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. |
| 8628 | I hold that algebra and number are developments of logic [Jevons] |
| Full Idea: I hold that algebra is a highly developed logic, and number but logical discrimination. | |
| From: William S. Jevons (The Principles of Science [1879], p.156), quoted by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §15 | |
| A reaction: Thus Frege shows that logicism was an idea that was in the air before he started writing. Riemann's geometry and Boole's logic presumably had some influence here. |
| 13440 | Causation is the power of one property to produce another, and this gives time its direction [Esfeld] |
| Full Idea: The metaphysics of causation in terms of powers is linked with an intrinsic direction of time. There is a causal connection if an F-property produces a G. One can argue that causation thus is the basis for the direction of time. | |
| From: Michael Esfeld (Humean metaphysics vs metaphysics of Powers [2010], 7.2) | |
| A reaction: I think this is my preferred metaphysic - that both time and causation are primitive, but the direction of time is the result of the causal process. Viewing some new world, we would just say that time went in whichever direction the causation went. |