3 ideas
| 10632 | The real numbers may be introduced by abstraction as ratios of quantities [Hale, by Hale/Wright] |
| Full Idea: The real numbers may be introduced by abstraction as ratios of quantities. ..They are not defined by Dedekind cuts; rather, the cuts constitute a domain with the properties that are a necessary precondition. | |
| From: report of Bob Hale (Reals by Abstraction [1998]) by B Hale / C Wright - Intro to 'The Reason's Proper Study' 3.3 | |
| A reaction: This is Hale's neo-logicist attempt to derive the real numbers from Hume's Principle. |
| 6004 | The cardinal virtues are theoretical (based on knowledge), and others are 'non-theoretical' [Hecato, by Dorandi] |
| Full Idea: Hecato defined the cardinal virtues as 'theoretical', that is, based on knowledge, and to these he opposed those that are 'non-theoretical', for example, health, beauty, strength of spirit, and courage. | |
| From: report of Hecato (fragments/reports [c.70 BCE]) by Tiziano Dorandi - Hecato of Rhodes | |
| A reaction: Mostly these are Aristotle's external and non-external virtues, except that courage is here included among the former, implying, presumably, that it is more of a natural gift than an intellectual achievement. |
| 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'). |