6 ideas
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
| From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
| From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
| A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |
| 7458 | The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking] |
| Full Idea: The credibility of a witness is in part a function of the story being reported. When the story claims to have infinite value, the temptation to lie for personal benefit is asymptotically infinite. | |
| From: report of Pierre Simon de Laplace (Philosophical Essay on Probability [1820], Ch.XI) by Ian Hacking - The Emergence of Probability Ch.8 | |
| A reaction: Laplace seems to especially have reports of miracles in mind. This observation certainly dashes any dreams one might have of producing a statistical measure of the reliability of testimony. |
| 3441 | If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace] |
| Full Idea: An intelligence knowing at an instant the whole universe could know the movement of the largest bodies and atoms in one formula, provided his intellect were powerful enough to subject all data to analysis. Past and future would be present to his eyes. | |
| From: Pierre Simon de Laplace (Philosophical Essay on Probability [1820]), quoted by Mark Thornton - Do we have free will? p.70 |
| 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. |