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. |
| 4038 | Properties are sets of their possible instances (which separates 'renate' from 'cordate') [Lewis, by Mellor/Oliver] |
| Full Idea: Lewis agrees that properties cannot be sets of their actual instances, but claims they can be sets of their possible instances. This would distinguish coextensive properties like being cordate and renate, since they might be separated. | |
| From: report of David Lewis (Modal Realism at Work: Properties [1986]) by DH Mellor / A Oliver - Introduction to 'Properties' §10 | |
| A reaction: Sounds wrong. Two properties could be obviously different even if they could never be separated. In this world a creature might briefly survive without kidneys. |
| 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 |