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. |
| 12887 | A whole must have one characteristic, an internal relation, and a structure [Rescher/Oppenheim] |
| Full Idea: A whole must possess an attribute peculiar to and characteristic of it as a whole; there must be a characteristic relation of dependence between the parts; and the whole must have some structure which gives it characteristics. | |
| From: Rescher,N/Oppenheim,P (Logical Analysis of Gestalt Concepts [1955], p.90), quoted by Peter Simons - Parts 9.2 | |
| A reaction: Simons says these are basically sensible conditions, and tries to fill them out. They seem a pretty good start, and I must resist the temptation to rush to borderline cases. |
| 20643 | Consilience is a common groundwork of explanation [Whewell] |
| Full Idea: Consilience is the jumping together of knowledge by the linking of facts and fact-based theory across disciplines to create a common groundwork of explanation. | |
| From: William Whewell (The Philosophy of the Inductive Sciences [1840]), quoted by Peter Watson - Convergence Intro 'United' | |
| A reaction: Apparently this is the first use of the word, which was popularised by E.O. Wilson in recent times. If, as I do, you dream of a final theory, in philosophy as well as in science, then you have to be a fan of consilience. |