3 ideas
| 23766 | Don't be tossed to and fro with every wind of doctrine, by cunning deceptive men [Paul] |
| Full Idea: Henceforth be no more children, tossed to and fro, and carried about with every wind of doctrine, by the sleight of men, and cunning craftiness, whereby they lie in wait to deceive. | |
| From: St Paul (10: Ephesians [c.55], 4:14) | |
| A reaction: One quoted to me by a learned religious friend, in response to Idea 23767. I sympathise. I find it extraordinary the nonsense that students of philosophy can be led into, when they swallow some specious argument. |
| 18170 | The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine] |
| Full Idea: The Axiom of Reducibility is self-effacing: if it is true, the ramification it is meant to cope with was pointless to begin with. | |
| From: Willard Quine (Introduction to Russell's Theory of Types [1967], p.152), quoted by Penelope Maddy - Naturalism in Mathematics I.1 | |
| A reaction: Maddy says the rejection of Reducibility collapsed the ramified theory of types into the simple theory. |
| 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. |