5 ideas
| 18256 | Quantity is inconceivable without the idea of addition [Frege] |
| Full Idea: There is so intimate a connection between the concepts of addition and of quantity that one cannot begin to grasp the latter without the former. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], p.2), quoted by Michael Dummett - Frege philosophy of mathematics 22 'Quantit' | |
| A reaction: Frege offers good reasons for making cardinals prior to ordinals, though plenty of people disagree. |
| 9831 | Geometry appeals to intuition as the source of its axioms [Frege] |
| Full Idea: The elements of all geometrical constructions are intuitions, and geometry appeals to intuition as the source of its axioms. | |
| From: Gottlob Frege (Rechnungsmethoden (dissertation) [1874], Ch.6), quoted by Michael Dummett - Frege philosophy of mathematics | |
| A reaction: Very early Frege, but he stuck to this view, while firmly rejecting intuition as a source of arithmetic. Frege would have known well that Euclid's assumption about parallels had been challenged. |
| 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'). |