7 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. |
| 10792 | The substitutional quantifier is not in competition with the standard interpretation [Kripke, by Marcus (Barcan)] |
| Full Idea: Kripke proposes that the substitutional quantifier is not a replacement for, or in competition with, the standard interpretation. | |
| From: report of Saul A. Kripke (A Problem about Substitutional Quantification? [1976]) by Ruth Barcan Marcus - Nominalism and Substitutional Quantifiers p.165 |
| 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. |
| 23674 | If an attempted poisoning results in benefits, we still judge the agent a poisoner [Reid] |
| Full Idea: If a man should give to his neighbour a potion which he really believes will poison him, but which, in the event, proves salutary, and does much good; in moral estimation, he is a poisoner, and not a benefactor. | |
| From: Thomas Reid (Essays on Active Powers 3: Princs of action [1788], 5) | |
| A reaction: I take Reid to mean that morality concerns how we assess the agent, and not the results of his actions. Mill and Bentham concede that we judge people this way, but don't think morality mainly concerns judging people. |
| 23675 | We shouldn't do to others what would be a wrong to us in similar circumstances [Reid] |
| Full Idea: It is a first principle of morals, that we ought not to do to another what we should think wrong to be done to us in like circumstances. | |
| From: Thomas Reid (Essays on Active Powers 3: Princs of action [1788], 6) | |
| A reaction: This negative form of the rule is more plausible than the positive form, presumably because there is more consensus about what we all dislike than what we all prefer. But presents for people that they would like, not that you like. |
| 23672 | To be virtuous, we must care about duty [Reid] |
| Full Idea: A man cannot be virtuous, if he has no regard to duty. | |
| From: Thomas Reid (Essays on Active Powers 3: Princs of action [1788], 5) | |
| A reaction: Thus are Aristotle and Kant united in a simple sentence. Aristotle thinks that a virtuous person thereby sees what is the right thing to do, but I take 'duty' to imply a requirement which comes not from good character but from external society. |
| 23673 | Every worthy man has a principle of honour, and knows what is honourable [Reid] |
| Full Idea: I presume it will be granted, that, in every man of real worth, there is a principle of honour, a regard to what is honourable or dishonourable, very distinct from a regard to his interest. | |
| From: Thomas Reid (Essays on Active Powers 3: Princs of action [1788], 5) | |
| A reaction: Note that there is a 'principle' of honour in a person's character, and there are also actions which are intrinsically honourable or not. I fear that only the worthy are honourable, and only the honourable are worthy! |