4 ideas
| 10053 | Geometrical axioms imply the propositions, but the former may not be true [Russell] |
| Full Idea: We must only assert of various geometries that the axioms imply the propositions, not that the axioms are true and therefore that the propositions are true. | |
| From: Bertrand Russell (Foundations of Geometry [1897], Intro vii), quoted by Alan Musgrave - Logicism Revisited §4 | |
| A reaction: Clearly the truth of the axioms can remain a separate issue from whether they actually imply the theorems. The truth of the axioms might be as much a metaphysical as an empirical question. Musgrave sees this as the birth of if-thenism. |
| 10052 | Geometry is united by the intuitive axioms of projective geometry [Russell, by Musgrave] |
| Full Idea: Russell sought what was common to Euclidean and non-Euclidean systems, found it in the axioms of projective geometry, and took a Kantian view of them. | |
| From: report of Bertrand Russell (Foundations of Geometry [1897]) by Alan Musgrave - Logicism Revisited §4 | |
| A reaction: Russell's work just preceded Hilbert's famous book. Tarski later produced some logical axioms for geometry. |
| 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? |
| 6570 | Imagine millions made happy on condition that one person suffers endless lonely torture [James] |
| Full Idea: Consider a case in which millions could be made permanently happy on the one simple condition that a certain lost soul on the far-off edge of things should lead a life of lonely torture. | |
| From: William James (The Will to Believe [1896], p.188), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.2 | |
| A reaction: This seems to be one of the earliest pinpointings of a key problem with utilitiarianism, which is that other values than happiness (in this case, fairness) seem to be utterly overruled. If we ignore fairness, why shouldn't we ignore happiness? |