6 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. |
| 22076 | Being is only perceptible to itself as becoming [Schelling] |
| Full Idea: Being is only perceptible to itself in the state of becoming. | |
| From: Friedrich Schelling (Of Human Freedom [1809], p.403), quoted by Jean-François Courtine - Schelling p.90 | |
| A reaction: Is the Enlightenment the era of Being, and the Romantic era that of Becoming? They like process, fluidity, even chaos. |
| 22074 | We must show that the whole of nature, because it is effective, is grounded in freedom [Schelling] |
| Full Idea: What is required is to show that everything that is effective (nature, the world of things) is grounded in activity, life, freedom. | |
| From: Friedrich Schelling (Of Human Freedom [1809], p.351), quoted by Jean-François Courtine - Schelling | |
| A reaction: I take the ancestor of this view of nature to be the monads of Leibniz, as the active principle in nature. Because this is an idealist view, it starts with the absolute freedom of the Self, and presumably sees nature in its own image. |
| 22075 | Only idealism has given us the genuine concept of freedom [Schelling] |
| Full Idea: Until the discovery of idealism, the genuine concept of freedom has been missing from every modern system, whether it be that of Leibniz or of Spinoza. | |
| From: Friedrich Schelling (Of Human Freedom [1809], p.345), quoted by Jean-François Courtine - Schelling p.87 | |
| A reaction: Spinoza denied free will, and Leibniz fudged it. Evidently more medieval theological accounts were not good enough. I presume Fichte is Schelling's hero, and he seems to see freedom as axiomatic about the Self. |
| 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? |