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. |
| 12709 | Motion is not absolute, but consists in relation [Leibniz] |
| Full Idea: In reality motion is not something absolute, but consists in relation. | |
| From: Gottfried Leibniz (On Motion [1677], A6.4.1968), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3 | |
| A reaction: It is often thought that motion being relative was invented by Einstein, but Leibniz wholeheartedly embraced 'Galilean relativity', and refused to even consider any absolute concept of motion. Acceleration is a bit trickier than velocity. |
| 19035 | General Relativity allows substantivalism about space-time - that it has independent properties [Hoefer] |
| Full Idea: General Relativity describes space-time in a way that allows it to exist with determinate properties not reducible to the properties and relations of its material contents. Hence nearly all physicists and philosophers writing on GR are substantivalists. | |
| From: Carl Hoefer (The Metaphysics of Space-Time Substantivalism [1996], p.5), quoted by Barbara Vetter - Potentiality 7.3 | |
| A reaction: I'm encouraged by this, as I instinctly favour substantivalism. Imagine removing all the objects from space-time, one by one. What happens as you approach the end of the task? Once they are removed, can they be replaced? |