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! |
| 3460 | Superactors and superspartans count against behaviourism [Putnam, by Searle] |
| Full Idea: Putnam proposed the superactor/superspartan objection to behaviourism. | |
| From: report of Hilary Putnam (Brains and Behaviour [1963]) by John Searle - The Rediscovery of the Mind Ch. 2.II | |
| A reaction: This is a beautiful compression of the obvious counterexamples, which are behaviour-wth-no-experience, and experience-with-no-behaviour. Presumably, though, Spartans are disposed to go 'aagh!' when they get home, and there are no 'super' actors. |
| 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? |