7 ideas
| 12036 | Xenophanes began the concern with knowledge [Annas] |
| Full Idea: Xenophanes begins a long concern with knowledge and its grounds. | |
| From: Julia Annas (Ancient Philosophy: very short introduction [2000], Intro) | |
| A reaction: Having that on his cv ought to make Xenophanes more famous than he is. |
| 12046 | Plato was the first philosopher who was concerned to systematize his ideas [Annas] |
| Full Idea: In the ancient world Plato was seen as a pivotal figure, the first philosopher who was concerned to systematize his ideas. | |
| From: Julia Annas (Ancient Philosophy: very short introduction [2000], Ch.6) |
| 15938 | Platonists ruin infinity, which is precisely a growing structure which is never completed [Dummett] |
| Full Idea: The platonist destroys the whole essence of infinity, which lies in the conception of a structure which is always in growth, precisely because the process of construction is never completed. | |
| From: Michael Dummett (Elements of Intuitionism [1977], p.57), quoted by Thomas J. McKay - Plural Predication | |
| A reaction: I don't warm to intuitionism, but I warm to this conception of infinity. Completed infinities are convenient reifications for mathematicians. |
| 15939 | For intuitionists it is constructed proofs (which take time) which make statements true [Dummett] |
| Full Idea: For an intuitionist a mathematical statement is rendered true or false by a proof or disproof, that is, by a construction, and constructions are effected in time. | |
| From: Michael Dummett (Elements of Intuitionism [1977], p.336), quoted by Shaughan Lavine - Understanding the Infinite VI.2 | |
| A reaction: Lavine is quoting this to draw attention to the difficulties of thinking of it as all taking place 'in time', especially when dealing with infinities. |
| 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? |
| 12037 | Euripides's Medea is a key case of reason versus the passions [Annas] |
| Full Idea: Euripides's Medea has remained a key case for discussion of reason and the passions. | |
| From: Julia Annas (Ancient Philosophy: very short introduction [2000], Ch.1) |
| 12040 | Virtue is a kind of understanding of moral value [Annas] |
| Full Idea: There is a widespread view in ancient ethics that virtue is a kind of understanding of moral value. | |
| From: Julia Annas (Ancient Philosophy: very short introduction [2000], Ch.3) | |
| A reaction: In Aristotle's case, this coincides with his apparent view that 'understanding' is the aim of all areas of human thought. See Idea 12038. |