3 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. |
| 8800 | If you would deny a truth if you know the full evidence, then knowledge has social aspects [Harman, by Sosa] |
| Full Idea: If one reads of a genuine assassination, but then fails to read the reports next day which untruthfully deny the event, one probably does not know of the event. But we must conclude that knowledge has a further 'social aspect'. | |
| From: report of Gilbert Harman (Induction [1970], §IV) by Ernest Sosa - The Raft and the Pyramid Appx | |
| A reaction: I doubt if this is enough to support an externalist account of defeasibility. Wise people don't 'know' of an event after one report. For 24 hours the Royalists thought they had won Marston Moor! You know he's dead when you see the Zapruder film. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |