3 ideas
10855 | Actual infinities are not allowed in mathematics - only limits which may increase without bound [Gauss] |
Full Idea: I protest against the use of an infinite quantity as an actual entity; this is never allowed in mathematics. The infinite is only a manner of speaking, in which one properly speaks of limits ...which are permitted to increase without bound. | |
From: Carl Friedrich Gauss (Letter to Shumacher [1831]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable Ch.7 |
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? |
19745 | The nature of people is decided by the government and politics of their society [Rousseau] |
Full Idea: Everything is rooted in politics, and whatever might be attempted, no people would ever be other than the nature of their government made them. | |
From: Jean-Jacques Rousseau (The Confessions [1770], 9-1756) | |
A reaction: A striking anticipation of one of Marx's most important ideas - that society is not created by individual minds, because the nature of consciousness is created by society. The central idea in the subject of sociology, I think. |