6 ideas
| 9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor] |
| Full Idea: The author entirely overlooks the fact that the 'extension of a concept' in general may be quantitatively completely indeterminate. Only in certain cases is the 'extension of a concept' quantitatively determinate. | |
| From: George Cantor (Review of Frege's 'Grundlagen' [1885], 1932:440), quoted by William W. Tait - Frege versus Cantor and Dedekind | |
| A reaction: Cantor presumably has in mind various infinite sets. Tait is drawing our attention to the fact that this objection long precedes Russell's paradox, which made the objection more formal (a language Frege could understand!). |
| 7458 | The reliability of witnesses depends on whether they benefit from their observations [Laplace, by Hacking] |
| Full Idea: The credibility of a witness is in part a function of the story being reported. When the story claims to have infinite value, the temptation to lie for personal benefit is asymptotically infinite. | |
| From: report of Pierre Simon de Laplace (Philosophical Essay on Probability [1820], Ch.XI) by Ian Hacking - The Emergence of Probability Ch.8 | |
| A reaction: Laplace seems to especially have reports of miracles in mind. This observation certainly dashes any dreams one might have of producing a statistical measure of the reliability of testimony. |
| 3441 | If a supreme intellect knew all atoms and movements, it could know all of the past and the future [Laplace] |
| Full Idea: An intelligence knowing at an instant the whole universe could know the movement of the largest bodies and atoms in one formula, provided his intellect were powerful enough to subject all data to analysis. Past and future would be present to his eyes. | |
| From: Pierre Simon de Laplace (Philosophical Essay on Probability [1820]), quoted by Mark Thornton - Do we have free will? p.70 |
| 299 | What is fine is always difficult [Plato] |
| Full Idea: The proverb says 'Anything fine is difficult'. | |
| From: Plato (Hippias Major [c.392 BCE], 304e) | |
| A reaction: attributed (as usual) to Solon |
| 297 | What is fine is the parent of goodness [Plato] |
| Full Idea: Fineness is the father of goodness. | |
| From: Plato (Hippias Major [c.392 BCE], 297b) |
| 298 | While sex is very pleasant, it should be in secret, as it looks contemptible [Plato] |
| Full Idea: As for sex, everyone agrees that, while it is extremely pleasant, it should be indulged in (if at all) in secret, because it is a highly contemptible sight. | |
| From: Plato (Hippias Major [c.392 BCE], 299a) |