3 ideas
| 13166 | Essences are no use in mathematics, if all mathematical truths are necessary [Mancosu] |
| Full Idea: Essences and essential properties do not seem to be useful in mathematical contexts, since all mathematical truths are regarded as necessary (though Kit Fine distinguishes between essential and necessary properties). | |
| From: Paolo Mancosu (Explanation in Mathematics [2008], §6.1) | |
| A reaction: I take the proviso in brackets to be crucial. This represents a distortion of notion of an essence. There is a world of difference between the central facts about the nature of a square and the peripheral inferences derivable from it. |
| 1655 | If goodness needs true opinion but not knowledge, you can skip the 'examined life' [Vlastos on Plato] |
| Full Idea: If true opinion without knowledge does suffice to guide action aright, the great mass of men and women may be spared the pain and hazards of the "examined" life. | |
| From: comment on Plato (The Apology [c.383 BCE], 38a) by Gregory Vlastos - Socrates: Ironist and Moral Philosopher p.125 |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |