5 ideas
| 10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
| Full Idea: Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter. | |
| From: Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6 | |
| A reaction: This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well. |
| 14979 | Being alone doesn't guarantee intrinsic properties; 'being alone' is itself extrinsic [Lewis, by Sider] |
| Full Idea: The property of 'being alone in the world' is an extrinsic property, even though it has had by an object that is alone in the world. | |
| From: report of David Lewis (Extrinsic Properties [1983]) by Theodore Sider - Writing the Book of the World 01.2 | |
| A reaction: I always choke on my cornflakes whenever anyone cites a true predicate as if it were a genuine property. This is a counterexample to Idea 14978. Sider offers another more elaborate example from Lewis. |
| 15454 | Extrinsic properties come in degrees, with 'brother' less extrinsic than 'sibling' [Lewis] |
| Full Idea: Properties may be more or less intrinsic; being a brother has more of an admixture of intrinsic structure than being a sibling does, yet both are extrinsic. | |
| From: David Lewis (Extrinsic Properties [1983], I) | |
| A reaction: I suppose the point is that a brother is intrinsically male - but then a sibling is intrinsically human. A totally extrinsic relation would be one between entities which shared virtually no categories of existence. |
| 15455 | Total intrinsic properties give us what a thing is [Lewis] |
| Full Idea: The way something is is given by the totality of its intrinsic properties. | |
| From: David Lewis (Extrinsic Properties [1983], I) | |
| A reaction: No. Some properties are intrinsic but trivial. The 'important' ones fix the identity (if the identity is indeed 'fixed'). |
| 11911 | Some philosophers always want more from morality; for others, nature is enough [Blackburn] |
| Full Idea: The history of moral theory is largely a history of battles between people who want more (truth, absolutes...) - Plato, Locke, Cudworth, Kant, Nagel - and people content with what we have (nature) - Aristotle, Epicurus, Hobbes, Hume, Stevenson. | |
| From: Simon Blackburn (Précis of 'Ruling Passions' [2002], p.133) | |
| A reaction: [Thanks to Neil Sinclair for this one] As a devotee of Aristotle, I like this. I'm always impressed, though, by people who go the extra mile in morality, because they are in the grips of purer and loftier ideals than I am. They also turn into monsters! |