3 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. |
| 3102 | Why don't we experience or remember going to sleep at night? [Magee] |
| Full Idea: As a child it was incomprehensible to me that I did not experience going to sleep, and never remembered it. When my sister said 'Nobody remembers that', I just thought 'How does she know?' | |
| From: Bryan Magee (Confessions of a Philosopher [1997], Ch.I) | |
| A reaction: This is actually evidence for something - that we do not have some sort of personal identity which is separate from consciousness, so that "I am conscious" would literally mean that an item has a property, which it can lose. |
| 1558 | Clearly the gods ignore human affairs, or they would have given us justice [Thrasymachus] |
| Full Idea: The gods pay no attention to human affairs; if they did, they would not have ignored justice, which is the greatest good for men; for we see that men do not act with justice. | |
| From: Thrasymachus (fragments/reports [c.426 BCE], B8), quoted by Hermias - Notes on Plato's 'Phaedrus' 239.22 |