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. |
| 14528 | Maybe modal thought is unavoidable, as a priori recognition of necessary truth-preservation in reasoning [Hale/Hoffmann,A] |
| Full Idea: There are 'transcendental' arguments saying that modal thought is unavoidable - recognition, a priori, of the necessarily truth-preserving character of some forms of inference is a precondition for rational thought in general, and scientific theorizing. | |
| From: Bob Hale/ Aviv Hoffmann (Introduction to 'Modality' [2010], 1) | |
| A reaction: So the debate about the status of logical truths and valid inference, are partly debates about whether out thought has to involve modality, or whether it could just be about the actual world. I take possibilities and necssities to be features of nature. |
| 23688 | Noncognitivism tries to avoid both naturalism and mysterious morality [Hacker-Wright] |
| Full Idea: Noncognitivism is an attempt to avoid the alleged problems of naturalism without the mysteries of Moore's non-naturalism. | |
| From: John Hacker-Wright (Philippa Foot's Moral Thought [2013], 1) | |
| A reaction: R.M. Hare is the best example of this approach. Moore's Open Question argument was said to prove the Naturalistic Fallacy, which imagined that morality could be a feature of nature. It led Moore to platonism. I prefer Philippa Foot. |