5 ideas
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| Full Idea: Archimedes gave a sort of definition of 'straight line' when he said it is the shortest line between two points. | |
| From: report of Archimedes (fragments/reports [c.240 BCE]) by Gottfried Leibniz - New Essays on Human Understanding 4.13 | |
| A reaction: Commentators observe that this reduces the purity of the original Euclidean axioms, because it involves distance and measurement, which are absent from the purest geometry. |
| 19696 | There are reasons 'for which' a belief is held, reasons 'why' it is believed, and reasons 'to' believe it [Neta] |
| Full Idea: We must distinguish between something's being a 'reason for which' a creature believes something, and its being a 'reason why' a creature believes something. ...We must also distinguish a 'reason for which' from a 'reason to' believe something. | |
| From: Ram Neta (The Basing Relation [2011], Intro) | |
| A reaction: He doesn't spell the distinctions out clearly. I take it that 'for which' is my personal justification, 'why' is the dodgy prejudices that cause my belief. and 'to' is some actual good reasons, of which I may be unaware. |
| 19697 | The basing relation of a reason to a belief should both support and explain the belief [Neta] |
| Full Idea: A reason has a 'basing relation' with a belief if it (i) rationally supports holding the belief, and (ii) explains why the belief is held. | |
| From: Ram Neta (The Basing Relation [2011], Intro) | |
| A reaction: Presumably a false reason would fit this account. Why not talk of 'grounding', or is that word now reserved for metaphysics? If I hypnotise you into a belief, would my hypnotic power be the basing reason? Fits (ii), but not (i). |
| 5845 | Niceratus learnt the whole of Homer by heart, as a guide to goodness [Xenophon] |
| Full Idea: Niceratus said that his father, because he was concerned to make him a good man, made him learn the whole works of Homer, and he could still repeat by heart the entire 'Iliad' and 'Odyssey'. | |
| From: Xenophon (Symposium [c.391 BCE], 3.5) | |
| A reaction: This clearly shows the status which Homer had in the teaching of morality in the time of Socrates, and it is precisely this acceptance of authority which he was challenging, in his attempts to analyse the true basis of virtue |
| 5833 | Education is the greatest of human goods [Xenophon] |
| Full Idea: Education is the greatest of human goods. | |
| From: Xenophon (Apology of Socrates [c.392 BCE], 22) | |
| A reaction: Of course, one might ask what education is for, and arrive at a greater good. If you ask what is the greatest good which a society can provide for you, or which you can give to your children, this seems to me a good answer. |