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3 ideas
| 14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
| Full Idea: It is obvious that a relation which is symmetrical and transitive must be reflexive throughout its domain. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], II) | |
| A reaction: Compare Idea 13543! The relation will return to its originator via its neighbours, rather than being directly reflexive? |
| 14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
| Full Idea: The relation of 'asymmetry' is incompatible with the converse. …The relation 'husband' is asymmetrical, so that if a is the husband of b, b cannot be the husband of a. | |
| From: Bertrand Russell (Introduction to Mathematical Philosophy [1919], V) | |
| A reaction: This is to be contrasted with 'non-symmetrical', where there just happens to be no symmetry. |
| 20105 | Storms are wonderful expressions of free powers! [Nietzsche] |
| Full Idea: How different the lightning, the storm, the hail, free powers, without ethics! How happy, how powerful they are, pure will, untarnished by intellect! | |
| From: Friedrich Nietzsche (Works (refs to 8 vol Colli and Montinari) [1885], 2.122), quoted by Rüdiger Safranski - Nietzsche: a philosophical biography 02 | |
| A reaction: Nietzsche was a perfect embodiment of the Romantic Movement! I take this to be a deep observation, since I think raw powers are the most fundamental aspect of nature. Schopenhauer is behind this idea. |