can survive; and the only order they conceive is the existing one. | |
| From: Simone Weil (The Power of Words [1934], p.249) | |
| A reaction: She sympathises with them, because a new order is such an unknown. But it always struck me as weird that traditions are preserved because they are traditions, and not because they are good. (My old school, for example!). |
| 23828 | National prestige consists of behaving as if you could beat the others in a war [Weil] |
| Full Idea: What is called national prestige consists in behaving always in such a way as to demoralise other nations by giving them the impression that, if it comes to war, one would certainly defeat them. | |
| From: Simone Weil (The Power of Words [1934], p.244) | |
| A reaction: It's true. No nation gains prestige because of the happy lives of its citizens, or the creativity of its culture. |
| 23827 | Modern wars are fought in the name of empty words which are given capital letters [Weil] |
| Full Idea: For our contemporaries the role of Helen in the Trojan War is is played by words with capital letters. …When empty words are given capital letters, then, on the slightest pretext, men will begin shedding blood for them and piling up ruin in their name. | |
| From: Simone Weil (The Power of Words [1934], p.241) | |
| A reaction: This seems particularly true of the 1930s, where specific dogmatic ideologies seemed to grip and divide people. Simple aggressive nationalism seems to be the cause of current wars, now the fear of Communism has diminished. |