5 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. |
| 23405 | Rituals escape natural chaos, and benefit everyone, by reshaping our motivations [Xunzi (Xun Kuang), by Norden] |
| Full Idea: For Xunzi, everyone is better off with rituals …because they allow us to escape the chaotic state of nature. They do not merely set rules for entitlement, though. They are effective because they reshape human motivation. | |
| From: report of Xunzi (Xun Kuang) (The Xunzi [c.250 BCE]) by Bryan van Norden - Intro to Classical Chinese Philosophy 10.2 | |
| A reaction: Rituals are a basic part of Confucianist thinking, and may be puzzling to outsiders. At there worst rituals are brain-washing, but teaching children good manners is a sort of ritual, meant to channel feelings in a healthy direction |
| 23406 | Rituals don't arise from human nature; they are the deliberate creations of a sage [Xunzi (Xun Kuang)] |
| Full Idea: Rituals and standards of righteousness and proper models and measures are produced from the deliberate efforts of the sage; they are not produced from people's nature. | |
| From: Xunzi (Xun Kuang) (The Xunzi [c.250 BCE], 23), quoted by Bryan van Norden - Intro to Classical Chinese Philosophy 10.III | |
| A reaction: This is not to say that the sage is not in tune with nature. Human nature is often seen as a sprouting seed, which needs careful husbandry to bring out its best. |
| 7903 | The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna] |
| Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom. | |
| From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88) | |
| A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate'). |