3 ideas
| 8728 | Intuitionist mathematics deduces by introspective construction, and rejects unknown truths [Brouwer] |
| Full Idea: Mathematics rigorously treated from the point of view of deducing theorems exclusively by means of introspective construction, is called intuitionistic mathematics. It deviates from classical mathematics, which believes in unknown truths. | |
| From: Luitzen E.J. Brouwer (Consciousness, Philosophy and Mathematics [1948]), quoted by Stewart Shapiro - Thinking About Mathematics 1.2 | |
| A reaction: Clearly intuitionist mathematics is a close cousin of logical positivism and the verification principle. This view would be anathema to Frege, because it is psychological. Personally I believe in the existence of unknown truths, big time! |
| 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? |
| 6581 | Hume thought (unlike Locke) that property is a merely conventional relationship [Hume, by Fogelin] |
| Full Idea: Hume thought (in contrast to Locke) that property reflects a conventional (rather than natural) relationship determined by the laws that protect people from having things taken from them. | |
| From: report of David Hume (Nine political essays [1741]) by Robert Fogelin - Walking the Tightrope of Reason Ch.3 | |
| A reaction: It seems pretty obvious that the idea of property was invented by the powerful, to protect their gains against the weak. I suspect that you might till a piece of land simply in order to assert ownership of it, just as you might bring in colonists. |